rectified hexadecazetton,
equatorial cross-section of rene-first barn
wrt. oca
wrt. rasa
- general polytopal classes:
- Wythoffian polyzetta
- analogs:
- rectified hypercube rCn
links
| Acronym | recto |
| Name |
rectified octeract, rectified hexadecazetton, equatorial cross-section of rene-first barn |
| Circumradius | sqrt(7/2) = 1.870829 |
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Inradius wrt. oca | 7/4 = 1.75 |
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Inradius wrt. rasa | 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), 0) & all permutations, all changes of sign |
| Volume | 40319/2520 = 15.999603 |
| Surface | (4+40312 sqrt(2))/315 = 180.996118 |
| Dihedral angles | |
| Face vector | 1024, 7168, 16128, 19712, 15456, 7616, 2160, 272 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
o3o3o3o3o3o3x4o . . . . . . . . | 1024 | 14 | 42 7 | 70 21 | 70 35 | 42 35 | 14 21 | 2 7 ----------------+------+------+------------+------------+------------+----------+----------+------- . . . . . . x . | 2 | 7168 | 6 1 | 15 6 | 20 15 | 15 20 | 6 15 | 1 6 ----------------+------+------+------------+------------+------------+----------+----------+------- . . . . . o3x . | 3 | 3 | 14336 * | 5 1 | 10 5 | 10 10 | 5 10 | 1 5 . . . . . . x4o | 4 | 4 | * 1792 ♦ 0 6 | 0 15 | 0 20 | 0 15 | 0 6 ----------------+------+------+------------+------------+------------+----------+----------+------- . . . . o3o3x . ♦ 4 | 6 | 4 0 | 17920 * | 4 1 | 6 4 | 4 6 | 1 4 . . . . . o3x4o ♦ 12 | 24 | 8 6 | * 1792 ♦ 0 5 | 0 10 | 0 10 | 0 5 ----------------+------+------+------------+------------+------------+----------+----------+------- . . . o3o3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 14336 * | 3 1 | 3 3 | 1 3 . . . . o3o3x4o ♦ 32 | 96 | 64 24 | 16 8 | * 1120 ♦ 0 4 | 0 6 | 0 4 ----------------+------+------+------------+------------+------------+----------+----------+------- . . o3o3o3o3x . ♦ 6 | 15 | 20 0 | 15 0 | 6 0 | 7168 * | 2 1 | 1 2 . . . o3o3o3x4o ♦ 80 | 320 | 320 80 | 160 40 | 32 10 | * 448 | 0 3 | 0 3 ----------------+------+------+------------+------------+------------+----------+----------+------- . o3o3o3o3o3x . ♦ 7 | 21 | 35 0 | 35 0 | 21 0 | 7 0 | 2048 * | 1 1 . . o3o3o3o3x4o ♦ 192 | 960 | 1280 240 | 960 160 | 384 60 | 64 12 | * 112 | 0 2 ----------------+------+------+------------+------------+------------+----------+----------+------- o3o3o3o3o3o3x . ♦ 8 | 28 | 56 0 | 70 0 | 56 0 | 28 0 | 8 0 | 256 * . o3o3o3o3o3x4o ♦ 448 | 2688 | 4480 672 | 4480 560 | 2688 280 | 896 84 | 128 14 | * 16
o3o3o3o3o3o3x4/3o . . . . . . . . | 1024 | 14 | 42 7 | 70 21 | 70 35 | 42 35 | 14 21 | 2 7 ------------------+------+------+------------+------------+------------+----------+----------+------- . . . . . . x . | 2 | 7168 | 6 1 | 15 6 | 20 15 | 15 20 | 6 15 | 1 6 ------------------+------+------+------------+------------+------------+----------+----------+------- . . . . . o3x . | 3 | 3 | 14336 * | 5 1 | 10 5 | 10 10 | 5 10 | 1 5 . . . . . . x4/3o | 4 | 4 | * 1792 ♦ 0 6 | 0 15 | 0 20 | 0 15 | 0 6 ------------------+------+------+------------+------------+------------+----------+----------+------- . . . . o3o3x . ♦ 4 | 6 | 4 0 | 17920 * | 4 1 | 6 4 | 4 6 | 1 4 . . . . . o3x4/3o ♦ 12 | 24 | 8 6 | * 1792 ♦ 0 5 | 0 10 | 0 10 | 0 5 ------------------+------+------+------------+------------+------------+----------+----------+------- . . . o3o3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 14336 * | 3 1 | 3 3 | 1 3 . . . . o3o3x4/3o ♦ 32 | 96 | 64 24 | 16 8 | * 1120 ♦ 0 4 | 0 6 | 0 4 ------------------+------+------+------------+------------+------------+----------+----------+------- . . o3o3o3o3x . ♦ 6 | 15 | 20 0 | 15 0 | 6 0 | 7168 * | 2 1 | 1 2 . . . o3o3o3x4/3o ♦ 80 | 320 | 320 80 | 160 40 | 32 10 | * 448 | 0 3 | 0 3 ------------------+------+------+------------+------------+------------+----------+----------+------- . o3o3o3o3o3x . ♦ 7 | 21 | 35 0 | 35 0 | 21 0 | 7 0 | 2048 * | 1 1 . . o3o3o3o3x4/3o ♦ 192 | 960 | 1280 240 | 960 160 | 384 60 | 64 12 | * 112 | 0 2 ------------------+------+------+------------+------------+------------+----------+----------+------- o3o3o3o3o3o3x . ♦ 8 | 28 | 56 0 | 70 0 | 56 0 | 28 0 | 8 0 | 256 * . o3o3o3o3o3x4/3o ♦ 448 | 2688 | 4480 672 | 4480 560 | 2688 280 | 896 84 | 128 14 | * 16
x3o3x *b3o3o3o3o3o . . . . . . . . | 1024 | 7 7 | 21 7 21 | 21 35 35 | 35 35 35 | 35 21 21 | 21 7 7 | 7 1 1 -------------------+------+-----------+----------------+----------------+----------------+---------------+---------------+----------- x . . . . . . . | 2 | 3584 * | 6 1 0 | 6 15 0 | 15 20 0 | 20 15 0 | 15 6 0 | 6 1 0 . . x . . . . . | 2 | * 3584 | 0 1 6 | 6 0 15 | 15 0 20 | 20 0 15 | 15 0 6 | 6 0 1 -------------------+------+-----------+----------------+----------------+----------------+---------------+---------------+----------- x3o . . . . . . | 3 | 3 0 | 7168 * * | 1 5 0 | 5 10 0 | 10 10 0 | 10 5 0 | 5 1 0 x . x . . . . . | 4 | 2 2 | * 1792 * ♦ 6 0 0 | 15 0 0 | 20 0 0 | 15 0 0 | 6 0 0 . o3x . . . . . | 3 | 0 3 | * * 7168 | 1 0 5 | 5 0 10 | 10 0 10 | 10 0 5 | 5 0 1 -------------------+------+-----------+----------------+----------------+----------------+---------------+---------------+----------- x3o3x . . . . . ♦ 12 | 12 12 | 4 6 4 | 1792 * * ♦ 5 0 0 | 10 0 0 | 10 0 0 | 5 0 0 x3o . *b3o . . . . ♦ 4 | 6 0 | 4 0 0 | * 8960 * | 1 4 0 | 4 6 0 | 6 4 0 | 4 1 0 . o3x *b3o . . . . ♦ 4 | 0 6 | 0 0 4 | * * 8960 | 1 0 4 | 4 0 6 | 6 0 4 | 4 0 1 -------------------+------+-----------+----------------+----------------+----------------+---------------+---------------+----------- x3o3x *b3o . . . . ♦ 32 | 48 48 | 32 24 32 | 8 8 8 | 1120 * * ♦ 4 0 0 | 6 0 0 | 4 0 0 x3o . *b3o3o . . . ♦ 5 | 10 0 | 10 0 0 | 0 5 0 | * 7168 * | 1 3 0 | 3 3 0 | 3 1 0 . o3x *b3o3o . . . ♦ 5 | 0 10 | 0 0 10 | 0 0 5 | * * 7168 | 1 0 3 | 3 0 3 | 3 0 1 -------------------+------+-----------+----------------+----------------+----------------+---------------+---------------+----------- x3o3x *b3o3o . . . ♦ 80 | 160 160 | 160 80 160 | 40 80 80 | 10 16 16 | 448 * * | 3 0 0 | 3 0 0 x3o . *b3o3o3o . . ♦ 6 | 15 0 | 20 0 0 | 0 15 0 | 0 6 0 | * 3584 * | 1 2 0 | 2 1 0 . o3x *b3o3o3o . . ♦ 6 | 0 15 | 0 0 20 | 0 0 15 | 0 0 6 | * * 3584 | 1 0 2 | 2 0 1 -------------------+------+-----------+----------------+----------------+----------------+---------------+---------------+----------- x3o3x *b3o3o3o . . ♦ 192 | 480 480 | 640 240 640 | 160 480 480 | 60 192 192 | 12 32 32 | 112 * * | 2 0 0 x3o . *b3o3o3o3o . ♦ 7 | 21 0 | 35 0 0 | 0 35 0 | 0 21 0 | 0 7 0 | * 1024 * | 1 1 0 . o3x *b3o3o3o3o . ♦ 7 | 0 21 | 0 0 35 | 0 0 35 | 0 0 21 | 0 0 7 | * * 1024 | 1 0 1 -------------------+------+-----------+----------------+----------------+----------------+---------------+---------------+----------- x3o3x *b3o3o3o3o . ♦ 448 | 1344 1344 | 2240 672 2240 | 560 2240 2240 | 280 1344 1344 | 84 448 448 | 14 64 64 | 16 * * x3o . *b3o3o3o3o3o ♦ 8 | 28 0 | 56 0 0 | 0 70 0 | 0 56 0 | 0 28 0 | 0 8 0 | * 128 * . o3x *b3o3o3o3o3o ♦ 8 | 0 28 | 0 0 56 | 0 0 70 | 0 0 56 | 0 0 28 | 0 0 8 | * * 128
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