多面体 » 多面体諸量再掲

多面体諸量再掲

多面体諸量

多面体を今までとは違った方法で作ってゆこうとして模索しています。
その製作に必要な諸量は手元にある資料からではなく
このブログから得ることにしています。
自分で作成しているのにまとまりがなく探すのに苦労することが多々あります。
そこで６桁に桁数を落としてリストとしてまとめてみました。

多面体諸量 稜寸は1として


 面積 体積 基本数 頂芯寸 稜芯寸 S面芯寸 M面芯寸 L面芯寸
01 [3,3,3] 1.73205 .117851 .577350 .612372 .353553 .204124 
02 [3,3,3,3] 3.46410 .471405 .707107 .707107 .500000 .408248 
03 [4,4,4] 6.00000 1.00000 .816497 .866025 .707107 .500000 
04 [3,3,3,3,3 8.66025 2.18169 .850651 .951057 .809017 .755761 
05 [3,4,3,4] 9.46410 2.35702 .866025 1.00000 .866025 .816497 .707107 
06 [3,6,6] 12.1244 2.71058 .904534 1.17260 1.06066 1.02062 .612372 
07 [3,3,3,3,4 19.8564 7.88948 .928191 1.34371 1.24722 1.21336 1.14261 
08 [3,4,4,4] 21.4641 8.71405 .933949 1.39897 1.30656 1.27427 1.20711 
09 [5,5,5] 20.6457 7.66312 .934172 1.40126 1.30902 1.11352 
10 [4,6,6] 26.7846 11.3137 .948683 1.58114 1.50000 1.41421 1.22474 
11 [3,5,3,5] 29.3060 13.8355 .951057 1.61803 1.53884 1.51152 1.37638 
12 [3,8,8] 32.4347 13.5997 .959683 1.77882 1.70711 1.68252 1.20711 
13 [3,3,3,3,5 55.2867 37.6166 .972733 2.15584 2.09705 2.07709 1.98092 
14 [3,4,5,4] 59.3060 41.6153 .974608 2.23295 2.17625 2.15702 2.11803 2.06457
15 [4,6,8] 61.7552 41.7990 .976451 2.31761 2.26303 2.20711 2.09077 1.91421
16 [5,6,6] 72.6073 55.2877 .979432 2.47802 2.42705 2.32744 2.26728 
17 [3,10,10] 100.991 85.0397 .985722 2.96945 2.92705 2.91278 2.48990 
18 [4,6,10] 174.292 206.803 .991317 3.80239 3.76938 3.73607 3.66854 3.44095


 仰角 S接合角 M接合角 L接合角 S面角 M面角 L面角 二面角1 二面角2
01 54.7356 60.0000 35.2644 SS 70.5288 
02 45.0000 45.0000 54.7356 SS 109.471 
03 35.2644 60.0000 45.0000 SS 90.0000 
04 31.7175 36.0000 69.0948 SS 138.190 
05 30.0000 35.2644 54.7356 70.5288 54.7356 SM 125.264 
06 25.2394 33.5573 73.2213 74.2068 35.2644 SM 109.471 MM 70.5288
07 21.8454 32.5940 49.6241 76.6173 66.3661 SS 153.235 SM 142.983
08 20.9410 32.3684 49.2105 77.2356 67.5000 SM 144.736 MM 135.000
09 20.9052 60.0000 58.2825 SS 116.565 
10 18.4349 48.1897 65.9052 70.5288 54.7356 SM 125.264 MM 109.471
11 18.0000 31.7175 58.2825 79.1877 63.4349 SM 142.623 
12 16.3249 31.3997 74.3001 80.2644 45.0000 SM 125.264 MM 90.0000
13 13.4106 30.9317 56.2732 82.0877 70.8422 SS 164.175 SM 152.930
14 12.9393 30.8657 46.5129 56.1085 82.3774 76.7175 71.5651 SM 159.095 ML 148.283
15 12.4589 46.3990 62.4877 71.1133 77.2356 67.5000 57.7644 SM 144.736 SL 135.000
16 11.6407 55.6906 62.1547 73.5278 69.0948 SM 142.623 MM 138.190
17 9.69372 30.4803 74.7598 84.3401 58.2825 SM 142.623 MM 116.565
18 7.55605 45.5041 60.8810 73.6149 82.3774 76.7175 65.9052 SM 159.095 SL 148.283

二面角3
15 ML 125.264
18 ML 142.623
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双対多面体諸量　稜芯寸はもとの多面体の稜芯寸とイコールとして


  双対面積 双対体積 稜芯寸 面芯寸 S頂芯寸 M頂芯寸 L頂芯寸
01 [3,3,3] 1.73205 .117851 .353553 .204124 .612372 
02 [3,3,3,3] 3.00000 .353553 .500000 .353553 .612372 
03 [4,4,4] 6.92820 1.33333 .707107 .577350 1.00000 
04 [3,3,3,3,3] 7.88597 1.80902 .809017 .688191 .866025 
05 [3,4,3,4] 9.54594 2.38649 .866025 .750000 .918559 1.06066 
06 [3,6,6] 17.9098 5.72756 1.06066 .959403 1.10227 1.83712 
07 [3,3,3,3,4] 19.2994 7.44740 1.24722 1.15766 1.28204 1.36141 
08 [3,4,4,4] 21.5135 8.75069 1.30656 1.22026 1.33967 1.41421 
09 [5,5,5] 22.6728 9.24181 1.30902 1.22285 1.53884 
10 [4,6,6] 30.1869 14.3189 1.50000 1.42302 1.59099 1.83712 
11 [3,5,3,5] 30.3381 14.8002 1.53884 1.46353 1.56665 1.72048 
12 [3,8,8] 42.6918 23.3137 1.70711 1.63828 1.73205 2.41421 
13 [3,3,3,3,5] 55.2805 37.5884 2.09705 2.03987 2.11721 2.22000 
14 [3,4,5,4] 59.7674 42.2554 2.17625 2.12099 2.19565 2.23607 2.29397
15 [4,6,8] 67.4248 49.6638 2.26303 2.20974 2.32038 2.44949 2.67542
16 [5,6,6] 75.5655 59.8764 2.42705 2.37713 2.53093 2.59808 
17 [3,10,10] 115.570 111.149 2.92705 2.88526 2.94139 3.44095 
18 [4,6,10] 183.196 228.179 3.76938 3.73665 3.80298 3.87298 4.12915


S稜寸 M稜寸 L稜寸 双対稜寸 S 双対稜寸 M 双対稜寸 L
01 .500000 SS 1.00000 
02 .353553 SS .707107 
03 .707107 SS 1.41421 
04 .309017 SS .618034 
05 .306186 .612372 SM .918559 
06 .300000 1.50000 SM 1.80000 MM 3.00000 
07 .296733 .545776 SS .593465 SM .842509 
08 .295990 .541196 SM .837186 MM 1.08239 
09 .809017 SS 1.61803 
10 .530330 1.06066 SM 1.59099 MM 2.12132 
11 .293893 .769421 SM 1.06331 
12 .292893 1.70711 SM 2.00000 MM 3.41421 
13 .291450 .728538 SS .582900 SM 1.01999 
14 .291249 .513743 .725417 SM .804992 ML 1.23916 
15 .512670 .937379 1.42707 SM 1.45005 SL 1.93974 ML 2.36445
16 .717645 .927051 SM 1.64470 MM 1.85410 
17 .290089 1.80902 SM 2.09911 MM 3.61803 
18 .504458 .889829 1.68572 SM 1.39429 SL 2.19017 ML 2.57555


  二面角 S仰角  M仰角 L仰角 Sかど角/2 Mかど角/2 Lかど角/2 SML接合角
01 70.5288 54.7356 30.0000 60
02 90.0000 35.2644 45.0000 60
03 109.471 45.0000 30.0000 45
04 116.565 20.9052 54.0000 60
05 120.000 19.4712 35.2644 54.7356 35.2644 60  45
06 129.521 15.7932 54.7356 56.4427 16.7787 60  30
07 136.309 13.3827 23.6339 57.4060 40.3759 60  45
08 138.118 12.7644 22.5000 57.6316 40.7895 60  45
09 138.190 31.7175 30.0000 36 
10 143.130 19.4712 35.2644 41.8103 24.0948 45  30
11 144.000 10.8123 26.5651 58.2825 31.7175 60  36
12 147.350 9.73561 45.0000 58.6003 15.6999 60  22.5
13 153.179 7.91232 19.1578 59.0683 33.7268 60  36
14 154.121 7.62263 13.2825 18.4349 59.1343 43.4871 33.8915 60  45  36
15 155.082 12.7644 22.5000 32.2356 43.6010 27.5123 18.8867 45  30  22.5
16 156.719 16.4722 20.9052 34.3094 27.8453 36  30
17 160.613 5.65989 31.7175 59.5197 15.2402 60  18 
18 164.888 7.62263 13.2825 24.0948 44.4959 29.1190 16.3851 45  30  18

2015年7月26日

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