31: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]; } }32: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]; } }33: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]], [[0,1,2],[0,0,1],[-3,1,2]], [[0,0,1],[3,-1,2],[0,-1,2]], [[-1,1,2],[0,1,2],[1,-1,1]], 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[[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]], 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[[3,1,2],[-1,1,1],[-3,2,2]], [[3,1,2],[0,0,1],[-3,2,2]], [[1,0,1],[1,-1,2],[2,-1,2]], [[1,0,1],[-1,1,2],[2,-1,2]], [[-3,-1,2],[0,0,1],[-1,0,2]], [[-3,-1,2],[1,-1,1],[3,-2,2]], [[0,1,2],[0,0,1],[3,-1,2]], [[3,1,2],[0,0,1],[1,0,2]], [[-1,0,1],[1,-1,2],[-2,1,2]], [[0,-1,2],[0,0,1],[-3,1,2]], [[-3,-1,2],[0,0,1],[3,-2,2]], [[3,1,2],[-1,1,1],[1,0,2]], [[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]]} } })35:T41a,{ const rgb_to_hex = rgb => '#' + rgb.map(x => ("0" + x.toString(16)).substr(-2,2)).join(''); const colorlist = [ ['red', [197,36,49]], ['yellow', [240,169,1]], ['blue', [6,96,141]], ['green', [8,141,50]], ['orange', [231,101,0]], ['purple', [122,66,171]], ['black', [40,40,42]], ['white', [238,241,247]], ['olive', [116,104,1]], ['lavender', [144,127,227]], ['maroon', [131,17,71]], ['rose', [252,106,171]], ['navy', [52,48,136]], ['brown', [105,54,1]], ['apple', [129,191,30]], ['sand', [187,144,85]], ['turquoise', [47,174,151]], ['coral', [254,140,139]], ['sulfur', [196,231,81]], ['cinnamon', [144,56,14]], ['spruce', [12,84,55]], ['magenta', [219,41,118]], ['snubPentagon', [170,27,111]], ['snubTriangle', [153,158,0]], ['snubDiagonal', [229,221,185]], ['slate', [102,126,153]], ['mauve', [146,82,131]], ['ivory', [229,221,185]], ] return colorlist.map(([c, rgb]) => `${c}: "${rgb_to_hex(rgb)}"`).join(',\n') }36:[] 2f:{"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"},{"id":190,"value":"md`* * *\n\n### Golden Integers\n\nThe key property to know about the golden ratio ${tex`\\varphi`} is that ${tex`\\varphi^2 = \\varphi + 1`}.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2,"value":"gprint = function gprint(a) {\n const [a0, a1=0] = a, sign = (a1 > 0) ? '+' : '';\n return tex`${a0} ${sign} ${a1}\\varphi`; }","pinned":false,"hidden":false,"mode":"ojs"},{"id":95,"value":"tex`\\varphi = \\dfrac{1 + \\sqrt{5}}{2} \\approx ${PHI.toFixed(4)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":66,"value":"PHI = 0.5 * (Math.sqrt(5) + 1)","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"id":45,"value":"gsquare = function gsquare(x) {\n return gmul(x, x); }","pinned":true,"hidden":false,"mode":"ojs"},{"id":309,"value":"md`* * *`","pinned":false,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"id":2210,"value":"lcm = function lcm(a, b) {\n return a / gcd(a, b) * b; }","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"id":1005,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":188,"value":"md`* * *\n### Golden Rationals `","pinned":false,"hidden":false,"mode":"ojs"},{"id":122,"value":"// grprint = function grprint(a) {\n// const [a0, a1=0, ad=1] = a, sign = (a1 > 0) ? '+' : '';\n// return tex`\\dfrac{${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}}{${ad}}`; }","pinned":false,"hidden":false,"mode":"ojs"},{"id":2192,"value":"grprint = function grprint(a) {\n return tex`${grprintraw(a)}`; }","pinned":false,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"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"},{"id":437,"value":"grsum = function grsum(vec) {\n return vec.reduce(gradd, [0]); }","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"id":269,"value":"grdiv = function grdiv(a, b) {\n return grmul(a, grinv(b)); }","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"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"},{"id":394,"value":"grsquare = function grsquare(x=[0]) {\n return grmul(x, x); }","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"id":607,"value":"vprint = {\n return function vprint(v) {\n return tex`\\left[${v.map(grprintraw).join(',')}\\right]`; }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2196,"value":"quatprint = function quatprint (v) {\n v = [...v.values()].map(([a0=0, a1=0, ad=1]=[]) => [a0, a1, ad]);\n const denom = v.map(([,,ad]) => ad);\n const denom_lcm = denom.reduce(lcm)\n \n const fraction = (denom_lcm == 1) ? '' : grprintraw([1,,denom_lcm]);\n v = v.map((a,i) => grmul(a, [denom_lcm]));\n return tex`${fraction}\\left \\langle ${v.map(grprintraw).join(',')}\\right \\rangle `\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2242,"value":"mat33print = function mat33print (M) {\n M = [...M.values()].map(([a0=0, a1=0, ad=1]=[]) => [a0, a1, ad]);\n const denom = M.map(([,,ad]) => ad);\n const denom_lcm = denom.reduce(lcm)\n \n const fraction = (denom_lcm == 1) ? '' : grprintraw([1,,denom_lcm]);\n M = M.map((a,i) => grmul(a, [denom_lcm]));\n \n const matrix = M.map((a, i) => grprintraw(a) + (((i-2) % 3) ? `&` : `\\\\\\\\`)).join('');\n return tex`${fraction}\\begin{bmatrix} ${matrix}\\end{bmatrix} `\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":44,"value":"quadrance = function quadrance(v) {\n return [...v.values()].map(grsquare).reduce(gradd, [0]); }","pinned":true,"hidden":false,"mode":"ojs"},{"id":504,"value":"scalarmul = function scalarmul(s, v) {\n return [...v.values()].map((vi=[0]) => grmul(s, vi)); }","pinned":true,"hidden":false,"mode":"ojs"},{"id":507,"value":"vectoradd = function vectoradd(u, v) {\n return [...u.values()].map((ui=[0], i) => gradd(ui, v[i]||[0])); }","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"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"},{"id":2276,"value":"scott_matrices = golden_icosahedral_symmetry.matrices.map(rows => [].concat(...rows))","pinned":false,"hidden":false,"mode":"ojs"},{"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"},{"id":2792,"value":"mat33print(red_rotation)","pinned":false,"hidden":false,"mode":"ojs"},{"id":2794,"value":"quatprint(icosahedral_quaternions_vzome[3])","pinned":false,"hidden":false,"mode":"ojs"},{"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])}

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1854,"value":"html`Quaternions and Matrices as Jacob might order them:
\n(But realistically I’d probably want to think more about it)\n\n\n${icosahedral_quaternions.map(\n (q, i) => html`\n \n \n \n `)}\n

${tex`${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))}

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":881,"value":"md`Blue \n${deduplicate(icosahedral_symmetry([[2],[0],[0]])).map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":890,"value":"md`Yellow \n${deduplicate(icosahedral_symmetry([[1], [1], [1]])).map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":898,"value":"md`Red \n${deduplicate(icosahedral_symmetry([[,1], [1], [0]])).map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":903,"value":"md`Green \n${deduplicate(icosahedral_symmetry([[2], [2], [0]])).map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":1248,"value":"md`Big Zomeball \n${deduplicate(icosahedral_symmetry([[2,2], [,1], [1]])).map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":1325,"value":"md`Zomeball Vertices \n${deduplicate(icosahedral_symmetry([[1,0,1], [-1,1,2], [2,-1,2]])).map(vprint)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":970,"value":"deduplicate = function deduplicate(array) {\n const set = new Set();\n return array.filter(item => {\n if (set.has(JSON.stringify(item))) return false;\n set.add(JSON.stringify(item)); return true;\n });\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":425,"value":"orbit = {\n const v = [[-1, 1], [-1], [0, -1]]; // φ⁻ -1 -φ\n return function orbit(u) {\n // Reduce to the 'kite' shape at the corner of one octant:\n u = u.map(grabs); // absolute value of each coordinate\n u = transform(red_rotation, u).map(grabs);\n u = transform(red_rotation, u).map(grabs);\n\n // Now reflect the top triangle of the kite onto the bottom triangle:\n let d = dot(u, v); d = grmul([-grgreater([0], d), 0, 2], d);\n u = vectoradd(u, scalarmul(d, v));\n \n // Now return rational coordinates of a gnomonic (tangent) projection.\n return scalarmul(grinv(u[0]), [u[1], u[2]]);\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":3288,"value":"// Version of transform which doesn't normalize inputs\n// and tries not to create too many extra arrays.\n// Not sure whether the performance boost is worth it.\ntransform_in_place = {\n const x = function grmul(a, b) {\n const [a0, a1, ad] = a, [b0, b1, bd] = b;\n return simplify3(a0*b0 + a1*b1, a0*b1 + a1*b0 + a1*b1, ad*bd); }\n \n const a = function gradd3(a, b, c) {\n const [a0, a1, ad] = a, [b0, b1, bd] = b, [c0, c1, cd] = c;\n return simplify3(a0*bd*cd + b0*ad*cd + c0*ad*bd, a1*bd*cd + b1*ad*cd + c1*ad*bd, ad*bd*cd); }\n \n return function transform_in_place(M, v) {\n // Apply 3x3 linear transformation matrix M to 3x1 vector v, return v.\n const [m00, m01, m02,\n m10, m11, m12,\n m20, m21, m22] = M;\n const [v0, v1, v2] = v;\n v[0] = a(x(v0, m00), x(v1, m01), x(v2, m02));\n v[1] = a(x(v0, m10), x(v1, m11), x(v2, m12));\n v[2] = a(x(v0, m20), x(v1, m21), x(v2, m22));\n return v;\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2302,"value":"$32","pinned":true,"hidden":false,"mode":"ojs"},{"id":3308,"value":"orbit2([[0], [0], [0]])","pinned":false,"hidden":false,"mode":"ojs"},{"id":2850,"value":"html`\n\n${icosahedral_quaternions_vzome.map(\n (q, i) => {\n const vv = [[5,-3],[2,-1],[2,0]];\n\n // const v = [[1,0,1]].concat(orbit2(vv)[0]); // [[1],[0],[0]] // [[1],[2,-1],[5,-3]]; // [[1], [2,-1,2],[-3,2,2]]; // [[1],[0],[2,-1]] // [[1],[-1,1],[0]] // \n const v = [[1],[2,-1],[5,-3]];\n const qv = quattransform(q, v);\n const [o, qvr, reflect] = orbit2(qv);\n const qv2 = scalarmul([1-2*reflect], quattransform(qvr, v));\n return html`\n \n \n \n \n \n `\n })}\n

${tex`${i}`}

${quatprint(q)}

${quatprint(qvr)}

${quatprint(qv)}

${quatprint(qv2)}

`","pinned":false,"hidden":false,"mode":"ojs"},{"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"},{"id":2591,"value":"import {golden_icosahedral_symmetry} from '@vorth/wip-importing-vzome-shapes'","pinned":false,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"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"},{"id":2352,"value":"md`Test \n${deduplicate(icosahedral_symmetry([[1], [-8,5], [5,-3]])).map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":2356,"value":"md`${icosahedral_quaternions_vzome.map(q => quattransform(q, [[3], [2,-1], [5,-3]])).map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":2406,"value":"vprint(orbit([[3], [2,-1], [5,-3]]))","pinned":true,"hidden":false,"mode":"ojs"},{"id":2385,"value":"vprint(orbit([[3], [2,-1], [5,-3]]))","pinned":true,"hidden":false,"mode":"ojs"},{"id":529,"value":"vprint(orbit([[2], [0], [0]])) // blue orbit = 0 0","pinned":true,"hidden":false,"mode":"ojs"},{"id":488,"value":"vprint(orbit([[-1,1], [1], [,1]])) // another blue orbit","pinned":true,"hidden":false,"mode":"ojs"},{"id":470,"value":"vprint(orbit([[1], [1], [1]])) // yellow orbit = 0 φ⁻²","pinned":true,"hidden":false,"mode":"ojs"},{"id":721,"value":"vprint(orbit([[1], [1,1], [0]])) // another yellow orbit","pinned":true,"hidden":false,"mode":"ojs"},{"id":554,"value":"vprint(orbit([[,1], [1], [0]])) // red orbit = φ⁻ 0","pinned":true,"hidden":false,"mode":"ojs"},{"id":629,"value":"vprint(orbit([[2], [2], [0]])) // green orbit = φ⁻² φ⁻⁴","pinned":true,"hidden":false,"mode":"ojs"},{"id":2313,"value":"vprint(orbit([[1], [-8,5], [5,-3]]))","pinned":true,"hidden":false,"mode":"ojs"},{"id":2327,"value":"orbit([[1], [1,1], [0]]).map(grfloat)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2330,"value":"orbit([[,1], [1], [0]]).map(grfloat)","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"id":733,"value":"md`Powers of ${tex`\\varphi`}:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":690,"value":"vprint([...range(10)].map((i) => grpow([,1], i)))","pinned":true,"hidden":false,"mode":"ojs"},{"id":670,"value":"vprint([...range(10)].map((i) => grpow([,1], -i)))","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"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"},{"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"},{"id":2965,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":3025,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":3090,"value":"md`${solid_connectors.strutGeometries.blue.vertices.map(vprint)}`","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"id":3105,"value":"orbit2(solid_connectors.strutGeometries.blue.prototypeVector)","pinned":false,"hidden":false,"mode":"ojs"},{"id":3112,"value":"$35","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W36","stdlib":"1","titling":"auto"}