| Acronym | brav |
| Name |
birectified pentacosidodecayotton, equatorial cross-section of riv-first brake |
| Circumradius | sqrt(3/2) = 1.224745 |
|
Inradius wrt. brene | 1/sqrt(2) = 0.707107 |
|
Inradius wrt. rek | 1/sqrt(2) = 0.707107 |
| Coordinates | (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0, 0) & all permutations, all changes of sign |
| Volume | 1679 sqrt(2)/2520 = 0.942248 |
| Surface | 1679/140 = 11.992857 |
|
Dihedral angles
(at margins) | |
| Face vector | 672, 12096, 48384, 102816, 133056, 102144, 41472, 7056, 530 |
| Confer |
|
It shall be noted, although there are different facet types, that there is just a single inradius throughout. In fact this is a common property for all (n-1)-rectified n2-orthoplexes. (Cases n < 3 had been trivial however, as there was just a single facet type. This is the first relevant case, but extends beyond the same.)
Incidence matrix according to Dynkin symbol
o3o3x3o3o3o3o3o4o . . . . . . . . . | 672 ♦ 36 | 36 180 | 12 180 480 | 60 480 720 | 160 720 576 | 240 576 192 | 192 192 3 | 64 3 ------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+------- . . x . . . . . . | 2 | 12096 | 2 10 | 1 20 40 | 10 80 80 | 40 160 80 | 80 160 32 | 80 64 1 | 32 2 ------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+------- . o3x . . . . . . | 3 | 3 | 8064 * | 1 10 0 | 10 40 0 | 40 80 0 | 80 80 0 | 80 32 0 | 32 1 . . x3o . . . . . | 3 | 3 | * 40320 | 0 2 8 | 1 16 24 | 8 48 32 | 24 64 16 | 16 16 1 | 16 2 ------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+------- o3o3x . . . . . . ♦ 4 | 6 | 4 0 | 2016 * * ♦ 10 0 0 | 40 0 0 | 80 0 0 | 80 0 0 | 32 0 . o3x3o . . . . . ♦ 6 | 12 | 4 4 | * 20160 * | 1 8 0 | 8 24 0 | 24 32 0 | 32 16 0 | 16 1 . . x3o3o . . . . ♦ 4 | 6 | 0 4 | * * 80640 | 0 2 6 | 1 12 12 | 6 24 8 | 12 16 1 | 8 2 ------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+------- o3o3x3o . . . . . ♦ 10 | 30 | 20 10 | 5 5 0 | 4032 * * ♦ 8 0 0 | 24 0 0 | 32 0 0 | 16 0 . o3x3o3o . . . . ♦ 10 | 30 | 10 20 | 0 5 5 | * 32256 * | 1 6 0 | 6 12 0 | 12 8 0 | 8 1 . . x3o3o3o . . . ♦ 5 | 10 | 0 10 | 0 0 5 | * * 96768 | 0 2 4 | 1 8 4 | 4 8 1 | 4 2 ------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+------- o3o3x3o3o . . . . ♦ 20 | 90 | 60 60 | 15 30 15 | 6 6 0 | 5376 * * ♦ 6 0 0 | 12 0 0 | 8 0 . o3x3o3o3o . . . ♦ 15 | 60 | 20 60 | 0 15 30 | 0 6 6 | * 32256 * | 1 4 0 | 4 4 0 | 4 1 . . x3o3o3o3o . . ♦ 6 | 15 | 0 20 | 0 0 15 | 0 0 6 | * * 64512 | 0 2 2 | 1 4 1 | 2 2 ------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+------- o3o3x3o3o3o . . . ♦ 35 | 210 | 140 210 | 35 105 105 | 21 42 21 | 7 7 0 | 4608 * * | 4 0 0 | 4 0 . o3x3o3o3o3o . . ♦ 21 | 105 | 35 140 | 0 35 105 | 0 21 42 | 0 7 7 | * 18432 * | 1 2 0 | 2 1 . . x3o3o3o3o3o . ♦ 7 | 21 | 0 35 | 0 0 35 | 0 0 21 | 0 0 7 | * * 18432 | 0 2 1 | 1 2 ------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+------- o3o3x3o3o3o3o . . ♦ 56 | 420 | 280 560 | 70 280 420 | 56 168 168 | 28 56 28 | 8 8 0 | 2304 * * | 2 0 . o3x3o3o3o3o3o . ♦ 28 | 168 | 56 280 | 0 70 280 | 0 56 168 | 0 28 56 | 0 8 8 | * 4608 * | 1 1 . . x3o3o3o3o3o4o ♦ 14 | 84 | 0 280 | 0 0 560 | 0 0 672 | 0 0 448 | 0 0 128 | * * 144 | 0 2 ------------------+-----+-------+------------+------------------+------------------+------------------+------------------+---------------+------- o3o3x3o3o3o3o3o . ♦ 84 | 756 | 504 1260 | 126 630 1260 | 126 504 756 | 84 252 252 | 36 72 36 | 9 9 0 | 512 * . o3x3o3o3o3o3o4o ♦ 112 | 1344 | 448 4480 | 0 1120 8960 | 0 1792 10752 | 0 1792 7168 | 0 1024 2048 | 0 256 16 | * 18
o3o3o *b3o3o3o3x3o3o . . . . . . . . . | 672 ♦ 36 | 180 36 | 480 180 12 | 720 480 60 | 576 720 160 | 96 96 576 240 | 3 96 96 192 | 3 32 32 ---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+----------- . . . . . . x . . | 2 | 12096 | 10 2 | 40 20 1 | 80 80 10 | 80 160 40 | 16 16 160 80 | 1 32 32 80 | 2 16 16 ---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+----------- . . . . . o3x . . | 3 | 3 | 40320 * | 8 2 0 | 24 16 1 | 32 48 8 | 8 8 64 24 | 1 8 8 16 | 2 8 8 . . . . . . x3o . | 3 | 3 | * 8064 | 0 10 1 | 0 40 10 | 0 80 40 | 0 0 80 80 | 0 16 16 80 | 1 16 16 ---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+----------- . . . . o3o3x . . ♦ 4 | 6 | 4 0 | 80640 * * | 6 2 0 | 12 12 1 | 4 4 24 6 | 1 8 8 12 | 2 4 4 . . . . . o3x3o . ♦ 6 | 12 | 4 4 | * 20160 * | 0 8 1 | 0 24 8 | 0 0 32 24 | 0 8 8 32 | 1 8 8 . . . . . . x3o3o ♦ 4 | 6 | 0 4 | * * 2016 ♦ 0 0 10 | 0 0 40 | 0 0 0 80 | 0 0 0 80 | 0 16 16 ---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+----------- . . . o3o3o3x . . ♦ 5 | 10 | 10 0 | 5 0 0 | 96768 * * | 4 2 0 | 2 2 8 1 | 4 4 4 1 | 2 2 2 . . . . o3o3x3o . ♦ 10 | 30 | 20 10 | 5 5 0 | * 32256 * | 0 6 1 | 0 0 12 6 | 0 4 4 12 | 1 4 4 . . . . . o3x3o3o ♦ 10 | 30 | 10 20 | 0 5 5 | * * 4032 ♦ 0 0 8 | 0 0 0 24 | 0 0 0 32 | 0 8 8 ---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+----------- . o . *b3o3o3o3x . . ♦ 6 | 15 | 20 0 | 15 0 0 | 6 0 0 | 64512 * * | 1 1 2 0 | 1 2 2 1 | 2 1 1 . . . o3o3o3x3o . ♦ 15 | 60 | 60 20 | 30 15 0 | 6 6 0 | * 32256 * | 0 0 4 1 | 0 2 2 4 | 1 2 2 . . . . o3o3x3o3o ♦ 20 | 90 | 60 60 | 15 30 15 | 0 6 6 | * * 5376 ♦ 0 0 0 6 | 0 0 0 12 | 0 4 4 ---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+----------- o3o . *b3o3o3o3x . . ♦ 7 | 21 | 35 0 | 35 0 0 | 21 0 0 | 7 0 0 | 9216 * * * | 1 2 0 0 | 2 1 0 . o3o *b3o3o3o3x . . ♦ 7 | 21 | 35 0 | 35 0 0 | 21 0 0 | 7 0 0 | * 9216 * * | 1 0 2 0 | 2 0 1 . o . *b3o3o3o3x3o . ♦ 21 | 105 | 140 35 | 105 35 0 | 42 21 0 | 7 7 0 | * * 18432 * | 0 1 1 1 | 1 1 1 . . . o3o3o3x3o3o ♦ 35 | 210 | 210 140 | 105 105 35 | 21 42 21 | 0 7 7 | * * * 4608 | 0 0 0 4 | 0 2 2 ---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+----------- o3o3o *b3o3o3o3x . . ♦ 14 | 84 | 280 0 | 560 0 0 | 672 0 0 | 448 0 0 | 64 64 0 0 | 144 * * * | 2 0 0 o3o . *b3o3o3o3x3o . ♦ 28 | 168 | 280 56 | 280 70 0 | 168 56 0 | 56 28 0 | 8 0 8 0 | * 2304 * * | 1 1 0 . o3o *b3o3o3o3x3o . ♦ 28 | 168 | 280 56 | 280 70 0 | 168 56 0 | 56 28 0 | 0 8 8 0 | * * 2304 * | 1 0 1 . o . *b3o3o3o3x3o3o ♦ 56 | 420 | 560 280 | 420 280 70 | 168 168 56 | 28 56 28 | 0 0 8 8 | * * * 2304 | 0 1 1 ---------------------+-----+-------+------------+------------------+------------------+------------------+----------------------+--------------------+----------- o3o3o *b3o3o3o3x3o . ♦ 112 | 1344 | 4480 448 | 8960 1120 0 | 10752 1792 0 | 7168 1792 0 | 1024 1024 1024 0 | 16 128 128 0 | 18 * * o3o . *b3o3o3o3x3o3o ♦ 84 | 756 | 1260 504 | 1260 630 126 | 756 504 126 | 252 252 84 | 36 0 72 36 | 0 9 0 9 | * 256 * . o3o *b3o3o3o3x3o3o ♦ 84 | 756 | 1260 504 | 1260 630 126 | 756 504 126 | 252 252 84 | 0 36 72 36 | 0 0 9 9 | * * 256
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