Acronym | henne |
Name |
demi-enneract, Gosset polytope 16,1 |
Circumradius | 3/sqrt(8) = 1.060660 |
Inradius wrt. ene | 7/sqrt(72) = 0.824958 |
Inradius wrt. hocto | 1/sqrt(8) = 0.353553 |
Coordinates | (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8)) & all even permutations, all even changes of sign |
Volume | 2833 sqrt(2)/90720 = 0.044163 |
Surface | 943/840 = 1.122619 |
Dihedral angles
(at margins) | |
Face vector | 256, 4608, 21504, 37632, 36288, 23520, 9888, 2448, 274 |
Confer |
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External links |
Incidence matrix according to Dynkin symbol
x3o3o *b3o3o3o3o3o3o . . . . . . . . . | 256 ♦ 36 | 252 | 84 504 | 126 630 | 126 504 | 84 252 | 36 72 | 9 9 ---------------------+-----+------+-------+------------+------------+------------+----------+----------+------- x . . . . . . . . | 2 | 4608 ♦ 14 | 7 42 | 21 70 | 35 70 | 35 42 | 21 14 | 7 2 ---------------------+-----+------+-------+------------+------------+------------+----------+----------+------- x3o . . . . . . . | 3 | 3 | 21504 | 1 6 | 6 15 | 15 20 | 20 15 | 15 6 | 6 1 ---------------------+-----+------+-------+------------+------------+------------+----------+----------+------- x3o3o . . . . . . ♦ 4 | 6 | 4 | 5376 * ♦ 6 0 | 15 0 | 20 0 | 15 0 | 6 0 x3o . *b3o . . . . . ♦ 4 | 6 | 4 | * 32256 | 1 5 | 5 10 | 10 10 | 10 5 | 5 1 ---------------------+-----+------+-------+------------+------------+------------+----------+----------+------- x3o3o *b3o . . . . . ♦ 8 | 24 | 32 | 8 8 | 4032 * ♦ 5 0 | 10 0 | 10 0 | 5 0 x3o . *b3o3o . . . . ♦ 5 | 10 | 10 | 0 5 | * 32256 | 1 4 | 4 6 | 6 4 | 4 1 ---------------------+-----+------+-------+------------+------------+------------+----------+----------+------- x3o3o *b3o3o . . . . ♦ 16 | 80 | 160 | 40 80 | 10 16 | 2016 * ♦ 4 0 | 6 0 | 4 0 x3o . *b3o3o3o . . . ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 21504 | 1 3 | 3 3 | 3 1 ---------------------+-----+------+-------+------------+------------+------------+----------+----------+------- x3o3o *b3o3o3o . . . ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 | 672 * | 3 0 | 3 0 x3o . *b3o3o3o3o . . ♦ 7 | 21 | 35 | 0 35 | 0 21 | 0 7 | * 9216 | 1 2 | 2 1 ---------------------+-----+------+-------+------------+------------+------------+----------+----------+------- x3o3o *b3o3o3o3o . . ♦ 64 | 672 | 2240 | 560 2240 | 280 1344 | 84 448 | 14 64 | 144 * | 2 0 x3o . *b3o3o3o3o3o . ♦ 8 | 28 | 56 | 0 70 | 0 56 | 0 28 | 0 8 | * 2304 | 1 1 ---------------------+-----+------+-------+------------+------------+------------+----------+----------+------- x3o3o *b3o3o3o3o3o . ♦ 128 | 1792 | 7168 | 1792 8960 | 1120 7168 | 448 3584 | 112 1024 | 16 128 | 18 * x3o . *b3o3o3o3o3o3o ♦ 9 | 36 | 84 | 0 126 | 0 126 | 0 84 | 0 36 | 0 9 | * 256
o3o3o3o3o3o3o3o4s demi( . . . . . . . . . ) | 256 ♦ 36 | 252 | 84 504 | 126 630 | 126 504 | 84 252 | 36 72 | 9 9 --------------------------+-----+------+-------+------------+------------+------------+----------+----------+------- . . . . . . . o4s | 2 | 4608 ♦ 14 | 7 42 | 21 70 | 35 70 | 35 42 | 21 14 | 7 2 --------------------------+-----+------+-------+------------+------------+------------+----------+----------+------- sefa( . . . . . . o3o4s ) | 3 | 3 | 21504 | 1 6 | 6 15 | 15 20 | 20 15 | 15 6 | 6 1 --------------------------+-----+------+-------+------------+------------+------------+----------+----------+------- . . . . . . o3o4s ♦ 4 | 6 | 4 | 5376 * ♦ 6 0 | 15 0 | 20 0 | 15 0 | 6 0 sefa( . . . . . o3o3o4s ) ♦ 4 | 6 | 4 | * 32256 | 1 5 | 5 10 | 10 10 | 10 5 | 5 1 --------------------------+-----+------+-------+------------+------------+------------+----------+----------+------- . . . . . o3o3o4s ♦ 8 | 24 | 32 | 8 8 | 4032 * ♦ 5 0 | 10 0 | 10 0 | 5 0 sefa( . . . . o3o3o3o4s ) ♦ 5 | 10 | 10 | 0 5 | * 32256 | 1 4 | 4 6 | 6 4 | 4 1 --------------------------+-----+------+-------+------------+------------+------------+----------+----------+------- . . . . o3o3o3o4s ♦ 16 | 80 | 160 | 40 80 | 10 16 | 2016 * ♦ 4 0 | 6 0 | 4 0 sefa( . . . o3o3o3o3o4s ) ♦ 6 | 15 | 20 | 0 15 | 0 6 | * 21504 | 1 3 | 3 3 | 3 1 --------------------------+-----+------+-------+------------+------------+------------+----------+----------+------- . . . o3o3o3o3o4s ♦ 32 | 240 | 640 | 160 480 | 60 192 | 12 32 | 672 * | 3 0 | 3 0 sefa( . . o3o3o3o3o3o4s ) ♦ 7 | 21 | 35 | 0 35 | 0 21 | 0 7 | * 9216 | 1 2 | 2 1 --------------------------+-----+------+-------+------------+------------+------------+----------+----------+------- . . o3o3o3o3o3o4s ♦ 64 | 672 | 2240 | 560 2240 | 280 1344 | 84 448 | 14 64 | 144 * | 2 0 sefa( . o3o3o3o3o3o3o4s ) ♦ 8 | 28 | 56 | 0 70 | 0 56 | 0 28 | 0 8 | * 2304 | 1 1 --------------------------+-----+------+-------+------------+------------+------------+----------+----------+------- . o3o3o3o3o3o3o4s ♦ 128 | 1792 | 7168 | 1792 8960 | 1120 7168 | 448 3584 | 112 1024 | 16 128 | 18 * sefa( o3o3o3o3o3o3o3o4s ) ♦ 9 | 36 | 84 | 0 126 | 0 126 | 0 84 | 0 36 | 0 9 | * 256 starting figure: o3o3o3o3o3o3o3o4x
xo3oo3ox *b3oo3oo3oo3oo3oo&#x → height = 1/sqrt(2) = 0.707107 (hocto || alternate hocto) o.3o.3o. *b3o.3o.3o.3o.3o. & | 256 ♦ 28 8 | 168 84 | 56 280 224 28 | 70 280 56 350 | 56 168 70 336 | 28 56 56 196 | 8 8 28 64 | 1 8 9 --------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+--------- x. .. .. .. .. .. .. .. & | 2 | 3584 * ♦ 12 2 | 6 30 12 1 | 15 40 6 30 | 20 30 15 40 | 15 12 20 30 | 6 2 15 12 | 1 6 2 oo3oo3oo *b3oo3oo3oo3oo3oo&#x | 2 | * 1024 ♦ 0 14 | 0 0 42 7 | 0 0 21 70 | 0 0 35 70 | 0 0 35 42 | 0 0 21 14 | 0 7 2 --------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+--------- x.3o. .. .. .. .. .. .. & | 3 | 3 0 | 14336 * | 1 5 1 0 | 5 10 1 5 | 10 10 5 10 | 10 5 10 10 | 5 1 10 5 | 1 5 1 xo .. .. .. .. .. .. ..&#x & | 3 | 1 2 | * 7168 | 0 0 6 1 | 0 0 6 15 | 0 0 15 20 | 0 0 20 15 | 0 0 15 6 | 0 6 1 --------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+--------- x.3o.3o. .. .. .. .. .. & ♦ 4 | 6 0 | 4 0 | 3584 * * * ♦ 5 0 1 0 | 10 0 5 0 | 10 0 10 0 | 5 0 10 0 | 1 5 0 x.3o. .. *b3o. .. .. .. .. & ♦ 4 | 6 0 | 4 0 | * 17920 * * | 1 4 0 1 | 4 6 1 4 | 6 4 4 6 | 4 1 6 4 | 1 4 1 xo3oo .. .. .. .. .. ..&#x & ♦ 4 | 3 3 | 1 3 | * * 14336 * | 0 0 1 5 | 0 0 5 10 | 0 0 10 10 | 0 0 10 5 | 0 5 1 xo .. ox .. .. .. .. ..&#x ♦ 4 | 2 4 | 0 4 | * * * 1792 ♦ 0 0 6 0 | 0 0 15 0 | 0 0 20 0 | 0 0 15 0 | 0 6 0 --------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+--------- x.3o.3o. *b3o. .. .. .. .. & ♦ 8 | 24 0 | 32 0 | 8 8 0 0 | 2240 * * * ♦ 4 0 1 0 | 6 0 4 0 | 4 0 6 0 | 1 4 0 x.3o. .. *b3o.3o. .. .. .. & ♦ 5 | 10 0 | 10 0 | 0 5 0 0 | * 14336 * * | 1 3 0 1 | 3 3 1 3 | 3 1 3 3 | 1 3 1 xo3oo3ox .. .. .. .. ..&#x ♦ 8 | 12 12 | 8 24 | 2 0 8 6 | * * 1792 * ♦ 0 0 5 0 | 0 0 10 0 | 0 0 10 0 | 0 5 0 xo3oo .. *b3oo .. .. .. ..&#x & ♦ 5 | 6 4 | 4 6 | 0 1 4 0 | * * * 17920 | 0 0 1 4 | 0 0 4 6 | 0 0 6 4 | 0 4 1 --------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+--------- x.3o.3o. *b3o.3o. .. .. .. & ♦ 16 | 80 0 | 160 0 | 40 80 0 0 | 10 16 0 0 | 896 * * * ♦ 3 0 1 0 | 3 0 3 0 | 1 3 0 x.3o. .. *b3o.3o.3o. .. .. & ♦ 6 | 15 0 | 20 0 | 0 15 0 0 | 0 6 0 0 | * 7168 * * | 1 2 0 1 | 2 1 1 2 | 1 2 1 xo3oo3ox *b3oo .. .. .. ..&#x ♦ 16 | 48 32 | 64 96 | 16 16 64 24 | 2 0 8 16 | * * 1120 * ♦ 0 0 4 0 | 0 0 6 0 | 0 4 0 xo3oo .. *b3oo3oo .. .. ..&#x & ♦ 6 | 10 5 | 10 10 | 0 5 10 0 | 0 1 0 5 | * * * 14336 | 0 0 1 3 | 0 0 3 3 | 0 3 1 --------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+--------- x.3o.3o. *b3o.3o.3o. .. .. & ♦ 32 | 240 0 | 640 0 | 160 480 0 0 | 60 192 0 0 | 12 32 0 0 | 224 * * * | 2 0 1 0 | 1 2 0 x.3o. .. *b3o.3o.3o.3o. .. & ♦ 7 | 21 0 | 35 0 | 0 35 0 0 | 0 21 0 0 | 0 7 0 0 | * 2048 * * | 1 1 0 1 | 1 1 1 xo3oo3ox *b3oo3oo .. .. ..&#x ♦ 32 | 160 80 | 320 320 | 80 160 320 80 | 20 32 40 160 | 2 0 10 32 | * * 448 * | 0 0 3 0 | 0 3 0 xo3oo .. *b3oo3oo3oo .. ..&#x & ♦ 7 | 15 6 | 20 15 | 0 15 20 0 | 0 6 0 15 | 0 1 0 6 | * * * 7168 | 0 0 1 2 | 0 2 1 --------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+--------- x.3o.3o. *b3o.3o.3o.3o. .. & ♦ 64 | 672 0 | 2240 0 | 560 2240 0 0 | 280 1344 0 0 | 84 448 0 0 | 14 64 0 0 | 32 * * * | 1 1 0 x.3o. .. *b3o.3o.3o.3o.3o. & ♦ 8 | 28 0 | 56 0 | 0 70 0 0 | 0 56 0 0 | 0 28 0 0 | 0 8 0 0 | * 256 * * | 1 0 1 xo3oo3ox *b3oo3oo3oo .. ..&#x ♦ 64 | 480 192 | 1280 960 | 320 960 1280 240 | 120 384 160 960 | 24 64 60 384 | 2 0 12 64 | * * 112 * | 0 2 0 xo3oo .. *b3oo3oo3oo3oo ..&#x & ♦ 8 | 21 7 | 35 21 | 0 35 35 0 | 0 21 0 35 | 0 7 0 21 | 0 1 0 7 | * * * 2048 | 0 1 1 --------------------------------+-----+-----------+------------+-----------------------+-----------------------+---------------------+-------------------+-----------------+--------- x.3o.3o. *b3o.3o.3o.3o.3o. & ♦ 128 | 1792 0 | 7168 0 | 1792 8960 0 0 | 1120 7168 0 0 | 448 3584 0 0 | 112 1024 0 0 | 16 128 0 0 | 2 * * xo3oo3ox *b3oo3oo3oo3oo ..&#x ♦ 128 | 1344 448 | 4480 2688 | 1120 4480 4480 672 | 560 2688 560 4480 | 168 896 280 2688 | 28 128 84 896 | 2 0 14 128 | * 16 * xo3oo .. *b3oo3oo3oo3oo3oo&#x & ♦ 9 | 28 8 | 56 28 | 0 70 56 0 | 0 56 0 70 | 0 28 0 56 | 0 8 0 28 | 0 1 0 8 | * * 256
ooooo3oxooo3ooooo3ooxoo3ooooo3oooxo3ooooo3oooox&#xt → all heights = sqrt(2)/3 = 0.471405 (pt || pseudo rene || pseudo trene || pseudo inv. brene || dual ene) ...
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