| Acronym | tarn |
| Name |
trirectified enneract, trirectified octadecayotton |
| Circumradius | sqrt(3) = 1.732051 |
| Coordinates | (1, 1, 1, 1, 1, 1, 0, 0, 0)/sqrt(2) & all permutations, all changes of sign |
| Face vector | 5376, 96768, 290304, 387072, 294336, 141792, 42144, 7056, 530 |
| Confer |
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Incidence matrix according to Dynkin symbol
o3o3o3o3o3x3o3o4o . . . . . . . . . | 5376 ♦ 36 | 90 72 | 120 180 48 | 90 240 120 6 | 36 180 160 15 | 6 72 120 20 | 12 48 15 | 8 6 ------------------+------+-------+---------------+---------------------+-------------------------+------------------------+----------------------+---------------+------- . . . . . x . . . | 2 | 96768 | 5 4 | 10 20 4 | 10 40 20 1 | 5 40 40 5 | 1 20 40 10 | 4 20 10 | 4 5 ------------------+------+-------+---------------+---------------------+-------------------------+------------------------+----------------------+---------------+------- . . . . o3x . . . | 3 | 3 | 161280 * | 4 4 0 | 6 16 4 0 | 4 24 16 1 | 1 16 24 4 | 4 16 6 | 4 4 . . . . . x3o . . | 3 | 3 | * 129024 | 0 5 2 | 0 10 10 1 | 0 10 20 5 | 0 5 20 10 | 1 10 10 | 2 5 ------------------+------+-------+---------------+---------------------+-------------------------+------------------------+----------------------+---------------+------- . . . o3o3x . . . ♦ 4 | 6 | 4 0 | 161280 * * | 3 4 0 0 | 3 12 4 0 | 1 12 12 1 | 4 12 3 | 4 3 . . . . o3x3o . . ♦ 6 | 12 | 4 4 | * 161280 * | 0 4 2 0 | 0 6 8 1 | 0 4 12 4 | 1 8 6 | 2 4 . . . . . x3o3o . ♦ 4 | 6 | 0 4 | * * 64512 | 0 0 5 1 | 0 0 10 5 | 0 0 10 10 | 0 5 10 | 1 5 ------------------+------+-------+---------------+---------------------+-------------------------+------------------------+----------------------+---------------+------- . . o3o3o3x . . . ♦ 5 | 10 | 10 0 | 5 0 0 | 96768 * * * | 2 4 0 0 | 1 8 4 0 | 4 8 1 | 4 2 . . . o3o3x3o . . ♦ 10 | 30 | 20 10 | 5 5 0 | * 129024 * * | 0 3 2 0 | 0 3 6 1 | 1 6 3 | 2 3 . . . . o3x3o3o . ♦ 10 | 30 | 10 20 | 0 5 5 | * * 64512 * | 0 0 4 1 | 0 0 6 4 | 0 4 6 | 1 4 . . . . . x3o3o4o ♦ 8 | 24 | 0 32 | 0 0 16 | * * * 4032 ♦ 0 0 0 5 | 0 0 0 10 | 0 0 10 | 0 5 ------------------+------+-------+---------------+---------------------+-------------------------+------------------------+----------------------+---------------+------- . o3o3o3o3x . . . ♦ 6 | 15 | 20 0 | 15 0 0 | 6 0 0 0 | 32256 * * * | 1 4 0 0 | 4 4 0 | 4 1 . . o3o3o3x3o . . ♦ 15 | 60 | 60 20 | 30 15 0 | 6 6 0 0 | * 64512 * * | 0 2 2 0 | 1 4 1 | 2 2 . . . o3o3x3o3o . ♦ 20 | 90 | 60 60 | 15 30 15 | 0 6 6 0 | * * 43008 * | 0 0 3 1 | 0 3 3 | 1 3 . . . . o3x3o3o4o ♦ 40 | 240 | 80 320 | 0 80 160 | 0 0 32 10 | * * * 2016 ♦ 0 0 0 4 | 0 0 6 | 0 4 ------------------+------+-------+---------------+---------------------+-------------------------+------------------------+----------------------+---------------+------- o3o3o3o3o3x . . . ♦ 7 | 21 | 35 0 | 35 0 0 | 21 0 0 0 | 7 0 0 0 | 4608 * * * | 4 0 0 | 4 0 . o3o3o3o3x3o . . ♦ 21 | 105 | 140 35 | 105 35 0 | 42 21 0 0 | 7 7 0 0 | * 18432 * * | 1 2 0 | 2 1 . . o3o3o3x3o3o . ♦ 35 | 210 | 210 140 | 105 105 35 | 21 42 21 0 | 0 7 7 0 | * * 18432 * | 0 2 1 | 1 2 . . . o3o3x3o3o4o ♦ 160 | 1440 | 960 1920 | 240 960 960 | 0 192 384 60 | 0 0 64 12 | * * * 672 | 0 0 3 | 0 3 ------------------+------+-------+---------------+---------------------+-------------------------+------------------------+----------------------+---------------+------- o3o3o3o3o3x3o . . ♦ 28 | 168 | 280 56 | 280 70 0 | 168 56 0 0 | 56 28 0 0 | 8 8 0 0 | 2304 * * | 2 0 . o3o3o3o3x3o3o . ♦ 56 | 420 | 560 280 | 420 280 70 | 168 168 56 0 | 28 56 28 0 | 0 8 8 0 | * 4608 * | 1 1 . . o3o3o3x3o3o4o ♦ 560 | 6720 | 6720 8960 | 3360 6720 4480 | 672 2688 2688 280 | 0 448 896 84 | 0 0 128 14 | * * 144 | 0 2 ------------------+------+-------+---------------+---------------------+-------------------------+------------------------+----------------------+---------------+------- o3o3o3o3o3x3o3o . ♦ 84 | 756 | 1260 504 | 1260 630 126 | 756 504 126 0 | 252 252 84 0 | 36 72 36 0 | 9 9 0 | 512 * . o3o3o3o3x3o3o4o ♦ 1792 | 26880 | 35840 35840 | 26880 35840 17920 | 10752 21504 14336 1120 | 1792 7168 7168 448 | 0 1024 2048 112 | 0 256 16 | * 18
o3o3o *b3x3o3o3o3o3o . . . . . . . . . | 5376 ♦ 36 | 72 90 | 24 24 180 120 | 6 60 60 240 90 | 15 80 80 180 36 | 20 60 60 72 6 | 15 24 24 12 | 6 4 4 ---------------------+------+-------+---------------+---------------------------+-------------------------------+------------------------------+--------------------------+--------------------+----------- . . . x . . . . . | 2 | 96768 | 4 5 | 2 2 20 10 | 1 10 10 40 10 | 5 20 20 40 5 | 10 20 20 20 1 | 10 10 10 4 | 5 2 2 ---------------------+------+-------+---------------+---------------------------+-------------------------------+------------------------------+--------------------------+--------------------+----------- . o . *b3x . . . . . | 3 | 3 | 129024 * | 1 1 5 0 | 1 5 5 10 0 | 5 10 10 10 0 | 10 10 10 5 0 | 10 5 5 1 | 5 1 1 . . . x3o . . . . | 3 | 3 | * 161280 | 0 0 4 4 | 0 2 2 16 6 | 1 8 8 24 4 | 4 12 12 16 1 | 6 8 8 4 | 4 2 2 ---------------------+------+-------+---------------+---------------------------+-------------------------------+------------------------------+--------------------------+--------------------+----------- o3o . *b3x . . . . . ♦ 4 | 6 | 4 0 | 32256 * * * | 1 5 0 0 0 | 5 10 0 0 0 | 10 10 0 0 0 | 10 5 0 0 | 5 1 0 . o3o *b3x . . . . . ♦ 4 | 6 | 4 0 | * 32256 * * | 1 0 5 0 0 | 5 0 10 0 0 | 10 0 10 0 0 | 10 0 5 0 | 5 0 1 . o . *b3x3o . . . . ♦ 6 | 12 | 4 4 | * * 161280 * | 0 1 1 4 0 | 1 4 4 6 0 | 4 6 6 4 0 | 6 4 4 1 | 4 1 1 . . . x3o3o . . . ♦ 4 | 6 | 0 4 | * * * 161280 | 0 0 0 4 3 | 0 2 2 12 3 | 1 6 6 12 1 | 3 6 6 4 | 3 2 2 ---------------------+------+-------+---------------+---------------------------+-------------------------------+------------------------------+--------------------------+--------------------+----------- o3o3o *b3x . . . . . ♦ 8 | 24 | 32 0 | 8 8 0 0 | 4032 * * * * ♦ 5 0 0 0 0 | 10 0 0 0 0 | 10 0 0 0 | 5 0 0 o3o . *b3x3o . . . . ♦ 10 | 30 | 20 10 | 5 0 5 0 | * 32256 * * * | 1 4 0 0 0 | 4 6 0 0 0 | 6 4 0 0 | 4 1 0 . o3o *b3x3o . . . . ♦ 10 | 30 | 20 10 | 0 5 5 0 | * * 32256 * * | 1 0 4 0 0 | 4 0 6 0 0 | 6 0 4 0 | 4 0 1 . o . *b3x3o3o . . . ♦ 10 | 30 | 10 20 | 0 0 5 5 | * * * 129024 * | 0 1 1 3 0 | 1 3 3 3 0 | 3 3 3 1 | 3 1 1 . . . x3o3o3o . . ♦ 5 | 10 | 0 10 | 0 0 0 5 | * * * * 96768 | 0 0 0 4 2 | 0 2 2 8 1 | 1 4 4 4 | 2 2 2 ---------------------+------+-------+---------------+---------------------------+-------------------------------+------------------------------+--------------------------+--------------------+----------- o3o3o *b3x3o . . . . ♦ 40 | 240 | 320 80 | 80 80 80 0 | 10 16 16 0 0 | 2016 * * * * ♦ 4 0 0 0 0 | 6 0 0 0 | 4 0 0 o3o . *b3x3o3o . . . ♦ 20 | 90 | 60 60 | 15 0 30 15 | 0 6 0 6 0 | * 21504 * * * | 1 3 0 0 0 | 3 3 0 0 | 3 1 0 . o3o *b3x3o3o . . . ♦ 20 | 90 | 60 60 | 0 15 30 15 | 0 0 6 6 0 | * * 21504 * * | 1 0 3 0 0 | 3 0 3 0 | 3 0 1 . o . *b3x3o3o3o . . ♦ 15 | 60 | 20 60 | 0 0 15 30 | 0 0 0 6 6 | * * * 64512 * | 0 1 1 2 0 | 1 2 2 1 | 2 1 1 . . . x3o3o3o3o . ♦ 6 | 15 | 0 20 | 0 0 0 15 | 0 0 0 0 6 | * * * * 32256 | 0 0 0 4 1 | 0 2 2 4 | 1 2 2 ---------------------+------+-------+---------------+---------------------------+-------------------------------+------------------------------+--------------------------+--------------------+----------- o3o3o *b3x3o3o . . . ♦ 160 | 1440 | 1920 960 | 480 480 960 240 | 60 192 192 192 0 | 12 32 32 0 0 | 672 * * * * | 3 0 0 0 | 3 0 0 o3o . *b3x3o3o3o . . ♦ 35 | 210 | 140 210 | 35 0 105 105 | 0 21 0 42 21 | 0 7 0 7 0 | * 9216 * * * | 1 2 0 0 | 2 1 0 . o3o *b3x3o3o3o . . ♦ 35 | 210 | 140 210 | 0 35 105 105 | 0 0 21 42 21 | 0 0 7 7 0 | * * 9216 * * | 1 0 2 0 | 2 0 1 . o . *b3x3o3o3o3o . ♦ 21 | 105 | 35 140 | 0 0 35 105 | 0 0 0 21 42 | 0 0 0 7 7 | * * * 18432 * | 0 1 1 1 | 1 1 1 . . . x3o3o3o3o3o ♦ 7 | 21 | 0 35 | 0 0 0 35 | 0 0 0 0 21 | 0 0 0 0 7 | * * * * 4608 | 0 0 0 4 | 0 2 2 ---------------------+------+-------+---------------+---------------------------+-------------------------------+------------------------------+--------------------------+--------------------+----------- o3o3o *b3x3o3o3o . . ♦ 560 | 6720 | 8960 6720 | 2240 2240 6720 3360 | 280 1344 1344 2688 672 | 84 448 448 448 0 | 14 64 64 0 0 | 144 * * * | 2 0 0 o3o . *b3x3o3o3o3o . ♦ 56 | 420 | 280 560 | 70 0 280 420 | 0 56 0 168 168 | 0 28 0 56 28 | 0 8 0 8 0 | * 2304 * * | 1 1 0 . o3o *b3x3o3o3o3o . ♦ 56 | 420 | 280 560 | 0 70 280 420 | 0 0 56 168 168 | 0 0 28 56 28 | 0 0 8 8 0 | * * 2304 * | 1 0 1 . o . *b3x3o3o3o3o3o ♦ 28 | 168 | 56 280 | 0 0 70 280 | 0 0 0 56 168 | 0 0 0 28 56 | 0 0 0 8 8 | * * * 2304 | 0 1 1 ---------------------+------+-------+---------------+---------------------------+-------------------------------+------------------------------+--------------------------+--------------------+----------- o3o3o *b3x3o3o3o3o . ♦ 1792 | 26880 | 35840 35840 | 8960 8960 35840 26880 | 1120 7168 7168 21504 10752 | 448 3584 3584 7168 1792 | 112 1024 1024 1024 0 | 16 128 128 0 | 18 * * o3o . *b3x3o3o3o3o3o ♦ 84 | 756 | 504 1260 | 126 0 630 1260 | 0 126 0 504 756 | 0 84 0 252 252 | 0 36 0 72 36 | 0 9 0 9 | * 256 * . o3o *b3x3o3o3o3o3o ♦ 84 | 756 | 504 1260 | 0 126 630 1260 | 0 0 126 504 756 | 0 0 84 252 252 | 0 0 36 72 36 | 0 0 9 9 | * * 256
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