birectified icosaxennon,
Gosset polytope 07,1,1
wrt. reday
wrt. barn
- general polytopal classes:
- Wythoffian polyxenna Coxeter-Elte-Gosset polytopes
- analogs:
- birectified hypercube brCn
links
| Acronym | brade |
| Name |
birectified dekeract, birectified icosaxennon, Gosset polytope 07,1,1 |
| Circumradius | 2 |
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Inradius wrt. reday | 4/sqrt(5) = 1.788854 |
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Inradius wrt. barn | 1/sqrt(2) = 0.707107 |
| Coordinates | (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0) & all permutations, all changes of sign |
| Face vector | 11520, 184320, 552960, 875520, 916608, 653184, 310560, 93120, 15540, 1044 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
o3o3o3o3o3o3o3x3o4o o3o3o3o3o3o3o3o3o4o | 11520 | 32 | 112 32 | 224 112 8 | 280 224 28 | 224 280 56 | 112 224 70 | 32 112 56 | 4 32 28 | 4 8 --------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+-------- . . . . . . . x . . | 2 | 184320 | 7 2 | 21 14 1 | 35 42 7 | 35 70 21 | 21 70 35 | 7 42 35 | 1 14 21 | 2 7 --------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+-------- . . . . . . o3x . . | 3 | 3 | 430080 * | 6 2 0 | 15 12 1 | 20 30 6 | 15 40 15 | 6 30 20 | 1 12 15 | 2 6 . . . . . . . x3o . | 3 | 3 | * 122880 | 0 7 1 | 0 21 7 | 0 35 21 | 0 35 35 | 0 21 35 | 0 7 21 | 1 7 --------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+-------- . . . . . o3o3x . . ♦ 4 | 6 | 4 0 | 645120 * * | 5 2 0 | 10 10 1 | 10 20 5 | 5 20 10 | 1 10 10 | 2 5 . . . . . . o3x3o . ♦ 6 | 12 | 4 4 | * 215040 * | 0 6 1 | 0 15 6 | 0 20 15 | 0 15 20 | 0 6 15 | 1 6 . . . . . . . x3o4o ♦ 6 | 12 | 0 8 | * * 15360 ♦ 0 0 7 | 0 0 21 | 0 0 35 | 0 0 35 | 0 0 21 | 0 7 --------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+-------- . . . . o3o3o3x . . ♦ 5 | 10 | 10 0 | 5 0 0 | 645120 * * | 4 2 0 | 6 8 1 | 4 12 4 | 1 8 6 | 2 4 . . . . . o3o3x3o . ♦ 10 | 30 | 20 10 | 5 5 0 | * 258048 * | 0 5 1 | 0 10 5 | 0 10 10 | 0 5 10 | 1 5 . . . . . . o3x3o4o ♦ 24 | 96 | 32 64 | 0 16 8 | * * 13440 ♦ 0 0 6 | 0 0 15 | 0 0 20 | 0 0 15 | 0 6 --------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+-------- . . . o3o3o3o3x . . ♦ 6 | 15 | 20 0 | 15 0 0 | 6 0 0 | 430080 * * | 3 2 0 | 3 6 1 | 1 6 3 | 2 3 . . . . o3o3o3x3o . ♦ 15 | 60 | 60 20 | 30 15 0 | 6 6 0 | * 215040 * | 0 4 1 | 0 6 4 | 0 4 6 | 1 4 . . . . . o3o3x3o4o ♦ 80 | 480 | 320 320 | 80 160 40 | 0 32 10 | * * 8064 ♦ 0 0 5 | 0 0 10 | 0 0 10 | 0 5 --------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+-------- . . o3o3o3o3o3x . . ♦ 7 | 21 | 35 0 | 35 0 0 | 21 0 0 | 7 0 0 | 184320 * * | 2 2 0 | 1 4 1 | 2 2 . . . o3o3o3o3x3o . ♦ 21 | 105 | 140 35 | 105 35 0 | 42 21 0 | 7 7 0 | * 122880 * | 0 3 1 | 0 3 3 | 1 3 . . . . o3o3o3x3o4o ♦ 240 | 1920 | 1920 1280 | 960 960 160 | 192 384 60 | 0 64 12 | * * 3360 ♦ 0 0 4 | 0 0 6 | 0 4 --------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+-------- . o3o3o3o3o3o3x . . ♦ 8 | 28 | 56 0 | 70 0 0 | 56 0 0 | 28 0 0 | 8 0 0 | 46080 * * | 1 2 0 | 2 1 . . o3o3o3o3o3x3o . ♦ 28 | 168 | 280 56 | 280 70 0 | 168 56 0 | 56 28 0 | 8 8 0 | * 46080 * | 0 2 1 | 1 2 . . . o3o3o3o3x3o4o ♦ 672 | 6720 | 8960 4480 | 6720 4480 560 | 2688 2688 280 | 448 896 84 | 0 128 14 | * * 960 | 0 0 3 | 0 3 --------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+-------- o3o3o3o3o3o3o3x . . ♦ 9 | 36 | 84 0 | 126 0 0 | 126 0 0 | 84 0 0 | 36 0 0 | 9 0 0 | 5120 * * | 2 0 . o3o3o3o3o3o3x3o . ♦ 36 | 252 | 504 84 | 630 126 0 | 504 126 0 | 252 84 0 | 72 36 0 | 9 9 0 | * 10240 * | 1 1 . . o3o3o3o3o3x3o4o ♦ 1792 | 21504 | 35840 14336 | 35840 17920 1792 | 21504 14336 1120 | 7168 7168 448 | 1024 2048 112 | 0 256 16 | * * 180 | 0 2 --------------------+-------+--------+---------------+---------------------+---------------------+--------------------+--------------------+-----------------+----------------+-------- o3o3o3o3o3o3o3x3o . ♦ 45 | 360 | 840 120 | 1260 210 0 | 1260 252 0 | 840 210 0 | 360 120 0 | 90 45 0 | 10 10 0 | 1024 * . o3o3o3o3o3o3x3o4o ♦ 4608 | 64512 | 129024 43008 | 161280 64512 5376 | 129024 64512 4032 | 64512 43008 2016 | 18432 18432 672 | 2304 4608 144 | 0 512 18 | * 20
o3x3o *b3o3o3o3o3o3o3o o3o3o *b3o3o3o3o3o3o3o | 11520 | 32 | 16 16 112 | 8 56 56 224 | 28 112 112 280 | 56 140 140 224 | 70 112 112 112 | 56 56 56 32 | 28 16 16 4 | 8 2 2 -----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+----------- . x . . . . . . . . | 2 | 184320 | 1 1 7 | 1 7 7 21 | 7 21 21 35 | 21 35 35 35 | 35 35 35 21 | 35 21 21 7 | 21 7 7 1 | 7 1 1 -----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+----------- o3x . . . . . . . . | 3 | 3 | 61440 * * | 1 7 0 0 | 7 21 0 0 | 21 35 0 0 | 35 35 0 0 | 35 21 0 0 | 21 7 0 0 | 7 1 0 . x3o . . . . . . . | 3 | 3 | * 61440 * | 1 0 7 0 | 7 0 21 0 | 21 0 35 0 | 35 0 35 0 | 35 0 21 0 | 21 0 7 0 | 7 0 1 . x . *b3o . . . . . . | 3 | 3 | * * 430080 | 0 1 1 6 | 1 6 6 15 | 6 15 15 20 | 15 20 20 15 | 20 15 15 6 | 15 6 6 1 | 6 1 1 -----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+----------- o3x3o . . . . . . . ♦ 6 | 12 | 4 4 0 | 15360 * * * ♦ 7 0 0 0 | 21 0 0 0 | 35 0 0 0 | 35 0 0 0 | 21 0 0 0 | 7 0 0 o3x . *b3o . . . . . . ♦ 6 | 12 | 4 0 4 | * 107520 * * | 1 6 0 0 | 6 15 0 0 | 15 20 0 0 | 20 15 0 0 | 15 6 0 0 | 6 1 0 . x3o *b3o . . . . . . ♦ 6 | 12 | 0 4 4 | * * 107520 * | 1 0 6 0 | 6 0 15 0 | 15 0 20 0 | 20 0 15 0 | 15 0 6 0 | 6 0 1 . x . *b3o3o . . . . . ♦ 4 | 6 | 0 0 4 | * * * 645120 | 0 1 1 5 | 1 5 5 10 | 5 10 10 10 | 10 10 10 5 | 10 5 5 1 | 5 1 1 -----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+----------- o3x3o *b3o . . . . . . ♦ 24 | 96 | 32 32 32 | 8 8 8 0 | 13440 * * * ♦ 6 0 0 0 | 15 0 0 0 | 20 0 0 0 | 15 0 0 0 | 6 0 0 o3x . *b3o3o . . . . . ♦ 10 | 30 | 10 0 20 | 0 5 0 5 | * 129024 * * | 1 5 0 0 | 5 10 0 0 | 10 10 0 0 | 10 5 0 0 | 5 1 0 . x3o *b3o3o . . . . . ♦ 10 | 30 | 0 10 20 | 0 0 5 5 | * * 129024 * | 1 0 5 0 | 5 0 10 0 | 10 0 10 0 | 10 0 5 0 | 5 0 1 . x . *b3o3o3o . . . . ♦ 5 | 10 | 0 0 10 | 0 0 0 5 | * * * 645120 | 0 1 1 4 | 1 4 4 6 | 4 6 6 4 | 6 4 4 1 | 4 1 1 -----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+----------- o3x3o *b3o3o . . . . . ♦ 80 | 480 | 160 160 320 | 40 80 80 80 | 10 16 16 0 | 8064 * * * ♦ 5 0 0 0 | 10 0 0 0 | 10 0 0 0 | 5 0 0 o3x . *b3o3o3o . . . . ♦ 15 | 60 | 20 0 60 | 0 15 0 30 | 0 6 0 6 | * 107520 * * | 1 4 0 0 | 4 6 0 0 | 6 4 0 0 | 4 1 0 . x3o *b3o3o3o . . . . ♦ 15 | 60 | 0 20 60 | 0 0 15 30 | 0 0 6 6 | * * 107520 * | 1 0 4 0 | 4 0 6 0 | 6 0 4 0 | 4 0 1 . x . *b3o3o3o3o . . . ♦ 6 | 15 | 0 0 20 | 0 0 0 15 | 0 0 0 6 | * * * 430080 | 0 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1 -----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+----------- o3x3o *b3o3o3o . . . . ♦ 240 | 1920 | 640 640 1920 | 160 480 480 960 | 60 192 192 192 | 12 32 32 0 | 3360 * * * ♦ 4 0 0 0 | 6 0 0 0 | 4 0 0 o3x . *b3o3o3o3o . . . ♦ 21 | 105 | 35 0 140 | 0 35 0 105 | 0 21 0 42 | 0 7 0 7 | * 61440 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0 . x3o *b3o3o3o3o . . . ♦ 21 | 105 | 0 35 140 | 0 0 35 105 | 0 0 21 42 | 0 0 7 7 | * * 61440 * | 1 0 3 0 | 3 0 3 0 | 3 0 1 . x . *b3o3o3o3o3o . . ♦ 7 | 21 | 0 0 35 | 0 0 0 35 | 0 0 0 21 | 0 0 0 7 | * * * 184320 | 0 1 1 2 | 1 2 2 1 | 2 1 1 -----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+----------- o3x3o *b3o3o3o3o . . . ♦ 672 | 6720 | 2240 2240 8960 | 560 2240 2240 6720 | 280 1344 1344 2688 | 84 448 448 448 | 14 64 64 0 | 960 * * * | 3 0 0 0 | 3 0 0 o3x . *b3o3o3o3o3o . . ♦ 28 | 168 | 56 0 280 | 0 70 0 280 | 0 56 0 168 | 0 28 0 56 | 0 8 0 8 | * 23040 * * | 1 2 0 0 | 2 1 0 . x3o *b3o3o3o3o3o . . ♦ 28 | 168 | 0 56 280 | 0 0 70 280 | 0 0 56 168 | 0 0 28 56 | 0 0 8 8 | * * 23040 * | 1 0 2 0 | 2 0 1 . x . *b3o3o3o3o3o3o . ♦ 8 | 28 | 0 0 56 | 0 0 0 70 | 0 0 0 56 | 0 0 0 28 | 0 0 0 8 | * * * 46080 | 0 1 1 1 | 1 1 1 -----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+----------- o3x3o *b3o3o3o3o3o . . ♦ 1792 | 21504 | 7168 7168 35840 | 1792 8960 8960 35840 | 1120 7168 7168 21504 | 448 3584 3584 7168 | 112 1024 1024 1024 | 16 128 128 0 | 180 * * * | 2 0 0 o3x . *b3o3o3o3o3o3o . ♦ 36 | 252 | 84 0 504 | 0 126 0 630 | 0 126 0 504 | 0 84 0 252 | 0 36 0 72 | 0 9 0 9 | * 5120 * * | 1 1 0 . x3o *b3o3o3o3o3o3o . ♦ 36 | 252 | 0 84 504 | 0 0 126 630 | 0 0 126 504 | 0 0 84 252 | 0 0 36 72 | 0 0 9 9 | * * 5120 * | 1 0 1 . x . *b3o3o3o3o3o3o3o ♦ 9 | 36 | 0 0 84 | 0 0 0 126 | 0 0 0 126 | 0 0 0 84 | 0 0 0 36 | 0 0 0 9 | * * * 5120 | 0 1 1 -----------------------+-------+--------+--------------------+----------------------------+----------------------------+---------------------------+-------------------------+-----------------------+--------------------+----------- o3x3o *b3o3o3o3o3o3o . ♦ 4608 | 64512 | 21504 21504 129024 | 5376 32256 32256 161280 | 4032 32256 32256 129024 | 2016 21504 21504 64512 | 672 9216 9216 18432 | 144 2304 2304 2304 | 18 256 256 0 | 20 * * o3x . *b3o3o3o3o3o3o3o ♦ 45 | 360 | 120 0 840 | 0 210 0 1260 | 0 252 0 1260 | 0 210 0 840 | 0 120 0 360 | 0 45 0 90 | 0 10 0 10 | * 512 * . x3o *b3o3o3o3o3o3o3o ♦ 45 | 360 | 0 120 840 | 0 0 210 1260 | 0 0 252 1260 | 0 0 210 840 | 0 0 120 360 | 0 0 45 90 | 0 0 10 10 | * * 512
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