[math-fun] The 394 primitive Heron tetrahedra with diameter<=16384

Generated by Warren D. Smith & Fred Lunnon, December 2011. "Heron" tetrahedra = all sides, face-areas, and volume = integers. "Primitive" = gcd(sidelengths)=1. [We proved the theorem that volume is always divisible by 168 but this is not true for any divisor greater than 168.] [A much larger list of Heron tetrahedra, up to diameter 70000, was constructed by Sascha Kurz but a bug in his program caused a small fraction of omissions -- 4%?.] Census: A=[diameter] B=[#primtets with diam<=A] C=[exponent in power law estimated from this & preceding count] A B C -------------------------------- 64 0 128 1 256 4 2.000 512 9 1.170 1024 27 1.585 2048 62 1.199 4096 129 1.057 8192 218 0.757 16384 394 0.854 [s01, s02, s12, s03, s13, s23] ------------------------------------------------- [117, 84, 51, 80, 53, 52], [160, 153, 25, 120, 56, 39], [203, 195, 148, 148, 195, 203], [225, 200, 65, 87, 156, 119], [318, 221, 203, 221, 175, 42], [319, 318, 175, 221, 210, 175], [319, 318, 175, 221, 252, 203], [429, 300, 261, 176, 275, 140], [468, 340, 232, 297, 225, 65], [595, 429, 208, 325, 276, 116], [595, 507, 116, 325, 276, 208], [595, 555, 100, 429, 208, 204], [612, 480, 156, 455, 319, 185], [671, 663, 580, 225, 544, 444], [680, 672, 104, 615, 185, 153], [680, 680, 208, 615, 185, 185], [697, 680, 153, 672, 185, 104], [697, 697, 306, 672, 185, 185], [741, 477, 420, 475, 304, 340], [780, 765, 219, 715, 221, 148], [884, 880, 84, 715, 205, 187], [884, 884, 168, 715, 205, 205], [888, 875, 533, 533, 875, 888], [925, 765, 520, 756, 533, 117], [935, 928, 345, 900, 145, 260], [990, 795, 663, 598, 436, 427], [990, 901, 793, 793, 901, 308], [1040, 925, 925, 533, 533, 756], [1073, 975, 448, 495, 952, 840], [1073, 1071, 520, 975, 448, 264], [1073, 1073, 896, 495, 952, 952], [1073, 1073, 896, 1071, 520, 520], [1073, 1073, 990, 448, 975, 975], [1073, 1073, 990, 896, 1073, 1073], [1105, 1073, 264, 952, 561, 495], [1105, 1073, 264, 975, 520, 448], [1105, 1105, 528, 952, 561, 561], [1105, 1105, 528, 975, 520, 520], [1113, 975, 348, 625, 572, 400], [1160, 1125, 595, 820, 660, 793], [1190, 1056, 218, 435, 925, 819], [1248, 1155, 765, 1040, 1040, 445], [1276, 924, 880, 765, 533, 555], [1344, 697, 697, 680, 680, 153], [1344, 697, 697, 697, 697, 306], [1358, 1221, 445, 654, 1040, 765], [1360, 1092, 548, 975, 865, 663], [1450, 1184, 1066, 825, 1025, 697], [1480, 1275, 1189, 1248, 1160, 261], [1480, 1275, 1189, 1275, 1189, 522], [1500, 1184, 572, 825, 975, 697], [1512, 925, 925, 765, 765, 520], [1512, 925, 925, 925, 925, 1040], [1624, 1575, 455, 1560, 1184, 825], [1769, 1480, 969, 1066, 1197, 570], [1804, 1479, 1183, 1183, 1479, 1804], [1885, 1258, 1001, 867, 1192, 425], [1904, 1105, 1105, 1073, 1073, 264], [1904, 1105, 1105, 1105, 1105, 528], [1904, 1813, 1365, 1300, 1332, 957], [1950, 1105, 1105, 1073, 1073, 264], [1950, 1105, 1105, 1105, 1105, 528], [2067, 2040, 333, 1732, 725, 644], [2067, 2067, 666, 1732, 725, 725], [2109, 1435, 884, 1189, 1300, 624], [2165, 2067, 644, 2040, 725, 333], [2165, 2165, 1288, 2040, 725, 725], [2167, 1590, 1105, 1105, 1590, 875], [2167, 1980, 1595, 1590, 1105, 1050], [2175, 1820, 425, 1776, 1599, 1276], [2257, 2023, 900, 1820, 969, 273], [2320, 1560, 776, 1233, 1105, 399], [2380, 2079, 455, 1716, 1184, 825], [2384, 1845, 1547, 1020, 1628, 1635], [2431, 2296, 2175, 1479, 1700, 2375], [2431, 2296, 2175, 1540, 1881, 1092], [2431, 2296, 2175, 1700, 1479, 1044], [2431, 2296, 2175, 2175, 2296, 2431], [2431, 2375, 1044, 2175, 2296, 1700], [2431, 2375, 1044, 2296, 2175, 1479], [2652, 2640, 252, 533, 2275, 2261], [2652, 2652, 504, 533, 2275, 2275], [2664, 2600, 1504, 1025, 2431, 2175], [2664, 2600, 1504, 1599, 2175, 2431], [2664, 2625, 1599, 656, 2600, 2431], [2664, 2625, 1599, 1025, 2431, 2600], [2664, 2625, 1599, 2431, 1025, 656], [2664, 2625, 1599, 2600, 656, 1025], [2665, 2431, 1092, 1540, 2175, 1881], [2665, 2665, 2184, 1540, 2175, 2175], [2720, 2109, 1859, 884, 1908, 1435], [2720, 2405, 1435, 884, 1908, 1859], [2805, 2340, 861, 1360, 1547, 1036], [2873, 2748, 1825, 1825, 2748, 2873], [2912, 2379, 715, 1768, 1320, 715], [2928, 2500, 1508, 2275, 1507, 1275], [2960, 2665, 425, 1628, 1924, 1647], [3080, 2665, 2665, 2431, 2431, 1092], [3080, 2665, 2665, 2665, 2665, 2184], [3111, 2639, 2180, 2180, 2639, 3111], [3179, 2640, 1771, 1476, 2275, 1428], [3211, 2625, 2378, 2028, 2275, 1353], [3219, 3179, 700, 3060, 507, 493], [3276, 2860, 592, 1485, 1989, 1595], [3277, 2652, 1925, 2052, 2555, 1680], [3444, 3360, 756, 3179, 925, 533], [3444, 3444, 1512, 3179, 925, 925], [3485, 2652, 2261, 2640, 2275, 252], [3485, 2779, 1044, 2405, 1140, 816], [3485, 3179, 1428, 2640, 2275, 1771], [3485, 3444, 533, 3360, 925, 756], [3485, 3485, 1066, 3360, 925, 925], [3485, 3485, 2856, 2640, 2275, 2275], [3542, 3179, 3179, 2275, 2275, 1476], [3762, 2431, 2431, 2175, 2175, 2296], [3774, 3731, 475, 3650, 416, 549], [3825, 2639, 1424, 2535, 2460, 1924], [3825, 3770, 2555, 1914, 2373, 3248], [3825, 3780, 585, 1628, 2665, 2600], [3825, 3825, 1170, 1628, 2665, 2665], [3850, 3277, 3277, 2555, 2555, 2052], [3944, 3900, 740, 3825, 1105, 1095], [3965, 3875, 840, 1364, 3723, 3627], [3965, 3965, 1680, 1364, 3723, 3723], [3965, 3965, 2728, 840, 3875, 3875], [3965, 3965, 2728, 1680, 3965, 3965], [4000, 3649, 2847, 3460, 2340, 3549], [4080, 2165, 2165, 2067, 2067, 644], [4080, 2165, 2165, 2165, 2165, 1288], [4104, 3277, 3277, 2652, 2652, 1925], [4104, 3277, 3277, 3277, 3277, 3850], [4147, 4134, 2275, 2958, 2639, 3276], [4181, 4100, 819, 3740, 1869, 1680], [4181, 4181, 1638, 3740, 1869, 1869], [4200, 2793, 2583, 2015, 2465, 2260], [4200, 4147, 493, 3900, 540, 533], [4225, 4199, 468, 4180, 615, 399], [4225, 4225, 936, 4180, 615, 615], [4256, 3477, 1045, 3400, 1160, 533], [4264, 2405, 1989, 2072, 2400, 1221], [4264, 2405, 1989, 2400, 2072, 155], [4344, 3885, 3315, 3392, 3848, 1235], [4453, 3828, 2275, 2772, 3485, 2640], [4514, 3731, 1275, 3640, 1938, 819], [4522, 3485, 3485, 2275, 2275, 2640], [4550, 4453, 4453, 3485, 3485, 2772], [4753, 4100, 3757, 3757, 4100, 1737], [4784, 4641, 1375, 2484, 2668, 2535], [5100, 2929, 2821, 2910, 2670, 221], [5232, 4879, 4225, 1768, 3880, 4505], [5249, 4628, 1173, 4250, 1449, 690], [5280, 3485, 3485, 2652, 2652, 2261], [5280, 3485, 3485, 3179, 3179, 1428], [5280, 3485, 3485, 3485, 3485, 2856], [5280, 3485, 3485, 3485, 3485, 4522], [5365, 4760, 2475, 3952, 2805, 1320], [5365, 5365, 4950, 3952, 2805, 2805], [5423, 4305, 1976, 3145, 2652, 1300], [5432, 4539, 2405, 4080, 4264, 1989], [5491, 4715, 2340, 3059, 4560, 3588], [5500, 5355, 845, 5040, 5084, 5355], [5512, 5215, 1887, 1887, 5215, 5512], [5525, 4715, 2880, 4301, 3468, 1932], [5525, 4884, 1603, 3432, 2197, 1980], [5544, 4453, 4453, 3828, 3828, 2275], [5544, 4453, 4453, 4453, 4453, 4550], [5577, 4305, 2196, 3145, 2848, 1300], [5577, 5423, 220, 3145, 2848, 2652], [5760, 5525, 5525, 3468, 3468, 4301], [5920, 4875, 1397, 3485, 4125, 2860], [5936, 5100, 3916, 3731, 5075, 2405], [6005, 4947, 3404, 4653, 3796, 1680], [6118, 4575, 2873, 2873, 4575, 3368], [6118, 5491, 5491, 4715, 4715, 2340], [6120, 5551, 1199, 3825, 3825, 2824], [6292, 6273, 4375, 3828, 4400, 2775], [6327, 5423, 1300, 4305, 2652, 1976], [6369, 5576, 4225, 4225, 5576, 6111], [6448, 6095, 1073, 3731, 2925, 2788], [6516, 4920, 2436, 3325, 4901, 2813], [6625, 6409, 4116, 3116, 6409, 6625], [6699, 5100, 2691, 4172, 3325, 976], [6699, 6042, 1455, 3325, 5404, 4199], [6720, 3485, 3485, 3444, 3444, 533], [6720, 3485, 3485, 3485, 3485, 1066], [6808, 6005, 6005, 3796, 3796, 4653], [6851, 5565, 2000, 4875, 2860, 1740], [7011, 6699, 5100, 4579, 3800, 4628], [7059, 5330, 2639, 4845, 2784, 1073], [7085, 7076, 357, 6960, 1325, 1276], [7085, 7085, 714, 6960, 1325, 1325], [7105, 5512, 1887, 5180, 3465, 1788], [7215, 5577, 2652, 5423, 2848, 220], [7293, 6565, 4732, 3480, 5859, 4165], [7293, 6868, 4165, 3480, 5859, 4732], [7325, 7072, 1853, 6328, 1347, 1160], [7395, 7011, 2352, 2405, 5740, 5236], [7395, 7395, 4704, 2405, 5740, 5740], [7400, 6273, 2783, 6048, 4264, 1665], [7400, 6273, 5537, 6048, 4264, 1665], [7480, 4181, 4181, 4100, 4100, 819], [7480, 4181, 4181, 4181, 4181, 1638], [7480, 5624, 5200, 4427, 4053, 2603], [7585, 7400, 1665, 4264, 6273, 6048], [7585, 7585, 3330, 4264, 6273, 6273], [7667, 6396, 4879, 5220, 3185, 3696], [7667, 6396, 4879, 6396, 4879, 7392], [7735, 6327, 2848, 4305, 4900, 2652], [7735, 6327, 2848, 5423, 2924, 1300], [7735, 7215, 1300, 5423, 2924, 2848], [7888, 4732, 3620, 4575, 3487, 857], [7950, 7469, 5525, 6783, 3393, 2548], [8075, 7917, 4756, 7605, 2000, 5772], [8120, 7800, 5920, 4125, 6851, 7875], [8120, 7800, 5920, 6851, 4125, 2275], [8120, 7875, 2275, 5920, 7800, 6851], [8160, 7215, 4305, 2848, 5504, 5423], [8160, 7700, 1300, 5577, 6327, 5423], [8250, 7626, 7560, 6401, 6601, 7735], [8288, 6396, 5500, 5775, 4879, 6771], [8360, 4225, 4225, 4199, 4199, 468], [8360, 4225, 4225, 4225, 4225, 936], [8385, 8364, 4407, 6880, 2623, 2516], [8400, 7395, 5085, 3920, 4928, 3875], [8428, 8160, 1300, 4305, 7735, 7215], [8428, 8160, 1300, 7735, 4305, 3145], [8432, 6380, 3404, 3825, 4879, 2665], [8484, 6625, 6409, 6409, 6625, 8484], [8528, 7585, 7585, 7400, 7400, 1665], [8528, 7585, 7585, 7585, 7585, 3330], [8602, 5525, 5525, 4715, 4715, 2880], [8602, 5525, 5525, 5525, 5525, 5760], [8645, 7056, 3451, 5820, 3965, 4764], [8721, 8424, 3375, 1417, 8140, 7735], [8721, 8424, 3375, 7412, 7735, 8140], [8800, 7216, 6864, 3625, 6825, 4329], [8840, 8535, 7625, 5952, 6536, 3927], [8925, 7708, 2533, 7520, 1885, 1692], [8925, 7708, 2533, 7708, 2533, 3384], [9020, 7395, 5915, 6864, 5852, 861], [9020, 8925, 2405, 8736, 1564, 1827], [9020, 8925, 2405, 8925, 2405, 3654], [9061, 7395, 5236, 7011, 5740, 2352], [9061, 8925, 1564, 8736, 2405, 1827], [9061, 9020, 861, 6864, 5915, 5852], [9061, 9061, 1722, 6864, 5915, 5915], [9061, 9061, 3128, 8736, 2405, 2405], [9295, 8215, 5916, 4785, 7216, 4732], [9306, 6005, 6005, 4947, 4947, 3404], [9306, 6005, 6005, 6005, 6005, 6808], [9367, 8800, 4329, 7216, 6825, 6864], [9425, 7599, 2464, 7215, 4160, 3936], [9435, 8352, 4389, 6740, 5075, 2548], [9435, 9435, 8778, 6740, 5075, 5075], [9471, 7800, 2529, 5920, 4321, 4040], [9605, 9228, 6253, 7800, 5605, 2772], [9646, 9605, 2829, 6500, 4554, 5865], [9673, 8840, 3927, 5952, 7625, 6536], [9673, 9673, 7854, 5952, 7625, 7625], [9700, 8584, 4836, 8125, 2325, 3069], [9773, 9435, 2548, 8352, 5075, 4389], [9773, 9773, 5096, 8352, 5075, 5075], [9835, 9074, 4125, 5920, 6165, 3570], [9840, 8976, 4032, 3145, 7735, 6601], [9840, 9840, 8064, 3145, 7735, 7735], [9881, 8938, 3681, 4920, 8569, 7462], [9881, 9881, 9840, 3681, 8938, 8938], [9997, 9605, 2772, 7800, 6253, 5605], [9997, 9997, 5544, 7800, 6253, 6253], [10324, 9840, 3124, 6771, 5525, 4557], [10324, 10324, 6248, 6771, 5525, 5525], [10400, 7656, 3416, 7025, 3825, 689], [10441, 6409, 5250, 5250, 6409, 1691], [10455, 9052, 4255, 8784, 2409, 4732], [10472, 9061, 9061, 5740, 5740, 7011], [10624, 8160, 2848, 5577, 7735, 6327], [10624, 8160, 2848, 7735, 5577, 3145], [10647, 7735, 5278, 6327, 7650, 2848], [10665, 8432, 2665, 6380, 4879, 3404], [10693, 8772, 2465, 7120, 5307, 4060], [10736, 10275, 2509, 9724, 3300, 1099], [10920, 9090, 2670, 9061, 2405, 1015], [10959, 10400, 689, 7656, 3825, 3416], [11165, 9860, 2523, 9724, 4059, 1632], [11210, 9605, 9605, 6253, 6253, 9228], [11232, 10089, 4329, 6136, 8120, 5015], [11275, 10136, 8619, 8619, 10136, 11275], [11285, 10324, 4557, 9840, 5525, 3124], [11285, 11285, 9114, 9840, 5525, 5525], [11375, 9280, 2385, 6832, 6545, 5168], [11655, 7820, 6929, 7728, 6825, 1196], [11655, 7820, 6929, 7820, 6929, 2392], [11660, 10812, 5512, 9945, 5215, 1887], [11687, 10545, 5740, 9945, 5512, 1740], [11687, 10812, 5215, 9945, 5512, 1887], [11687, 11660, 1887, 9945, 5512, 5215], [11687, 11660, 1887, 10812, 5215, 5512], [11700, 8316, 4176, 7735, 4225, 3199], [11704, 9020, 9020, 5915, 5915, 7395], [11713, 11615, 1512, 10488, 5215, 4991], [11713, 11713, 3024, 10488, 5215, 5215], [11737, 10032, 7975, 9828, 4625, 3900], [11832, 11165, 1885, 5460, 6732, 6475], [11849, 9840, 6601, 8976, 7735, 4032], [11904, 9673, 9673, 8840, 8840, 3927], [11904, 9673, 9673, 9673, 9673, 7854], [11951, 11440, 2415, 9028, 4329, 3468], [11951, 11737, 3900, 7975, 9828, 10032], [12096, 7400, 7400, 6273, 6273, 2783], [12096, 7400, 7400, 6273, 6273, 5537], [12155, 10373, 6336, 6035, 8364, 5460], [12325, 11685, 3920, 10659, 6188, 4788], [12325, 12325, 7840, 10659, 6188, 6188], [12444, 11895, 10431, 10556, 8720, 2431], [12528, 10731, 2091, 8372, 5780, 4403], [12528, 12441, 615, 12100, 1508, 1067], [12672, 12155, 12155, 8364, 8364, 6035], [12749, 12675, 4144, 11281, 3900, 3604], [12844, 11895, 2431, 11305, 2337, 1160], [12844, 12444, 1160, 11305, 2337, 2431], [13072, 8840, 8840, 7625, 7625, 8535], [13108, 12155, 1533, 7700, 10608, 9405], [13140, 10585, 6643, 4524, 10176, 7667], [13175, 11895, 8720, 10431, 10556, 12444], [13175, 12444, 2431, 8720, 11895, 10556], [13175, 12444, 2431, 10556, 10431, 8720], [13202, 11849, 11849, 7735, 7735, 8976], [13243, 10140, 9715, 10032, 8645, 1476], [13243, 11600, 11067, 10032, 8645, 5824], [13299, 12915, 4080, 10075, 3596, 4972], [13325, 10373, 8364, 8998, 6307, 3179], [13325, 12155, 5460, 10373, 8364, 6336], [13325, 13243, 1476, 8645, 10140, 10032], [13325, 13325, 2952, 8645, 10140, 10140], [13325, 13325, 10920, 10373, 8364, 8364], [13481, 11951, 3468, 11440, 4329, 2415], [13585, 10615, 3300, 6519, 8092, 5408], [13585, 12597, 4028, 11088, 5423, 4875], [13728, 9061, 9061, 9020, 9020, 861], [13728, 9061, 9061, 9061, 9061, 1722], [13775, 11687, 8700, 10127, 11248, 6500], [13804, 13260, 10064, 7119, 9065, 9879], [13804, 13520, 1012, 13169, 873, 689], [13920, 7085, 7085, 7076, 7076, 357], [13920, 7085, 7085, 7085, 7085, 714], [13923, 13524, 5397, 11492, 5525, 4240], [13949, 13760, 7293, 12376, 6435, 3432], [13949, 13949, 12870, 13760, 7293, 7293], [13965, 12325, 4972, 3955, 10472, 8580], [14022, 9061, 9061, 7395, 7395, 5236], [14022, 9061, 9061, 9061, 9061, 10472], [14036, 8415, 5863, 6936, 7420, 1887], [14162, 11713, 2595, 2595, 11713, 9220], [14229, 12259, 9100, 10005, 5712, 7084], [14229, 12259, 9100, 12259, 9100, 14168], [14300, 14212, 1584, 13949, 2091, 1365], [14300, 14300, 3168, 13949, 2091, 2091], [14365, 14300, 1365, 14212, 2091, 1584], [14365, 14365, 2730, 14212, 2091, 2091], [14469, 14450, 4541, 761, 14450, 14469], [14637, 10933, 10100, 10100, 10933, 14637], [14664, 11985, 2961, 10360, 9568, 6929], [14703, 13472, 1295, 1972, 12905, 11700], [14820, 10324, 4624, 10101, 6201, 3625], [14861, 9709, 6552, 8723, 6600, 1632], [14875, 13200, 2725, 12852, 4403, 2028], [15080, 14820, 500, 13621, 1557, 1309], [15140, 10556, 9456, 7175, 10485, 6069], [15159, 10441, 7000, 7000, 10441, 6409], [15170, 10175, 7215, 7232, 9282, 3393], [15184, 14841, 1225, 14412, 980, 735], [15400, 13108, 13108, 12155, 12155, 1533], [15540, 12852, 8736, 11315, 9061, 2405], [15555, 14948, 2827, 14820, 4725, 1952], [15600, 9997, 9997, 9605, 9605, 2772], [15600, 9997, 9997, 9997, 9997, 5544], [15677, 15555, 1952, 4725, 14948, 14820], [15677, 15677, 3904, 4725, 14948, 14948], [15677, 15677, 9450, 1952, 15555, 15555], [15677, 15677, 9450, 3904, 15677, 15677], [15725, 15540, 2405, 12852, 9061, 8736], [15725, 15725, 4810, 12852, 9061, 9061], [15840, 14796, 1332, 7975, 7975, 6929], [15900, 15587, 1403, 15312, 4284, 2915], [16031, 15600, 799, 12144, 10465, 9792], [16095, 15776, 2465, 15300, 5865, 4420], [16133, 13108, 9405, 10220, 12483, 8208], [16133, 13108, 9405, 10608, 12155, 7700], [16165, 15900, 2915, 4284, 15587, 15312], [16165, 16165, 5830, 4284, 15587, 15587], [16165, 16165, 8568, 2915, 15900, 15900], [16165, 16165, 8568, 5830, 16165, 16165], [16192, 14645, 1995, 10400, 10400, 8885], [16211, 15725, 1776, 13975, 7740, 8484], end