{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 3D Figures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Updated to work with Sage 9.0 (and prior versions) on Apr. 27, 2020." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[(0, 7, 6), (1, 3, 4), (2, 11, 5), (8, 10, 9)]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "[(0, 11, 9), (1, 7, 10), (2, 3, 8), (4, 5, 6)]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "[(0, 22, 14, 11),\n", " (1, 4, 15, 5),\n", " (2, 10, 12, 23),\n", " (3, 16, 13, 17),\n", " (6, 9, 8, 7),\n", " (18, 19, 20, 21)]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "[(0, 1, 2, 3),\n", " (4, 20, 17, 6),\n", " (5, 8, 16, 18),\n", " (7, 10, 21, 11),\n", " (9, 22, 19, 23),\n", " (12, 15, 14, 13)]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[(0, 45, 13, 17, 9), (1, 49, 14, 16, 8), (2, 48, 10, 15, 7), (3, 47, 11, 19, 6), (4, 46, 12, 18, 5), (20, 21, 22, 23, 24), (25, 30, 38, 56, 53), (26, 34, 39, 57, 52), (27, 33, 35, 58, 51), (28, 32, 36, 59, 50), (29, 31, 37, 55, 54), (40, 44, 43, 42, 41)]\n", "[(0, 4, 3, 2, 1), (5, 33, 36, 48, 40), (6, 32, 37, 49, 44), (7, 31, 38, 45, 43), (8, 30, 39, 46, 42), (9, 34, 35, 47, 41), (10, 19, 27, 23, 55), (11, 18, 26, 24, 59), (12, 17, 25, 20, 58), (13, 16, 29, 21, 57), (14, 15, 28, 22, 56), (50, 51, 52, 53, 54)]\n", "Proof for the Octahedron:\n", "Number of Cusps = 2\n", "Slope 1 yields cylinders given by a permutation that is a product of 2-cycles:\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(1,8)(2,9)(3,5)(4,7)(6,11)(10,12)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Vertical yields cylinders given by a permutation that is a product of 3-cycles.\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(1,7,10)(2,3,8)(4,5,6)(9,12,11)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Both directions are distinct periodic directions. No zero appears twice in any square.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 152 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Proof for the cube:\n", "Number of Cusps = 3\n", "Vertical yields cylinders given by a permutation that is a product of 4-cycles.\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(1,2,3,24)(4,20,17,6)(5,8,16,18)(7,10,21,11)(9,22,19,23)(12,15,14,13)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Slope 1 yields cylinders given by a permutation that is a product of 3-cycles.\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(1,20,11)(2,21,5)(3,18,23)(4,14,7)(6,22,13)(8,10,15)(9,16,12)(17,24,19)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Slope 2 yields cylinders given by a permutation that is a product of 2-cycles.\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(1,14)(2,15)(3,12)(4,8)(5,20)(6,16)(7,22)(9,10)(11,19)(13,24)(17,18)(21,23)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "All 3 directions are distinct periodic directions. No zero appears on both the top and bottom of any cylinder.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 294 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Proof for the Icosahedron:\n", "Number of Cusps = 3\n", "Vertical yields cylinders given by a permutation that is a product of 5-cycles.\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(1,60,4,3,2)(5,33,36,48,40)(6,32,37,49,44)(7,31,38,45,43)(8,30,39,46,42)(9,34,35,47,41)(10,19,27,23,55)(11,18,26,24,59)(12,17,25,20,58)(13,16,29,21,57)(14,15,28,22,56)(50,51,52,53,54)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Slope 1/3 yields cylinders given by a permutation that is a product of 3-cycles.\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(1,29,10)(2,28,11)(3,27,12)(4,26,13)(5,17,43)(6,18,42)(7,19,41)(8,15,40)(9,16,44)(14,60,25)(20,55,38)(21,59,37)(22,58,36)(23,57,35)(24,56,39)(30,54,49)(31,50,48)(32,51,47)(33,52,46)(34,53,45)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Slope 1/2 yields cylinders given by a permutation that is a product of 2-cycles.\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(1,15)(2,19)(3,18)(4,17)(5,42)(6,41)(7,40)(8,44)(9,43)(10,31)(11,32)(12,33)(13,34)(14,30)(16,60)(20,56)(21,55)(22,59)(23,58)(24,57)(25,45)(26,46)(27,47)(28,48)(29,49)(35,52)(36,51)(37,50)(38,54)(39,53)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "All 3 directions are distinct periodic directions. No zero appears on both the top and bottom of any cylinder.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 720 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Octahedron\n", "4\n", "[Infinity, 1]\n", "[3, 1]\n", "0\n", "1\n", "0\n", "\n", "\n", "Cube\n", "9\n", "[Infinity, 2, 1]\n", "[4, 2, 3]\n", "1\n", "0\n", "0\n", "\n", "\n", "Icosahedron\n", "10\n", "[Infinity, 2, 3]\n", "[5, 2, 3]\n", "0\n", "1\n", "0\n", "\n", "\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Number Field in s with defining polynomial x^4 - 5*x^2 + 5 with s = 1.175570504584947?" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "1.17557050458495" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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'RRTTTTTRTT',\n", " 'RTRRTRRTTT',\n", " 'RTTRTRRTTT',\n", " 'RTRTTRRTTT',\n", " 'RRTTTRRTTT',\n", " 'RTRRRTRTTT',\n", " 'RRRTRTTTTT',\n", " 'RTRRTTTTTT',\n", " 'RRTRTTTTTT',\n", " 'RTTTRRRTRRT',\n", " 'RTRTRTRTRRT',\n", " 'RTTRRRTTRRT',\n", " 'RTRRTTRRTRT',\n", " 'RRTRTTRRTRT',\n", " 'RTTTRRTRTRT',\n", " 'RTRRTRTRTRT',\n", " 'RTTRTRTRTRT',\n", " 'RRTRTRRTTRT',\n", " 'RTRTRTRTTRT',\n", " 'RTRRTRTTTRT',\n", " 'RTRTRTRRRTT',\n", " 'RRTRTRTRRTT',\n", " 'RTRTTRTRRTT',\n", " 'RTTRRTTRRTT',\n", " 'RRRTRTTRRTT',\n", " 'RTRRTTTRRTT',\n", " 'RRRTRRTTRTT',\n", " 'RRTTRRTTRTT',\n", " 'RRTRTRTTRTT',\n", " 'RRTTTRTTRTT',\n", " 'RTTRTTTTRTT',\n", " 'RTTTTTTTRTT',\n", " 'RRRTRTRRTTT',\n", " 'RTTTTTRRTTT',\n", " 'RRTRRRTRTTT',\n", " 'RTTRRTTRTTT',\n", " 'RTRRTRRTTTT',\n", " 'RRTTTRRTTTT',\n", " 'RRTTRRTTTTT',\n", " 'RTRTRTTTTTT',\n", " 'RRTTRTTTRRRT',\n", " 'RRTRTRTRTRRT',\n", " 'RTRTTRTRTRRT',\n", " 'RRTTTRTRRTRT',\n", " 'RTRTRTTRRTRT',\n", " 'RTRTTRRTRTRT',\n", " 'RTTRTTRTRTRT',\n", " 'RRTTRRTTRTRT',\n", " 'RTTRTRRRTTRT',\n", " 'RTRTRTRRTTRT',\n", " 'RRTRTRTRTTRT',\n", " 'RRRTTRTRTTRT',\n", " 'RRTTRTRTRRTT',\n", " 'RRTRRTTTRRTT',\n", " 'RTTTTTTRTRTT',\n", " 'RTTTRTTTTRTT',\n", " 'RTTTTTTRRTTT',\n", " 'RRTTRTTRTTTT',\n", " 'RRTRTTTRTRRRT',\n", " 'RTTRRTRTTTRRT',\n", " 'RTRTTRRTRRTRT',\n", " 'RRTRTTRRTRTRT',\n", " 'RTRTRRTRTRTRT',\n", " 'RTRRTRTRTRTRT',\n", " 'RTRTTRRTTRTRT',\n", " 'RTRRRTRTTTTRT',\n", " 'RTTRRTTTTTTRT',\n", " 'RRTTTRTTRTRTT',\n", " 'RRRTRTRTRRTTT',\n", " 'RTTRRTTTRRTRRT',\n", " 'RRTTRTRRTRTRRT',\n", " 'RRTRTRTRTRTRRT',\n", " 'RRTRRTRTRTRTRT',\n", " 'RRTTTTRRTRTRTT',\n", " 'RTRTTTTTTRRTTT',\n", " 'RTRTTTRTTRRTRRT',\n", " 'RRTTTRRTRTRTRRT',\n", " 'RRTRTRRTTRRTTRT']" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "There are 0 trajectories renormalized to short saddle connections.\n", "There are 31 trajectories renormalized to long saddle connections:\n", "['RRRTT', 'RTTTRT', 'RTRTRTT', 'RRRTTRRT', 'RRTTRTRT', 'RRTRTTTT', 'RRTTRRTRT', 'RRTRTRRTT', 'RRTRRTTTT', 'RTRRTTTTT', 'RRTTRTRRRT', 'RTRRTTRRRT', 'RTRRTRTRRT', 'RRTRTTRTRT', 'RRRTTRTTRT', 'RRRTTTTRTT', 'RTRTRTRTRRT', 'RTTRTRTRTRT', 'RTRTRTRTTRT', 'RRTTTRTTRTT', 'RRTTRTTTRRRT', 'RTRTTRTRTRRT', 'RRTTTRTRRTRT', 'RTTRTRRRTTRT', 'RRRTTRTRTTRT', 'RRTRRTTTRRTT', 'RTTTTTTRTRTT', 'RTTRRTRTTTRRT', 'RTRTTRRTRRTRT', 'RRTTTRTTRTRTT', 'RTTRRTTTRRTRRT']\n", "Polygon: (0, 0), (2, 0), (-s^2 + 4, -s^3 + 3*s), (1, -s^3 + 4*s), (s^2 - 2, -s^3 + 3*s)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " Coset Rep Exact Vector Length of Trajectory Vector of Trajectory\n", "1 & $RRRTT$ & $ \\left(-3 s^{2} + 12,\\,-5 s^{3} + 19 s\\right) $ & 16.2386 & (7.85410, 14.2128) \\\\\n", "2 & $RRRTTRRT$ & $ \\left(-21 s^{2} + 76,\\,-5 s^{3} + 19 s\\right) $ & 49.0816 & (46.9787, 14.2128) \\\\\n", "3 & $RTTTRT$ & $ \\left(-19 s^{2} + 72,\\,-7 s^{3} + 25 s\\right) $ & 49.1630 & (45.7426, 18.0171) \\\\\n", "4 & $RRTRTTTT$ & $ \\left(-16 s^{2} + 59,\\,-33 s^{3} + 120 s\\right) $ & 94.9181 & (36.8885, 87.4567) \\\\\n", "5 & $RTRRTTRRRT$ & $ \\left(-29 s^{2} + 106,\\,-27 s^{3} + 99 s\\right) $ & 98.0031 & (65.9230, 72.5173) \\\\\n", "6 & $RRTTRTRRRT$ & $ \\left(-30 s^{2} + 109,\\,-27 s^{3} + 98 s\\right) $ & 98.2417 & (67.5410, 71.3418) \\\\\n", "7 & $RRTRRTTTT$ & $ \\left(12 s^{2} - 41,\\,-41 s^{3} + 148 s\\right) $ & 110.117 & (-24.4164, 107.376) \\\\\n", "8 & $RTRRTTTTT$ & $ \\left(-18 s^{2} + 67,\\,-39 s^{3} + 142 s\\right) $ & 111.810 & (42.1246, 103.572) \\\\\n", "9 & $RTRTRTT$ & $ \\left(-23 s^{2} + 84,\\,-39 s^{3} + 141 s\\right) $ & 114.941 & (52.2148, 102.396) \\\\\n", "10 & $RRTTRTRT$ & $ \\left(3 s^{2} - 10,\\,-55 s^{3} + 199 s\\right) $ & 144.704 & (-5.85410, 144.586) \\\\\n", "11 & $RRRTTTTRTT$ & $ \\left(13 s^{2} - 42,\\,-55 s^{3} + 199 s\\right) $ & 146.570 & (-24.0344, 144.586) \\\\\n", "12 & $RRTTRRTRT$ & $ \\left(-68 s^{2} + 247,\\,-21 s^{3} + 76 s\\right) $ & 162.687 & (153.026, 55.2268) \\\\\n", "13 & $RRTRTRRTT$ & $ \\left(-66 s^{2} + 239,\\,-27 s^{3} + 98 s\\right) $ & 164.109 & (147.790, 71.3418) \\\\\n", "14 & $RTRRTRTRRT$ & $ \\left(-57 s^{2} + 208,\\,-63 s^{3} + 229 s\\right) $ & 211.047 & (129.228, 166.856) \\\\\n", "15 & $RRRTTRTTRT$ & $ \\left(-87 s^{2} + 318,\\,-29 s^{3} + 105 s\\right) $ & 211.985 & (197.769, 76.3215) \\\\\n", "16 & $RRTTRTTTRRRT$ & $ \\left(-82 s^{2} + 297,\\,-79 s^{3} + 286 s\\right) $ & 277.395 & (183.679, 207.870) \\\\\n", "17 & $RRTRTTRTRT$ & $ \\left(-168 s^{2} + 609,\\,-53 s^{3} + 192 s\\right) $ & 401.859 & (376.830, 139.606) \\\\\n", "18 & $RTTRTRRRTTRT$ & $ \\left(-103 s^{2} + 374,\\,-135 s^{3} + 487 s\\right) $ & 422.378 & (231.658, 353.182) \\\\\n", "19 & $RTTTTTTRTRTT$ & $ \\left(-88 s^{2} + 319,\\,-149 s^{3} + 536 s\\right) $ & 435.359 & (197.387, 388.041) \\\\\n", "20 & $RRTRRTTTRRTT$ & $ \\left(-98 s^{2} + 356,\\,-158 s^{3} + 572 s\\right) $ & 470.627 & (220.567, 415.740) \\\\\n", "21 & $RRTTTRTTRTT$ & $ \\left(40 s^{2} - 145,\\,-209 s^{3} + 756 s\\right) $ & 556.471 & (-89.7214, 549.190) \\\\\n", "22 & $RTRTRTRTRRT$ & $ \\left(-155 s^{2} + 562,\\,-171 s^{3} + 619 s\\right) $ & 568.635 & (347.795, 449.872) \\\\\n", "23 & $RRRTTRTRTTRT$ & $ \\left(-150 s^{2} + 544,\\,-198 s^{3} + 716 s\\right) $ & 619.524 & (336.705, 520.038) \\\\\n", "24 & $RRTTTRTRRTRT$ & $ \\left(-158 s^{2} + 572,\\,-198 s^{3} + 716 s\\right) $ & 628.894 & (353.649, 520.038) \\\\\n", "25 & $RTTRTRTRTRT$ & $ \\left(-362 s^{2} + 1312,\\,-114 s^{3} + 412 s\\right) $ & 865.091 & (811.728, 299.131) \\\\\n", "26 & $RTTRRTRTTTRRT$ & $ \\left(-241 s^{2} + 876,\\,-277 s^{3} + 1003 s\\right) $ & 909.040 & (542.946, 729.083) \\\\\n", "27 & $RTRTRTRTTRT$ & $ \\left(-380 s^{2} + 1377,\\,-125 s^{3} + 452 s\\right) $ & 912.920 & (851.853, 328.283) \\\\\n", "28 & $RTRTTRTRTRRT$ & $ \\left(-253 s^{2} + 916,\\,-279 s^{3} + 1009 s\\right) $ & 926.224 & (566.363, 732.888) \\\\\n", "29 & $RTTRRTTTRRTRRT$ & $ \\left(-15 s^{2} + 56,\\,-375 s^{3} + 1357 s\\right) $ & 986.655 & (35.2705, 986.025) \\\\\n", "30 & $RTRTTRRTRRTRT$ & $ \\left(15 s^{2} - 52,\\,-395 s^{3} + 1429 s\\right) $ & 1038.64 & (-31.2705, 1038.17) \\\\\n", "31 & $RRTTTRTTRTRTT$ & $ \\left(-650 s^{2} + 2352,\\,-282 s^{3} + 1020 s\\right) $ & 1631.66 & (1453.72, 740.945) \\\\\n", "Found 0 mistakes in the formula.\n", " Inverse of Coset Rep Exact Vector Length of Trajectory Vector of Trajectory\n", "10 & $\\big(T^2(T^2R)^2\\big)^{-1}$ & $ \\left(-52 s^{2} + 183,\\,-3 s^{3} + 12 s\\right) $ & 111.521 & (111.138, 9.23305) \\\\\n", "16 & $\\big(TR^3T^3(TR^3)^2TR\\big)^{-1}$ & $ \\left(-62 s^{2} + 227,\\,-89 s^{3} + 326 s\\right) $ & 277.350 & (141.318, 238.647) \\\\\n", "17 & $\\big(T^2(T^2R)^2R^2\\big)^{-1}$ & $ \\left(-48 s^{2} + 174,\\,-34 s^{3} + 126 s\\right) $ & 142.196 & (107.666, 92.8855) \\\\\n", "18 & $\\big(T^2RT(RTR^2)^2\\big)^{-1}$ & $ \\left(-88 s^{2} + 319,\\,-75 s^{3} + 272 s\\right) $ & 279.518 & (197.387, 197.910) \\\\\n", "19 & $\\big(T^2RT(TR^3)^3\\big)^{-1}$ & $ \\left(-64 s^{2} + 234,\\,-54 s^{3} + 198 s\\right) $ & 205.478 & (145.554, 145.035) \\\\\n", "20 & $\\big(T(TR)^2R(RT)^2R^2\\big)^{-1}$ & $ \\left(-94 s^{2} + 341,\\,-81 s^{3} + 294 s\\right) $ & 300.613 & (211.095, 214.025) \\\\\n", "21 & $\\big(T^2RT^3R^3TR\\big)^{-1}$ & $ \\left(-109 s^{2} + 390,\\,-13 s^{3} + 49 s\\right) $ & 242.130 & (239.366, 36.4832) \\\\\n", "22 & $\\big(TRT^3(TR)^2R^2\\big)^{-1}$ & $ \\left(-93 s^{2} + 334,\\,-19 s^{3} + 71 s\\right) $ & 212.102 & (205.477, 52.5981) \\\\\n", "23 & $\\big(T(R^2TR)^4R^2T^2R^2\\big)^{-1}$ & $ \\left(-66 s^{2} + 239,\\,-89 s^{3} + 322 s\\right) $ & 276.716 & (147.790, 233.944) \\\\\n", "24 & $\\big((TR)^2RT^2R^3TR\\big)^{-1}$ & $ \\left(-83 s^{2} + 302,\\,-91 s^{3} + 331 s\\right) $ & 305.441 & (187.297, 241.275) \\\\\n", "25 & $\\big(T^2(T^2R^3)^2TR^2\\big)^{-1}$ & $ \\left(-159 s^{2} + 576,\\,-13 s^{3} + 47 s\\right) $ & 357.899 & (356.267, 34.1320) \\\\\n", "26 & $\\big(T^6R^3T^2R^2\\big)^{-1}$ & $ \\left(-116 s^{2} + 418,\\,-6 s^{3} + 22 s\\right) $ & 258.195 & (257.692, 16.1150) \\\\\n", "27 & $\\big(T^2(T^2R)^2TR^3\\big)^{-1}$ & $ \\left(-165 s^{2} + 592,\\,-11 s^{3} + 41 s\\right) $ & 365.237 & (363.976, 30.3278) \\\\\n", "28 & $\\big(TRT^2(T^2R)^2R^2\\big)^{-1}$ & $ \\left(-164 s^{2} + 590,\\,-34 s^{3} + 126 s\\right) $ & 375.042 & (363.358, 92.8855) \\\\\n", "29 & $\\big(T^3(TR)^2R^2T^2R^3\\big)^{-1}$ & $ \\left(-117 s^{2} + 424,\\,-85 s^{3} + 311 s\\right) $ & 347.229 & (262.310, 227.512) \\\\\n", "30 & $\\big(T^2R^2(TR^3T)^2R^3\\big)^{-1}$ & $ \\left(-143 s^{2} + 522,\\,-23 s^{3} + 83 s\\right) $ & 329.919 & (324.379, 60.2066) \\\\\n", "31 & $\\big(T(TR^3TR)^2RTR^2\\big)^{-1}$ & $ \\left(-272 s^{2} + 984,\\,-48 s^{3} + 174 s\\right) $ & 621.137 & (608.105, 126.569) \\\\\n", "Found 0 mistakes in the formula.\n" ] } ], "source": [ "run code_from_the_article.ipynb" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from flatsurf.geometry.polyhedra import *\n", "from flatsurf.geometry.surface_objects import SaddleConnection" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# The dodecagon is a 3d solid, surface is the boundary realized as a Euclidean cone surface, and to_3d is the map\n", "# from the surface to the 3d object.\n", "dodecahedron,dodecahedron_boundary,to_3d = platonic_dodecahedron()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# The surface dodecahedron_boundary is defined over a different field.\n", "# The following is the 2D vector space containing the vertices, which we use\n", "# to convert vectors defined in Q[s].\n", "V = VectorSpace(dodecahedron_boundary.base_ring(), 2)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Converts and RGB color triple to a hexidecimal string\n", "def triple_to_hex(t):\n", " ret=\"\"\n", " for i in range(3):\n", " val = ceil(t[i]*255).hex()\n", " if len(val)==2:\n", " ret += val\n", " else:\n", " ret += \"0\" + val\n", " return ret" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [], "source": [ "sc_coords=[]\n", "for i in range(31):\n", " if i in shortest_table:\n", " # Take the holonomy vector from the shortest table (Table 4 of paper)\n", " holonomy_vector = V(shortest_table[i][1])\n", " else:\n", " # Take the holonomy vector from the list of coset representative (Table 3)\n", " holonomy_vector = V(sadd_conn_total_sort[i][1])\n", " \n", " sc = SaddleConnection(dodecahedron_boundary,(0,0),holonomy_vector)\n", " assert sc.holonomy() == holonomy_vector, \"Error in \"+str(i)\n", " sc3d = to_3d(sc.trajectory())\n", " coordinates_and_color_list = []\n", " for i in range(len(sc3d)-1):\n", " x,y,z = sc3d[i]\n", " coordinates_and_color_list.append((x,y,z, triple_to_hex(hue(QQ(i)/len(sc3d)))))\n", " sc_coords.append(coordinates_and_color_list)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "f = open(\"saddle_connections_3d.js\", \"w\")\n", "f.write(\"var dodecahedron_vertices = [\")\n", "verts = dodecahedron.vertices()\n", "for i in range(20):\n", " x,y,z = verts[i]\n", " t = \"[\"+(\"%.5f\"%x)+\",\"+(\"%.5f\"%y)+\",\"+(\"%.5f\"%z)+\"]\"\n", " if i < 19:\n", " f.write(t + \",\")\n", " else:\n", " f.write(t)\n", "f.write(\"];\\n\")\n", "f.write(\"var sc_data = [\")\n", "for i in range(31):\n", " coordinates_and_color_list = sc_coords[i]\n", " f.write(\"[\")\n", " for j in range(len(coordinates_and_color_list)):\n", " x,y,z,color = coordinates_and_color_list[j]\n", " t = \"[\"+(\"%.5f\"%x)+\",\"+(\"%.5f\"%y)+\",\"+(\"%.5f\"%z)+\",0x\"+color+\"]\"\n", " if j < len(coordinates_and_color_list)-1:\n", " f.write(t + \",\")\n", " else:\n", " f.write(t)\n", " if i<31-1:\n", " f.write(\"],\")\n", " else:\n", " f.write(\"]\")\n", "f.write(\"];\\n\")\n", "f.close()" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.0", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }