25:["$","title",null,{"children":"Zome Arithmetic | Chikita Isaac's Workspace | Observable"}] 49:T49a,// Reduce a proportion of 3 integers to lowest terms. // Make sure the sign of the third element is always positive. // Pre-cache results for integers less than 128. simplify3 = { const cachesize = 0x80; const cache = new Uint8Array(cachesize*cachesize*cachesize*3); for (let k = 0; k < cachesize; k++) { for (let j = 0; j < cachesize; j++) { for (let i = 0; i < cachesize; i++) { const g = gcdc(gcdc(i, j), k); const idx = ((k*cachesize + j)*cachesize + i)*3; cache[idx] = i/g, cache[idx+1] = j/g, cache[idx+2] = k/g; } } } cache[0] = cache[1] = cache[2] = 0; return function simplify3(v0, v1, v2) { if ((v0|0) !== v0 || (v1|0) !== v1 || (v2|0) !== v2) throw new TypeError('simplify3 operates only on integers.'); let s0 = (v0>0)-(v0<0), s1 = (v1>0)-(v1<0), s2 = (v2>0)-(v2<0); // signs v0 *= s0, v1 *= s1, v2 *= s2, s0 *= s2, s1 *= s2; if (v0 < cachesize && v1 < cachesize && v2 < cachesize) { const idx = ((v2*cachesize + v1)*cachesize + v0)*3; return [s0*cache[idx], s1*cache[idx+1], cache[idx+2]]; } const g = gcd(gcd(v0, v1), v2); return [s0*v0/g, s1*v1/g, v2/g]; } }4a:T9b0,orbit2 = { // Copy and normalize a golden rational. const grcopy = function grcopy([x0=0, x1=0, xd=1]=[]) { return [x0, x1, xd]; } // Return (a < 0); as a side effect, change a to abs(a), in place. const lt0_abs = function lt0_abs(a) { const float = a[0] + PHI * a[1], sign = ((float>0)-(float<0)); a[0] *= sign; a[1] *= sign; return +(sign < 0); } // Parity of the count of ones of an 8-bit integer in binary const hamming_parity = function hamming_parity(n) { n -= (n >> 1) & 0x55; n -= (n >> 2) & 0x33; return (n - (n >> 4)) & 0x01; } // Build up a lookup table for reflection bit patterns -> quaternions const orbit_quaternions = [...range(0x100)].map(rb => { let quat = [[1],,,]; if (rb & 0x80) quat = quatmul(quat, [,[1],,]); if (rb & 0x40) quat = quatmul(quat, [,,[1],]); if (rb & 0x20) quat = quatmul(quat, [,,,[1]]); quat = quatmul(quat, [[,1,2],[-1,,2],[1,-1,2],]); // conjugate of red_rotation if (rb & 0x10) quat = quatmul(quat, [,,[1],]); if (rb & 0x08) quat = quatmul(quat, [,,,[1]]); quat = quatmul(quat, [[,1,2],[-1,,2],[1,-1,2],]); if (rb & 0x04) quat = quatmul(quat, [,,[1],]); if (rb & 0x02) quat = quatmul(quat, [,,,[1]]); if (rb & 0x01) quat = quatmul(quat, [,[-1,1,2],[-1,,2],[,-1,2]]); const sign = quat.map(grsign).reduce((a, b) => a || b) || 1; return scalarmul([sign], quat); }); const v = [[-1, 1], [-1], [, -1]]; // φ⁻ -1 -φ // Find the orbit and orientation for a vector u. return function orbit2(u) { u = [grcopy(u[0]), grcopy(u[1]), grcopy(u[2])]; // Make a deep copy of 'u'. // Reduce to the 'kite' shape at the corner of one octant: const rbits = [lt0_abs(u[0]), lt0_abs(u[1]), lt0_abs(u[2])]; // rbits = reflection bits u = transform(red_rotation, u); rbits.push(lt0_abs(u[1]), lt0_abs(u[2])); u = transform(red_rotation, u); rbits.push(lt0_abs(u[1]), lt0_abs(u[2])); // Now reflect the top triangle of the kite onto the bottom triangle: let d = dot(u, v), ds = +grgreater([0], d); rbits.push(ds); d = grmul([-ds, 0, 2], d); u = vectoradd(u, scalarmul(d, v)); const orb = scalarmul(grinv(u[0]), [u[1], u[2]]); // coordinates of gnomonic projection const rbits_int = rbits.reduce((a, b) => (a << 1) + b); const rotation = orbit_quaternions[rbits_int]; const length = u[0]; const reflected = hamming_parity(rbits_int); return [orb, rotation, reflected, length]; } }4b:T573d,solid_connectors = ({ "name": "solid connectors", "connectorShape": { "vertices": [ [[-1,1,2],[0,-1,2],[-1,1,1]], [[0,1,2],[1,-1,1],[-1,1,2]], [[-1,1,1],[1,-1,2],[0,1,2]], [[1,0,1],[-1,1,2],[2,-1,2]], [[0,1,2],[-1,1,1],[-1,1,2]], [[-1,1,1],[-1,1,2],[0,1,2]], [[0,1,2],[0,0,1],[3,-1,2]], [[2,-1,2],[-1,0,1],[-1,1,2]], [[-2,1,2],[-1,0,1],[-1,1,2]], [[-2,1,2],[-1,0,1],[1,-1,2]], [[2,-1,2],[-1,0,1],[1,-1,2]], [[1,0,1],[1,-1,2],[-2,1,2]], [[0,1,2],[1,-1,1],[1,-1,2]], [[-1,1,1],[1,-1,2],[0,-1,2]], 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[[1,-1,1],[1,-1,2],[0,1,2]], [[-1,1,2],[2,-1,2],[1,0,1]], [[1,-1,2],[2,-1,2],[-1,0,1]], [[1,-1,2],[2,-1,2],[1,0,1]], [[1,-1,2],[-2,1,2],[1,0,1]], [[-1,1,2],[-2,1,2],[1,0,1]], [[3,-1,2],[0,-1,2],[0,0,1]], [[0,-1,2],[0,0,1],[-3,1,2]], [[1,-1,1],[1,-1,2],[0,-1,2]], [[1,-1,2],[-2,1,2],[-1,0,1]], [[1,-1,1],[-1,1,2],[0,-1,2]], [[0,-1,2],[1,-1,1],[1,-1,2]]], "polygons": [ [9, 40, 35, 34, 10], [0, 1, 2], [33, 51, 49], [25, 36, 37, 38], [41, 55, 42], [9, 32, 59, 40], [20, 21, 52, 48], [26, 33, 30, 29, 27], [3, 4, 5, 6], [27, 29, 44, 46], [50, 57, 56, 55, 58], [26, 38, 51, 33], [45, 47, 58], [18, 28, 57, 50], [40, 59, 56], [31, 48, 37, 43], [7, 8, 9, 10], [36, 41, 42, 43], [24, 46, 47, 45], [4, 30, 5], [15, 47, 46, 44, 16], [15, 50, 58, 47], [24, 45, 41, 36, 25], [11, 14, 19], [3, 6, 39], [1, 39, 6, 2], [8, 32, 9], [11, 12, 13, 14], [16, 22, 17], [0, 21, 20, 8, 7], [12, 34, 13], [35, 40, 56, 57], [0, 7, 54, 1], [15, 16, 17, 18], [3, 19, 22, 23, 4], [7, 10, 54], [41, 45, 58, 55], [3, 39, 11, 19], 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[[-2,0,1],[1,-1,2],[2,-1,2]], [[-1,0,1],[-1,1,2],[2,-1,2]], [[1,0,1],[-1,1,2],[-2,1,2]], [[-1,0,1],[1,-1,2],[2,-1,2]], [[0,1,1],[-1,1,2],[0,-1,2]], [[0,1,2],[0,0,1],[-3,1,2]], [[2,1,2],[-1,1,1],[-3,1,2]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [ [0, 1, 2, 3, 4, 5], [1, 8, 6, 2], [3, 9, 4], [8, 10, 7], [5, 11, 7, 10, 0], [12, 11, 5, 4], [6, 8, 7, 11, 12, 13], [13, 9, 3, 2, 6], [10, 1, 0], [12, 9, 13]] }, "red": { "prototypeVector": [[0,1,1],[1,0,1],[0,0,1]], "fullScaleVertices": [16, 17, 18, 19, 7, 12], "halfScaleVertices": [0, 1, 2, 20, 5, 6, 8, 9, 10, 11], "vertices": [ [[0,-1,2],[-2,1,1],[-1,1,2]], [[0,1,2],[2,-1,1],[-1,1,2]], [[-1,1,1],[3,-1,2],[2,-1,2]], [[0,1,2],[-1,1,1],[1,-1,2]], [[3,-1,2],[0,1,2],[0,0,1]], [[3,-3,2],[-2,1,2],[0,0,1]], [[0,-1,2],[-2,1,1],[1,-1,2]], [[0,-1,2],[1,-1,1],[-1,1,2]], [[1,-1,1],[-3,1,2],[2,-1,2]], [[1,-1,1],[-3,1,2],[-2,1,2]], [[-3,3,2],[2,-1,2],[0,0,1]], [[0,1,2],[2,-1,1],[1,-1,2]], [[-3,1,2],[0,-1,2],[0,0,1]], [[1,0,1],[-1,1,2],[2,-1,2]], [[1,0,1],[-1,1,2],[-2,1,2]], [[0,1,2],[-1,1,1],[-1,1,2]], [[-1,0,1],[1,-1,2],[2,-1,2]], [[0,-1,2],[1,-1,1],[1,-1,2]], [[-1,0,1],[1,-1,2],[-2,1,2]], [[0,0,1],[0,0,1],[0,0,1]], [[-1,1,1],[3,-1,2],[-2,1,2]]], "polygons": [ [0, 1, 2], [3, 4, 5, 6], [8, 9, 10], [9, 11, 10], [13, 14, 9, 8], [4, 15, 0, 5], [2, 1, 7, 16], [0, 8, 1], [14, 3, 6, 9], [8, 10, 1], [9, 6, 11], [5, 0, 2], [11, 20, 18, 17], [20, 2, 16, 18], [6, 5, 20], [1, 10, 12, 7], [6, 20, 11], [15, 13, 8, 0], [10, 11, 17, 12], [5, 2, 20]] }, "apple": { "prototypeVector": [[5,-3,1],[1,0,1],[0,1,1]], "fullScaleVertices": [0, 1, 4, 7, 8, 9, 10, 13, 14], "halfScaleVertices": [], "vertices": [ [[1,-1,4],[-3,0,4],[-6,-1,4]], [[-1,1,4],[-5,0,4],[-2,-3,4]], [[-3,3,4],[-3,4,4],[2,3,4]], [[-1,1,4],[-1,4,4],[-2,5,4]], [[1,-1,2],[-2,1,2],[-1,0,1]], [[1,-1,4],[5,0,4],[2,3,4]], [[-1,1,4],[3,0,4],[6,1,4]], [[1,-1,4],[1,-4,4],[2,-5,4]], [[3,-3,4],[3,-4,4],[-2,-3,4]], [[1,-1,2],[0,-1,2],[1,-1,1]], [[0,0,1],[-3,1,2],[0,-1,2]], [[0,0,1],[3,-1,2],[0,1,2]], [[-1,1,2],[2,-1,2],[1,0,1]], [[0,0,1],[0,0,1],[0,0,1]], [[1,-1,1],[1,-1,2],[0,-1,2]], [[-1,1,1],[-1,1,2],[0,1,2]], [[-1,1,2],[0,1,2],[-1,1,1]]], "polygons": [ [0, 1, 2, 3], [5, 6, 7, 8], [4, 10, 1, 0], [11, 12, 6, 5], [3, 5, 8, 0], [6, 2, 1, 7], [7, 1, 10, 9], [8, 7, 9, 14], [15, 2, 6, 12], [16, 11, 5, 3], [0, 8, 14, 4], [3, 2, 15, 16]] }, "sand": { "prototypeVector": [[-2,2,1],[-2,2,1],[2,0,1]], "fullScaleVertices": [0, 16, 1, 2, 3, 6, 11, 12, 13], "halfScaleVertices": [], "vertices": [ [[1,-1,2],[0,-1,2],[1,-1,1]], [[1,-1,2],[-2,1,2],[-1,0,1]], [[-1,-1,2],[0,-1,2],[0,-1,1]], [[-1,0,1],[-3,1,2],[-2,-1,2]], [[1,0,1],[1,1,2],[-2,3,2]], [[3,-1,2],[4,-1,2],[0,1,1]], [[1,-1,1],[1,-1,2],[0,-1,2]], [[-1,1,2],[0,1,2],[-1,1,1]], [[0,0,1],[3,-1,2],[0,1,2]], [[1,1,2],[0,1,2],[0,1,1]], [[-1,1,1],[-1,1,2],[0,1,2]], [[0,0,1],[-3,1,2],[0,-1,2]], [[-1,0,1],[-1,-1,2],[2,-3,2]], [[-3,1,2],[-4,1,2],[0,-1,1]], [[1,0,1],[3,-1,2],[2,1,2]], [[-1,1,2],[2,-1,2],[1,0,1]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [ [2, 3, 4, 5], [6, 1, 3, 2], [5, 4, 7, 8], [4, 9, 10, 7], [11, 13, 3, 1], [2, 5, 14, 12], [4, 3, 13, 9], [14, 5, 8, 15], [12, 13, 11, 0], [6, 2, 12, 0], [14, 9, 13, 12], [15, 10, 9, 14]] }, "blue": { "prototypeVector": [[1,0,1],[0,0,1],[0,0,1]], "fullScaleVertices": [0, 1, 4, 7, 8], "halfScaleVertices": [], "vertices": [ [[-1,0,1],[-1,1,2],[2,-1,2]], [[-1,0,1],[-1,1,2],[-2,1,2]], [[1,0,1],[-1,1,2],[-2,1,2]], [[1,0,1],[-1,1,2],[2,-1,2]], [[-1,0,1],[1,-1,2],[2,-1,2]], [[1,0,1],[1,-1,2],[2,-1,2]], [[1,0,1],[1,-1,2],[-2,1,2]], [[-1,0,1],[1,-1,2],[-2,1,2]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [[0, 1, 2, 3], [5, 6, 7, 4], [5, 4, 0, 3], [1, 7, 6, 2]] }, "olive": { "prototypeVector": [[0,1,1],[0,1,1],[2,-1,1]], "fullScaleVertices": [16, 17, 2, 18, 3, 7, 9, 13, 14, 15], "halfScaleVertices": [], "vertices": [ [[-1,2,2],[1,1,2],[-1,1,1]], [[0,1,1],[-1,2,2],[-1,1,2]], [[-1,0,1],[-3,0,2],[1,-1,2]], [[-3,0,2],[-1,-1,2],[0,0,1]], [[1,0,1],[3,0,2],[-1,1,2]], [[0,1,2],[-1,1,1],[1,-1,2]], [[3,-1,2],[0,1,2],[0,0,1]], [[1,-2,2],[-1,-1,2],[1,-1,1]], [[3,0,2],[1,1,2],[0,0,1]], [[0,-1,1],[1,-2,2],[1,-1,2]], [[0,1,2],[-1,1,1],[-1,1,2]], [[1,0,1],[-1,1,2],[2,-1,2]], [[1,0,1],[-1,1,2],[-2,1,2]], [[0,-1,2],[1,-1,1],[1,-1,2]], [[0,-1,2],[1,-1,1],[-1,1,2]], [[-1,0,1],[1,-1,2],[-2,1,2]], [[-1,0,1],[1,-1,2],[2,-1,2]], [[-3,1,2],[0,-1,2],[0,0,1]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [ [0, 1, 2, 3], [4, 5, 6], [7, 8, 4, 9], [0, 10, 11], [1, 12, 8], [0, 3, 9, 4], [2, 14, 3], [7, 9, 15], [3, 14, 16], [17, 2, 7, 13], [7, 2, 1, 8], [8, 12, 5], [4, 8, 5], [10, 0, 4, 6], [7, 15, 13], [1, 11, 12], [2, 17, 14], [0, 11, 1], [3, 16, 9], [9, 16, 15]] }, "coral": { "prototypeVector": [[-3,3,1],[0,0,1],[1,0,1]], "fullScaleVertices": [0, 1, 2, 7, 8, 9, 10, 14], "halfScaleVertices": [], "vertices": [ [[-3,0,2],[1,-1,2],[1,-1,1]], [[-3,0,2],[1,-1,2],[-1,0,1]], [[-1,0,1],[1,-1,2],[-2,1,2]], [[3,0,2],[1,-1,2],[-1,1,1]], [[1,0,1],[1,-1,2],[2,-1,2]], [[1,0,1],[-1,1,2],[2,-1,2]], [[3,0,2],[-1,1,2],[-1,1,1]], [[-3,0,2],[-1,1,2],[-1,0,1]], [[0,-1,2],[0,0,1],[-3,1,2]], [[-1,0,1],[-1,1,2],[-2,1,2]], [[-3,0,2],[-1,1,2],[1,-1,1]], [[3,0,2],[1,-1,2],[1,0,1]], [[0,1,2],[0,0,1],[3,-1,2]], [[3,0,2],[-1,1,2],[1,0,1]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [ [1, 2, 0], [3, 4, 5, 6], [8, 7, 9], [7, 10, 9], [1, 8, 2], [11, 4, 3], [0, 2, 9, 10], [11, 3, 1, 0], [12, 11, 13], [7, 1, 3, 6], [13, 6, 5], [0, 10, 13, 11], [10, 7, 6, 13], [12, 13, 5], [8, 1, 7], [11, 12, 4]] }, "sulfur": { "prototypeVector": [[-3,3,1],[2,-1,1],[0,0,1]], "fullScaleVertices": [16, 0, 3, 8, 9, 10, 13, 14, 15], "halfScaleVertices": [], "vertices": [ [[-9,3,2],[3,-2,2],[-2,1,2]], [[9,-3,2],[-5,4,2],[-2,1,2]], [[9,-3,2],[-5,4,2],[2,-1,2]], [[-9,3,2],[3,-2,2],[2,-1,2]], [[9,-3,2],[-3,2,2],[-2,1,2]], [[9,-3,2],[-3,2,2],[2,-1,2]], [[1,0,1],[1,-1,2],[2,-1,2]], [[1,0,1],[1,-1,2],[-2,1,2]], [[-1,0,1],[-1,1,2],[2,-1,2]], [[-1,0,1],[-1,1,2],[-2,1,2]], [[-1,0,1],[1,-1,2],[2,-1,2]], [[1,0,1],[-1,1,2],[-2,1,2]], [[1,0,1],[-1,1,2],[2,-1,2]], [[-9,3,2],[5,-4,2],[2,-1,2]], [[-1,0,1],[1,-1,2],[-2,1,2]], [[-9,3,2],[5,-4,2],[-2,1,2]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [ [0, 1, 2, 3], [4, 5, 6, 7], [0, 3, 8, 9], [11, 1, 4, 7], [11, 12, 2, 1], [13, 3, 2, 5], [14, 10, 13, 15], [14, 15, 0, 9], [15, 13, 5, 4], [13, 10, 8, 3], [2, 12, 6, 5], [1, 0, 15, 4]] }, "purple": { "prototypeVector": [[1,1,1],[1,0,1],[0,0,1]], "fullScaleVertices": [0, 1, 2, 18, 3, 4, 5, 9, 13, 14], "halfScaleVertices": [], "vertices": [ [[-1,0,1],[1,-1,2],[-2,1,2]], [[-3,1,2],[0,-1,2],[0,0,1]], [[0,-1,1],[3,-3,2],[2,-1,2]], [[0,-1,1],[3,-3,2],[-2,1,2]], [[0,-1,1],[1,-1,2],[2,-1,2]], [[0,-1,2],[1,-1,1],[1,-1,2]], [[0,1,1],[-1,1,2],[2,-1,2]], [[0,1,1],[-3,3,2],[2,-1,2]], [[0,1,2],[-1,1,1],[-1,1,2]], [[-1,0,1],[1,-1,2],[2,-1,2]], [[1,0,1],[-1,1,2],[-2,1,2]], [[0,1,1],[-1,1,2],[-2,1,2]], [[1,0,1],[-1,1,2],[2,-1,2]], [[0,-1,2],[1,-1,1],[-1,1,2]], [[0,-1,1],[1,-1,2],[-2,1,2]], [[0,1,1],[-3,3,2],[-2,1,2]], [[3,-1,2],[0,1,2],[0,0,1]], [[0,1,2],[-1,1,1],[1,-1,2]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [ [1, 2, 3], [6, 7, 8], [3, 5, 1], [10, 11, 6, 12], [2, 1, 13], [9, 0, 14, 4], [14, 3, 11, 15], [6, 2, 4, 7], [14, 0, 5], [2, 13, 4], [4, 13, 9], [16, 8, 7], [17, 15, 11], [8, 12, 6], [15, 16, 7], [15, 7, 4, 14], [11, 3, 2, 6], [15, 17, 16], [11, 10, 17], [14, 5, 3]] }, "rose": { "prototypeVector": [[2,-1,1],[-1,2,1],[0,0,1]], "fullScaleVertices": [16, 0, 1, 2, 3, 6, 7, 11, 15], "halfScaleVertices": [], "vertices": [ [[3,-2,2],[-2,-1,2],[1,-1,2]], [[-1,0,2],[-2,-1,2],[1,-1,2]], [[-2,1,2],[-1,0,1],[1,-1,2]], [[2,-1,2],[-1,0,1],[1,-1,2]], [[-3,2,2],[2,1,2],[-1,1,2]], [[1,0,2],[2,1,2],[-1,1,2]], [[3,-2,2],[-2,-1,2],[-1,1,2]], [[-1,0,2],[-2,-1,2],[-1,1,2]], [[-2,1,2],[1,0,1],[-1,1,2]], [[-3,2,2],[2,1,2],[1,-1,2]], [[-2,1,2],[1,0,1],[1,-1,2]], [[2,-1,2],[-1,0,1],[-1,1,2]], [[2,-1,2],[1,0,1],[-1,1,2]], [[2,-1,2],[1,0,1],[1,-1,2]], [[1,0,2],[2,1,2],[1,-1,2]], [[-2,1,2],[-1,0,1],[-1,1,2]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [ [0, 1, 2, 3], [4, 5, 6, 7], [8, 4, 9, 10], [11, 6, 0, 3], [5, 12, 13, 14], [8, 12, 5, 4], [11, 15, 7, 6], [6, 5, 14, 0], [4, 7, 1, 9], [7, 15, 2, 1], [1, 0, 14, 9], [9, 14, 13, 10]] }, "maroon": { "prototypeVector": [[-1,1,1],[3,-1,1],[1,-1,1]], "fullScaleVertices": [4, 5, 7, 8, 9, 10, 11, 12, 15], "halfScaleVertices": [], "vertices": [ [[-1,1,2],[0,1,2],[1,-1,1]], [[2,-1,2],[1,0,1],[1,-1,2]], [[1,0,2],[2,0,1],[0,-1,2]], [[-1,1,1],[2,1,2],[1,-2,2]], [[0,0,1],[0,0,1],[0,0,1]], [[1,-2,2],[0,-1,1],[0,1,2]], [[1,0,1],[2,1,2],[-1,0,2]], [[1,-1,1],[-2,-1,2],[-1,2,2]], [[-2,1,2],[-1,0,1],[-1,1,2]], [[-1,0,2],[-2,0,1],[0,1,2]], [[-1,0,1],[-2,-1,2],[1,0,2]], [[-3,1,2],[0,-1,2],[0,0,1]], [[1,-1,2],[0,-1,2],[-1,1,1]], [[-1,2,2],[0,1,1],[0,-1,2]], [[0,1,2],[-1,1,1],[1,-1,2]], [[0,-1,2],[1,-1,1],[-1,1,2]], [[3,-1,2],[0,1,2],[0,0,1]]], "polygons": [ [0, 1, 2, 3], [5, 2, 6, 7], [8, 9, 10, 11], [3, 2, 5, 10], [0, 3, 13, 14], [7, 12, 15, 5], [9, 7, 6, 13], [13, 6, 16, 14], [2, 1, 16, 6], [3, 10, 9, 13], [10, 5, 15, 11], [8, 12, 7, 9]] }, "lavender": { "prototypeVector": [[2,-1,1],[0,1,1],[2,-1,1]], "fullScaleVertices": [0, 1, 4, 5, 6, 7, 13, 14], "halfScaleVertices": [], "vertices": [ [[1,-1,1],[-2,-1,2],[5,-4,2]], [[3,-2,2],[-2,0,1],[4,-3,2]], [[-5,4,2],[0,1,1],[-4,3,2]], [[-3,2,1],[2,1,2],[-3,2,2]], [[5,-4,2],[0,-1,1],[4,-3,2]], [[3,-2,1],[-2,-1,2],[3,-2,2]], [[-2,1,2],[-1,0,1],[-1,1,2]], [[-3,1,2],[0,-1,2],[0,0,1]], [[-3,2,2],[2,0,1],[-4,3,2]], [[-1,1,1],[2,1,2],[-5,4,2]], [[3,-1,2],[0,1,2],[0,0,1]], [[2,-1,2],[1,0,1],[1,-1,2]], [[2,-1,2],[1,0,1],[-1,1,2]], [[-2,1,2],[-1,0,1],[1,-1,2]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [ [0, 1, 2, 3], [4, 5, 6, 7], [4, 0, 3, 8], [2, 9, 10], [8, 3, 11], [8, 11, 12], [9, 12, 10], [0, 4, 7], [9, 8, 12], [5, 1, 6], [8, 9, 5, 4], [3, 2, 10, 11], [1, 0, 13], [1, 13, 6], [0, 7, 13], [5, 9, 2, 1]] }, "spruce": { "prototypeVector": [[-3,2,1],[-3,2,1],[5,-2,1]], "fullScaleVertices": [0, 1, 6, 7, 10, 11, 12, 14], "halfScaleVertices": [], "vertices": [ [[-1,1,2],[-2,1,2],[-1,0,1]], [[1,-1,1],[-1,0,2],[-3,-1,2]], [[-1,1,1],[-3,2,2],[3,1,2]], [[0,0,1],[-3,2,2],[3,1,2]], [[1,-1,2],[2,-1,2],[1,0,1]], [[-1,1,2],[2,-1,2],[1,0,1]], [[0,0,1],[-1,0,2],[-3,-1,2]], [[1,-1,1],[3,-2,2],[-3,-1,2]], [[0,0,1],[3,-1,2],[0,1,2]], [[0,0,1],[1,0,2],[3,1,2]], [[1,-1,2],[-2,1,2],[-1,0,1]], [[0,0,1],[-3,1,2],[0,-1,2]], [[0,0,1],[3,-2,2],[-3,-1,2]], [[-1,1,1],[1,0,2],[3,1,2]], [[0,0,1],[0,0,1],[0,0,1]]], "polygons": [ [2, 3, 4, 5], [8, 4, 9], [10, 1, 11], [6, 1, 3, 2], [13, 9, 7, 12], [7, 1, 10], [12, 0, 6], [5, 13, 2], [9, 4, 3], [8, 9, 13], [0, 11, 6], [13, 12, 6, 2], [12, 7, 10, 0], [9, 3, 1, 7], [11, 1, 6], [8, 13, 5]] } } })4c:T4e91,solid_connectors_normalized = ({ "name": "solid connectors", "connectorShape": { "vertices": [[[-1,1,2],[0,-1,2],[-1,1,1]], [[0,1,2],[1,-1,1],[-1,1,2]], [[-1,1,1],[1,-1,2],[0,1,2]], 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Isaac","avatar_url":"https://avatars-next.observableusercontent.com/5f2909d79277de6d1b62b68b7fa0450afbfead99f832337373b3f8cf2570bfac","tier":null,"role":"editor"},{"type":"team","id":"a82c989b0517ab67","login":"chikita-isaac-ws","name":"Chikita Isaac's Workspace","avatar_url":"https://avatars-next.observableusercontent.com/664773ad6d6025fe532a321d1d3e013214eb695efdd0d4e9e5f4c5e6437fc4aa","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Zome Arithmetic","cells":[{"id":0,"value":"md`# Zome Arithmetic\n\n[Zome][] is a geometric construction system based on the symmetry system of\nthe icosahedron. Because of the pentagonal symmetries involved, the golden\nratio is fundamental to describing the metrical geometry of Zome shapes.\n\nFor the moment this notebook mostly sticks to business without a lot of\nexplanation.\n\n [Zome]: https://en.wikipedia.org/wiki/Zome\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":190,"value":"md`* * *\n\n### Golden Integers\n\nThe key property to know about the golden ratio ${tex`\\varphi`} is that ${tex`\\varphi^2 = \\varphi + 1`}.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"gprint = function gprint(a) {\n const [a0, a1=0] = a, sign = (a1 > 0) ? '+' : '';\n return tex`${a0} ${sign} ${a1}\\varphi`; }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":95,"value":"tex`\\varphi = \\dfrac{1 + \\sqrt{5}}{2} \\approx ${PHI.toFixed(4)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"PHI = 0.5 * (Math.sqrt(5) + 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":65,"value":"gfloat = function gfloat(a) {\n const [a0=0, a1=0] = a;\n return a0 + PHI * a1; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":162,"value":"tex`(a_0 + a_1\\varphi) + (b_0 + b_1\\varphi) \\\\[.2em]\n \\qquad = (a_0 + b_0) + (a_1 + b_1)\\varphi`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"gadd = function gadd(a, b) {\n const [a0=0, a1=0] = a, [b0=0, b1=0] = b;\n return [a0 + b0, a1 + b1]; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"tex`(a_0 + a_1\\varphi) - (b_0 + b_1\\varphi) \\\\[.2em]\n \\qquad = (a_0 - b_0) + (a_1 - b_1)\\varphi`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":875,"value":"gneg = function gneg(a) {\n const [a0=0, a1=0] = a;\n return [0 - a0, 0 - a1]; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"gsub = function gsub(a, b) {\n const [a0=0, a1=0] = a, [b0=0, b1=0] = b;\n return [a0 - b0, a1 - b1]; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":167,"value":"tex`\n(a_0 + a_1\\varphi)(b_0 + b_1\\varphi) \\\\[.2em]\n \\qquad = a_0b_0 + (a_0b_1 + a_1b_0)\\varphi + a_1b_1\\varphi^2 \\\\[.2em]\n \\qquad = (a_0b_0 + a_1b_1) + (a_0b_1 + a_1b_0 + a_1b_1)\\varphi\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"gmul = function gmul(a, b) {\n const [a0=0, a1=0] = a, [b0=0, b1=0] = b;\n return [a0*b0 + a1*b1, a0*b1 + a1*b0 + a1*b1]}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":320,"value":"gsign = function gsign(a) {\n const [a0=0, a1=0] = a, float = a0 + PHI * a1;\n return (float > 0) - (float < 0); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":311,"value":"gabs = function gabs(a) {\n const [a0=0, a1=0] = a, float = a0 + PHI * a1,\n sign = (float > 0) - (float < 0);\n return [a0 * sign, a1 * sign]; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"gsquare = function gsquare(x) {\n return gmul(x, x); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":309,"value":"md`* * *`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"gcd = function gcd(a, b) {\n a = Math.abs(a), b = Math.abs(b);\n while (b != 0) [a, b] = [b, a % b];\n return a;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1070,"value":"// GCD with caching\ngcdc = {\n const cachesize = 0x400;\n const cache = new Uint16Array(cachesize*cachesize);\n for (let j = 0; j < cachesize; j++) {\n for (let i = 0; i < cachesize; i++) {\n let a = i, b = j;\n while (b != 0) [a, b] = [b, a % b];\n cache[j*cachesize + i] = a;\n }\n }\n\n return function gcdc(a, b) {\n if ((a|0) !== a || (b|0) !== b)\n throw new TypeError('gcdc operates only on integers.');\n\n a *= (a>0)-(a<0), b *= (b>0)-(b<0); // absolute value\n while (a >= cachesize || b >= cachesize) {\n if (b == 0) return a;\n [a, b] = [b, a % b];\n }\n return cache[b*cachesize + a];\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2210,"value":"lcm = function lcm(a, b) {\n return a / gcd(a, b) * b; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":119,"value":"simplify = function simplify(vec) {\n const g = vec.reduce(gcd);\n return vec.map(x => x/g); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1005,"value":"$49","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":188,"value":"md`* * *\n### Golden Rationals `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":122,"value":"// grprint = function grprint(a) {\n// const [a0, a1=0, ad=1] = a, sign = (a1 > 0) ? '+' : '';\n// return tex`\\dfrac{${a0} ${sign} ${a1}\\varphi}{${ad}}`; }\ngrprintraw = function grprintraw(a) {\n const [a0=0, a1=0, ad=1] = a, sign = (a1 >= 0) ? '+' : '';\n const numer =\n (a1 == 0) ? `${a0}` :\n (a0 == 0 && a1 == 1) ? `\\\\varphi` : \n (a0 == 0 && a1 == -1) ? `- \\\\varphi` :\n // (a0 == 1 && a1 == -1) ? `- \\\\varphi^{-}` :\n // (a0 == -1 && a1 == 1) ? `\\\\varphi^{-}` :\n (a0 == 0) ? `${a1}\\\\varphi` : \n (a1 == 1) ? `${a0} + \\\\varphi` :\n (a1 == -1) ? `${a0} - \\\\varphi` :\n (a1 < 0) ? `${a0} ${a1}\\\\varphi` :\n `${a0} + ${a1}\\\\varphi`;\n return (ad == 1) ? numer : `\\\\dfrac{${numer}}{${ad}}`; }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2192,"value":"grprint = function grprint(a) {\n return tex`${grprintraw(a)}`; }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":306,"value":"grfloat = function grfloat(a) {\n const [a0=0, a1=0, ad=1] = a;\n return (a0 + PHI * a1) / ad; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":252,"value":"tex`\\dfrac{a_0 + a_1\\varphi}{a_d} + \\dfrac{b_0 + b_1\\varphi}{b_d} \\\\[.6em]\n \\qquad = \\dfrac{(a_0b_d + b_0a_d) + (a_1b_d + b_1a_d)\\varphi}{a_db_d}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":85,"value":"gradd = function gradd(a, b) {\n const [a0=0, a1=0, ad=1] = a, [b0=0, b1=0, bd=1] = b;\n return simplify3(a0*bd + b0*ad, a1*bd + b1*ad, ad*bd); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":437,"value":"grsum = function grsum(vec) {\n return vec.reduce(gradd, [0]); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":260,"value":"tex`\\dfrac{a_0 + a_1\\varphi}{a_d} - \\dfrac{b_0 + b_1\\varphi}{b_d} \\\\[.6em]\n \\qquad = \\dfrac{(a_0b_d - b_0a_d) + (a_1b_d - b_1a_d)\\varphi}{a_db_d}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":870,"value":"grneg = function grneg(a) {\n const [a0=0, a1=0, ad=1] = a;\n return [0 - a0, 0 - a1, ad]; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":149,"value":"grsub = function grsub(a, b) {\n const [a0=0, a1=0, ad=1] = a, [b0=0, b1=0, bd=1] = b;\n return simplify3(a0*bd - b0*ad, a1*bd - b1*ad, ad*bd); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":262,"value":"tex`\\left(\\dfrac{a_0 + a_1\\varphi}{a_d}\\right)\\left(\\dfrac{b_0 + b_1\\varphi}{b_d}\\right) \\\\[.6em]\n \\qquad = \\dfrac{(a_0b_0 + a_1b_1) + (a_0b_1 + a_1b_0 + a_1b_1)\\varphi}{a_db_d}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":152,"value":"grmul = function grmul(a, b) {\n const [a0=0, a1=0, ad=1] = a, [b0=0, b1=0, bd=1] = b;\n return simplify3(a0*b0 + a1*b1, a0*b1 + a1*b0 + a1*b1, ad*bd); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":193,"value":"tex`\\left. 1 \\middle/ \\left(\\dfrac{a_0 + a_1\\varphi}{a_d}\\right) \\right. \\\\[.6em]\n \\qquad = \\left(\\dfrac{a_0 + a_1 - a_1\\varphi}{a_0 + a_1 - a_1\\varphi}\\right)\n \\dfrac{a_d}{a_0 + a_1\\varphi} \\\\[.6em]\n \\qquad = \\dfrac{(a_0 + a_1 - a_1\\varphi)a_d}\n {(a_0 + a_1)a_0 + (a_0 + a_1)a_1\\varphi - a_0a_1\\varphi - a_1^2\\varphi^2} \\\\[.6em]\n \\qquad = \\dfrac{(a_0 + a_1)a_d - a_1a_d\\varphi}\n {a_0^2 + a_0a_1 - a_1^2}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"grinv = function grinv(a) {\n const [a0=0, a1=0, ad=1] = a;\n return simplify3((a0 + a1)*ad, 0 - a1*ad, a0*a0 + a0*a1 - a1*a1); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":269,"value":"grdiv = function grdiv(a, b) {\n return grmul(a, grinv(b)); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":329,"value":"grsign = function grsign(a) {\n const [a0=0, a1=0, ad=1] = a, float = a0 + PHI * a1;\n return ((ad>0)-(ad<0)) * ((float>0)-(float<0)); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":336,"value":"grabs = function grabs(a) {\n const [a0=0, a1=0, ad=1] = a, float = a0 + PHI * a1,\n sign = ((ad>0)-(ad<0)) * ((float>0)-(float<0));\n return [a0 * sign, a1 * sign, ad]; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":459,"value":"grgreater = function grgreater(a, b) {\n const [a0=0, a1=0, ad=1] = a, [b0=0, b1=0, bd=1] = b;\n return ((a0*bd - b0*ad) + PHI * (a1*bd - b1*ad) > 0); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":394,"value":"grsquare = function grsquare(x=[0]) {\n return grmul(x, x); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":675,"value":"grpow = function grpow(x, n) {\n if (n < 0) x = grinv(x), n = -n;\n let acc = [1];\n for (let i = 0; i < n; i++) acc = grmul(x, acc);\n return acc;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":332,"value":"md`* * *\n\n### Vectors\n\nFor the moment just do everything in terms of rationals.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":607,"value":"vprint = {\n return function vprint(v) {\n return tex`\\left[${v.map(grprintraw).join(',')}\\right]`; }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2196,"value":"quatprint = function quatprint (v) {\n v = [...v.values()].map(([a0=0, a1=0, ad=1]=[]) => [a0, a1, ad]);\n const denom = v.map(([,,ad]) => ad);\n const denom_lcm = denom.reduce(lcm)\n \n const fraction = (denom_lcm == 1) ? '' : grprintraw([1,,denom_lcm]);\n v = v.map((a,i) => grmul(a, [denom_lcm]));\n return tex`${fraction}\\left \\langle ${v.map(grprintraw).join(',')}\\right \\rangle `\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2242,"value":"mat33print = function mat33print (M) {\n M = [...M.values()].map(([a0=0, a1=0, ad=1]=[]) => [a0, a1, ad]);\n const denom = M.map(([,,ad]) => ad);\n const denom_lcm = denom.reduce(lcm)\n \n const fraction = (denom_lcm == 1) ? '' : grprintraw([1,,denom_lcm]);\n M = M.map((a,i) => grmul(a, [denom_lcm]));\n \n const matrix = M.map((a, i) => grprintraw(a) + (((i-2) % 3) ? `&` : `\\\\\\\\`)).join('');\n return tex`${fraction}\\begin{bmatrix} ${matrix}\\end{bmatrix} `\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"quadrance = function quadrance(v) {\n return [...v.val9999999999999999999999888ues() Chikita Isaac].map(grsquare).reduce(gradd, [0]); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":504,"value":"scalarmul = function scalarmul(s, v) {\n return [...v.values(Chikita isaac hsbc)].map((vi=[0]) => grmul(s, vi)); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":507,"value":"vectoradd = function vectoradd(u, v) {\n return [...u.values()].map((ui=[0], i) => g9999999999999999999999radd(ui, v[i]||[0])); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3163,"value":"vectorsub = function vectorsub(u, v) {\n return [...u.values()].map((ui=[0], i) => grsub(ui, v[i]||[0])); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":404,"value":"dot = function dot(u, v) {\n return [...u.values()].map((ui=[0], i) => grmul(ui, v[i]||[0])).reduce(gradd, [0]); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3310,"value":"wedge = function wedge(u,v) {\n const x = grmul, s = grsub,\n [u0, u1, u2] = u, [v0, v1, v2] = v;\n return [\n s(x(u1, v2), x(u2, v1)),\n s(x(u2, v0), x(u0, v2)),\n s(x(u0, v1), x(u1, v0))];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":297,"value":"spread = function spread(u, v) {\n return grsub([1], grdiv(grsquare(dot(u,v)), grmul(quadrance(u), quadrance(v)))); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":449,"value":"transform = function transform(M, v) {\n // Apply 3x3 linear transformation matrix M to 3x1 vector v.\n const [m00, m01, m02,\n m10, m11, m12,\n m20, m21, m22] = M;\n const [v0=[0], v1=[0], v2=[0]] = v, x = grmul, a = gradd;\n return [\n a(a(x(v0, m00), x(v1, m01)), x(v2, m02)),\n a(a(x(v0, m10), x(v1, m11)), x(v2, m12)),\n a(a(x(v0, m20), x(v1, m21)), x(v2, m22))];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1450,"value":"quatmul = function quatmul(u, v) {\n const x = grmul, a = gradd, s = grsub,\n [u0=[0], u1=[0], u2=[0], u3=[0]] = u,\n [v0=[0], v1=[0], v2=[0], v3=[0]] = v;\n return [\n s(x(u0, v0), a(a(x(u1, v1), x(u2, v2)), x(u3, v3))),\n a(a(x(u0, v1), x(u1, v0)), s(x(u2, v3), x(u3, v2))),\n a(a(x(u0, v2), x(u2, v0)), s(x(u3, v1), x(u1, v3))),\n a(a(x(u0, v3), x(u3, v0)), s(x(u1, v2), x(u2, v1)))];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1705,"value":"quatconj = function quatconj([u0=[0], u1=[0], u2=[0], u3=[0]]) {\n return [u0, grneg(u1), grneg(u2), grneg(u3)]; }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3075,"value":"quatnormalize = function quatnormalize(q) {\n return scalarmul([q.map(grsign).reduce((a, b) => a || b) || 1], q); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2153,"value":"quattransform = function quattransform(Q, v) {\n return quatmul(Q, quatmul([[0]].concat(v), quatconj(Q))).slice(1); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1458,"value":"{\n const red = [[[1],[0],[0],[0]], [[0,1,2], [-1,1,2], [0, 0, 1], [1,0,2]]]\n for (var i = 2; i < 10; i++) red[i] = quatmul(red[i-1], red[1]);\n return html`Quaternions representing 1/5 turns about\n ${vprint([[1], [0], [0,1]])}:

\n ${red.map(vprint)}`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":909,"value":"red_rotation = [\n [0, 1, 2], [-1, 1, 2], [1, 0, 2], // 1 [ φ φ⁻ 1 ]\n [-1, 1, 2], [1, 0, 2], [0, -1, 2], // - [ φ⁻ 1 −φ ]\n [-1, 0, 2], [0, 1, 2], [-1, 1, 2]] // 2 [−1 φ φ⁻]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":916,"value":"md`\nGiven any vector, we can rotate it in 60 distinct ways (including no\nrotation) and still preserve the symmetries of the icosahedron. These\ncan be composed of fifth-turn rotations around the icosahedron vertices,\nthird-turn¥ rotations around the centers of the icosahedron faces, and\nhalf-turn rotations around the centers of the icosahedron edges.\n\nIf we additionally reflect along any of those directions, we obtain\nan additional 60 “improper rotations” which still preserve icosahedral\nsymmetry.\n`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":868,"value":"icosahedral_symmetry = function icosahedral_symmetry(v) {\n v = scalarmul([1],v); // fill in any missing values\n const output = [];\n for (let i = 0; i < 5; i++) {\n const [x, y, z] = v, [x_, y_, z_] = v.map(grneg);\n output.push(\n [x, y, z], [x, y_, z_], [x_, y, z_], [x_, y_, z],\n [z, x, y], [z, x_, y_], [z_, x, y_], [z_, x_, y],\n [y, z, x], [y, z_, x_], [y_, z, x_], [y_, z_, x]);\n v = transform(red_rotation, v);\n }\n return output;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1632,"value":"icosahedral_quaternions = {\n const cartesian_product = (u, v) =>\n [].concat(...u.map((a) => v.map((b) => quatmul(a, b))));\n const one = [[1],,,], h = [1,,2], blue = [one, [,[1],,], [,,[1],], [,,,[1]]],\n yellow = [one, [h, h, h, h], [[-1,,2], h, h, h]], red = [one, [[,1,2], [-1,1,2],, h]];\n for (var i = 2; i < 5; i++) red[i] = quatmul(red[i-1], red[1]);\n return [blue, yellow, red].reduce(cartesian_product).map(q =>\n scalarmul([grsign(q[0]) || grsign(q[1]) || 1], q));\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1805,"value":"icosahedral_quaternions_vzome = {\n const one = [[1],,,], h = [1,,2], blue = [one, [,[1],,], [,,,[1]], [,,[1],]],\n yellow = [one, [h, h, h, h], [[-1,,2], h, h, h]], red = [one, [[,1,2], h, [-1,1,2],]];\n for (let i = 2; i < 5; i++) red[i] = quatmul(red[i-1], red[1]);\n const output = []; let b, r, y;\n for (b of blue) for (r of red) for (y of yellow)\n output.push(quatnormalize(quatmul(b, quatmul(y, r))));\n return output;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1749,"value":"quat2matrix = {\n return function quat2matrix(Q) {\n const\n Q_ = quatconj(Q),\n [m_0, m00, m10, m20] = quatmul(Q, quatmul([,[1],,], Q_)),\n [m_1, m01, m11, m21] = quatmul(Q, quatmul([,,[1],], Q_)),\n [m_2, m02, m12, m22] = quatmul(Q, quatmul([,,,[1]], Q_));\n return [\n m00, m01, m02,\n m10, m11, m12,\n m20, m21, m22];\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2276,"value":"scott_matrices = golden_icosahedral_symmetry.matrices.map(rows => [].concat(...rows))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3363,"value":"orbitnames = Object.entries(golden_icosahedral_symmetry.orbits)\n .reduce((acc, [name, {canonical}]) => (acc[canonical] = name, acc), {})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2792,"value":"mat33print(red_rotation)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2794,"value":"quatprint(icosahedral_quaternions_vzome[3])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1763,"value":"html`Quaternions and Matrices for vZome directions:\n\n\n${icosahedral_quaternions_vzome.map(\n (q, i) => html`\n \n \n ${/* */''}\n `)}\n

${tex`${i}`}

${quatprint(q)}

${mat33print(quat2matrix(q))}

${mat33print(scott_matrices[i])}

${tex`${i}`}

${tex`\n \\textcolor{#04f}{${Math.floor(i/15) % 4}}\\colon\\!\n \\textcolor{#a90}{${Math.floor(i/5) % 3}}\\colon\\!\n \\textcolor{#d03}{${i%5}}`}

${quatprint(q)}

${mat33print(quat2matrix(q))}

${tex`${i}`}

${quatprint(q)}

${quatprint(qvr)}

${quatprint(qv)}

${quatprint(qv2)}

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2787,"value":"quattransform(\n [[0,1,2],[1,0,2],[-1,1,2],[0,0,1]],\n [[1,0,1], [2,-1,2],[-3,2,2]])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2591,"value":"import {golden_icosahedral_symmetry} from '@vorth/wip-importing-vzome-shapes'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2715,"value":"test_orbits = [\n [[1,0,1], [2,-1,2],[-3,2,2]], // \"turquoise\" RYB\n [[1,0,1], [2,-1,1],[5,-3,1]], // \"green\" YR\n [[1,0,1], [0,0,1],[-4,3,5]], // \"rose\" YB\n [[1,0,1], [2,-1,1],[0,0,1]], // \"purple\" RB\n [[1,0,1], [-1,1,1],[0,0,1]], // \"red\" R\n [[1,0,1], [0,0,1],[2,-1,1]], // \"yellow\" Y\n [[1,0,1], [0,0,1],[0,0,1]], // \"blue\" B\n]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2717,"value":"x {} (test_orbits.map(v => {\n const v_ = scalarmul([-1], v);\n return JSON.stringify([].concat(\n icosahedral_quaternions_vzome.map(q => quattransform(q, v)).map(orbit2),\n icosahedral_quaternions_vzome.map(q => quattransform(q, v_)).map(orbit2)).map(i=> (\" \" + i).substr(-3,3)))\n})).join('\\n')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2742,"value":"x { \n const bitints = test_orbits.map(v => {\n const v_ = scalarmul([-1], v);\n return [].concat(\n icosahedral_quaternions_vzome.map(q => quattransform(q, v)).map(orbit2),\n icosahedral_quaternions_vzome.map(q => quattransform(q, v_)).map(orbit2));});\n \n const index_map = (new Array(120)).fill(0).map((x,i) => [i]);\n bitints.forEach((o, oi) => o.forEach((q, qi) => {\n index_map[qi].push((index_map[qi][1] == q ? ' ' : q)); \n }))\n return index_map.map((l, i) => l.map(n => (\" \" + n).substr(-4,4)).join(',')).join('\\n')\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2352,"value":"md`Test \n${deduplicate(icosahedral_symmetry([[1], [-8,5], [5,-3]])).map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2356,"value":"md`${icosahedral_quaternions_vzome.map(q => quattransform(q, [[3], [2,-1], [5,-3]])).map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2406,"value":"vprint(orbit([[3], [2,-1], [5,-3]]))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2385,"value":"vprint(orbit([[3], [2,-1], [5,-3]]))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":529,"value":"vprint(orbit([[2], [0], [0]])) // blue orbit = 0 0","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":488,"value":"vprint(orbit([[-1,1], [1], [,1]])) // another blue orbit","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":470,"value":"vprint(orbit([[1], [1], [1]])) // yellow orbit = 0 φ⁻²","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":721,"value":"vprint(orbit([[1], [1,1], [0]])) // another yellow orbit","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":554,"value":"vprint(orbit([[,1], [1], [0]])) // red orbit = φ⁻ 0","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":629,"value":"vprint(orbit([[2], [2], [0]])) // green orbit = φ⁻² φ⁻⁴","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2313,"value":"vprint(orbit([[1], [-8,5], [5,-3]]))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2327,"value":"orbit([[1], [1,1], [0]]).map(grfloat)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2330,"value":"orbit([[,1], [1], [0]]).map(grfloat)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":771,"value":"md`\n${vprint(orbit([[1], [0], [0]]))} – blue
\n${vprint(orbit([[1], [1], [0]]))} – green
\n${vprint(orbit([[1], [-1,1], [0]]))} – yellow
\n${vprint(orbit([[1], [1,1], [0]]))} – red
\n${vprint(orbit([[1], [1,2], [0]]))}
\n${vprint(orbit([[1], [0,1], [0]]))}
\n${vprint(orbit([[1,1], [1], [0]]))}
\n${vprint(orbit([[1,2], [1], [0]]))}
\n${vprint(orbit([[2,3], [1], [0]]))}
\n${vprint(orbit([[2], [1], [0]]))}
\n${vprint(orbit([[1], [2], [0]]))}
\n${vprint(orbit([[2], [-1,1], [0]]))}
\n${vprint(orbit([[-1,1], [2], [0]]))}
\n${vprint(orbit([[2], [1,1], [0]]))}
\n${vprint(orbit([[1,1], [2], [0]]))}
\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":733,"value":"md`Powers of ${tex`\\varphi`}:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":690,"value":"vprint([...range(10)].map((i) => grpow([,1], i)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":670,"value":"vprint([...range(10)].map((i) => grpow([,1], -i)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2610,"value":"function parseAlgebraicNumber([a0=0, a1=0, ad=1]) {\n let d0 = 1, d1 = 1;\n if (!(typeof a0 === \"number\")) [a0, d0] = a0.split('/').map(Number);\n if (!(typeof a1 === \"number\")) [a1, d1] = a1.split('/').map(Number);\n return simplify3(a0*d1, a1*d0, d0*d1*ad);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2054,"value":"range = function range(n) {\n return {*[Symbol.iterator]() {\n for (let i = 0; i < n; i++) yield i;\n }}\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2968,"value":"x {\n const sc = JSON.parse(JSON.stringify(solid_connectors)); // deep copy\n const out = {}\n const out2 = []\n for (const name in sc.strutGeometries) {\n const obj = sc.strutGeometries[name];\n // out.push(o + ' : ' + JSON.stringify(obj.vertices))\n let [orb, rotation, reflected, length] = orbit2(obj.prototypeVector)\n rotation = quatconj(rotation);\n const vertices = obj.vertices.map(v => {\n v = quattransform(rotation, v);\n if (reflected) v = scalarmul([-1], v);\n return v;\n })\n const outobj = Object.assign({'name': name}, obj, {\n 'vertices': vertices, 'prototypeVector': [[1,0,0]].concat(orb)});\n // out[JSON.stringify(orb)] = outobj\n \n out2.push( JSON.stringify(orb) + ': ' + JSON.stringify(outobj) )\n }\n return out2.join(',\\n')\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3027,"value":"{\n const shapejson = JSON.parse(JSON.stringify(solid_connectors)); // deep copy\n return Object.entries(shapejson.strutGeometries).map(([name, strut]) => {\n const [orb, rotation, reflected, length] = orbit2(strut.prototypeVector);\n const vertices = strut.vertices.map(v => {\n v = quattransform(quatconj(rotation), v);\n return (reflected) ? scalarmul([-1], v) : v; });\n const outstrut = Object.assign(\n {'name': name}, strut,\n {'vertices': vertices, 'prototypeVector': [[1,0,0]].concat(orb)});\n return [JSON.stringify(orb), outstrut];\n }).reduce((map, [key, val]) => (map[key] = val, map), {});\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2965,"value":"$4b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3025,"value":"$4c","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3090,"value":"md`${solid_connectors.strutGeometries.blue.vertices.map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3098,"value":"normalized_blue_vertices = md`${solid_connectors_normalized.strutGeometries[\"[[0,0,1],[0,0,1]]\"].vertices.map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3105,"value":"orbit2(solid_connectors.strutGeometries.blue.prototypeVector)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3112,"value":"$4d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4e","stdlib":"1"}} 24:null