| Acronym | tergoh |
| Name | tetrarectified Gosset octacomb 52,1 |
Incidence matrix according to Dynkin symbol
o3o3o3x3o3o3o3o *c3o (N → ∞) . . . . . . . . . | 48384N ♦ 50 | 150 100 | 100 300 50 100 | 25 200 25 300 100 50 | 50 5 200 50 150 100 10 | 50 10 100 50 30 50 | 25 10 20 25 10 | 5 5 5 ---------------------+--------+----------+-------------------+------------------------------------+--------------------------------------------------+------------------------------------------------------+-------------------------------------------+--------------------------------+------------- . . . x . . . . . | 2 | 1209600N | 6 4 | 6 24 3 6 | 2 24 3 36 12 4 | 8 1 36 12 24 18 1 | 12 4 24 18 6 12 | 8 6 6 12 3 | 2 4 3 ---------------------+--------+----------+-------------------+------------------------------------+--------------------------------------------------+------------------------------------------------------+-------------------------------------------+--------------------------------+------------- . . o3x . . . . . | 3 | 3 | 2419200N * | 2 4 1 0 | 1 8 2 6 4 0 | 4 1 12 8 4 6 0 | 6 4 8 12 1 4 | 4 6 2 8 1 | 1 4 2 . . . x3o . . . . | 3 | 3 | * 1612800N | 0 6 0 3 | 0 6 0 18 3 3 | 2 0 18 3 18 9 1 | 6 1 18 9 6 9 | 6 3 6 9 3 | 2 3 3 ---------------------+--------+----------+-------------------+------------------------------------+--------------------------------------------------+------------------------------------------------------+-------------------------------------------+--------------------------------+------------- . o3o3x . . . . . ♦ 4 | 6 | 4 0 | 1209600N * * * | 1 4 1 0 0 0 | 4 1 6 4 0 0 0 | 6 4 4 6 0 0 | 4 6 1 4 0 | 1 4 1 . . o3x3o . . . . ♦ 6 | 12 | 4 4 | * 2419200N * * | 0 2 0 3 1 0 | 1 0 6 2 3 3 0 | 3 1 6 6 1 3 | 3 3 2 6 1 | 1 3 2 . . o3x . . . . *c3o ♦ 4 | 6 | 4 0 | * * 604800N * | 0 0 2 0 4 0 | 0 1 0 8 0 6 0 | 0 4 0 12 0 4 | 0 6 0 8 1 | 0 4 2 . . . x3o3o . . . ♦ 4 | 6 | 0 4 | * * * 1209600N | 0 0 0 6 0 2 | 0 0 6 0 12 3 1 | 2 0 12 3 6 6 | 4 1 6 6 3 | 2 2 3 ---------------------+--------+----------+-------------------+------------------------------------+--------------------------------------------------+------------------------------------------------------+-------------------------------------------+--------------------------------+------------- o3o3o3x . . . . . ♦ 5 | 10 | 10 0 | 5 0 0 0 | 241920N * * * * * | 4 1 0 0 0 0 0 | 6 4 0 0 0 0 | 4 6 0 0 0 | 1 4 0 . o3o3x3o . . . . ♦ 10 | 30 | 20 10 | 5 5 0 0 | * 967680N * * * * | 1 0 3 1 0 0 0 | 3 1 3 3 0 0 | 3 3 1 3 0 | 1 3 1 . o3o3x . . . . *c3o ♦ 8 | 24 | 32 0 | 8 0 8 0 | * * 151200N * * * | 0 1 0 4 0 0 0 | 0 4 0 6 0 0 | 0 6 0 4 0 | 0 4 1 . . o3x3o3o . . . ♦ 10 | 30 | 10 20 | 0 5 0 5 | * * * 1451520N * * | 0 0 2 0 2 1 0 | 1 0 4 2 1 2 | 2 1 2 4 1 | 1 2 2 . . o3x3o . . . *c3o ♦ 10 | 30 | 20 10 | 0 5 5 0 | * * * * 483840N * | 0 0 0 2 0 3 0 | 0 1 0 6 0 3 | 0 3 0 6 1 | 0 3 2 . . . x3o3o3o . . ♦ 5 | 10 | 0 10 | 0 0 0 5 | * * * * * 483840N | 0 0 0 0 6 0 1 | 0 0 6 0 6 3 | 2 0 6 3 3 | 2 1 3 ---------------------+--------+----------+-------------------+------------------------------------+--------------------------------------------------+------------------------------------------------------+-------------------------------------------+--------------------------------+------------- o3o3o3x3o . . . . ♦ 15 | 60 | 60 20 | 30 15 0 0 | 6 6 0 0 0 0 | 161280N * * * * * * | 3 1 0 0 0 0 | 3 3 0 0 0 | 1 3 0 o3o3o3x . . . . *c3o ♦ 16 | 80 | 160 0 | 80 0 40 0 | 16 0 10 0 0 0 | * 15120N * * * * * ♦ 0 4 0 0 0 0 | 0 6 0 0 0 | 0 4 0 . o3o3x3o3o . . . ♦ 20 | 90 | 60 60 | 15 30 0 15 | 0 6 0 6 0 0 | * * 483840N * * * * | 1 0 2 1 0 0 | 2 1 1 2 0 | 1 2 1 . o3o3x3o . . . *c3o ♦ 40 | 240 | 320 80 | 80 80 80 0 | 0 16 10 0 16 0 | * * * 60480N * * * | 0 1 0 3 0 0 | 0 3 0 3 0 | 0 3 1 . . o3x3o3o3o . . ♦ 15 | 60 | 20 60 | 0 15 0 30 | 0 0 0 6 0 6 | * * * * 483840N * * | 0 0 2 0 1 1 | 1 0 2 2 1 | 1 1 2 . . o3x3o3o . . *c3o ♦ 20 | 90 | 60 60 | 0 30 15 15 | 0 0 0 6 6 0 | * * * * * 241920N * | 0 0 0 2 0 2 | 0 1 0 4 1 | 0 2 2 . . . x3o3o3o3o . ♦ 6 | 15 | 0 20 | 0 0 0 15 | 0 0 0 0 0 6 | * * * * * * 80640N | 0 0 0 0 6 0 | 0 0 6 0 3 | 2 0 3 ---------------------+--------+----------+-------------------+------------------------------------+--------------------------------------------------+------------------------------------------------------+-------------------------------------------+--------------------------------+------------- o3o3o3x3o3o . . . ♦ 35 | 210 | 210 140 | 105 105 0 35 | 21 42 0 21 0 0 | 7 0 7 0 0 0 0 | 69120N * * * * * | 2 1 0 0 0 | 1 2 0 o3o3o3x3o . . . *c3o ♦ 216 | 2160 | 4320 720 | 2160 1080 1080 0 | 432 432 270 0 216 0 | 72 27 0 27 0 0 0 | * 2240N * * * * | 0 3 0 0 0 | 0 3 0 . o3o3x3o3o3o . . ♦ 35 | 210 | 140 210 | 35 105 0 105 | 0 21 0 42 0 21 | 0 0 7 0 7 0 0 | * * 138240N * * * | 1 0 1 1 0 | 1 1 1 . o3o3x3o3o . . *c3o ♦ 160 | 1440 | 1920 960 | 480 960 480 240 | 0 192 60 192 192 0 | 0 0 32 12 0 32 0 | * * * 15120N * * | 0 1 0 2 0 | 0 2 1 . . o3x3o3o3o3o . ♦ 21 | 105 | 35 140 | 0 35 0 105 | 0 0 0 21 0 42 | 0 0 0 0 7 0 7 | * * * * 69120N * | 0 0 2 0 1 | 1 0 2 . . o3x3o3o3o . *c3o ♦ 35 | 210 | 140 210 | 0 105 35 105 | 0 0 0 42 21 21 | 0 0 0 0 7 7 0 | * * * * * 69120N | 0 0 0 2 1 | 0 1 2 ---------------------+--------+----------+-------------------+------------------------------------+--------------------------------------------------+------------------------------------------------------+-------------------------------------------+--------------------------------+------------- o3o3o3x3o3o3o . . ♦ 70 | 560 | 560 560 | 280 420 0 280 | 56 168 0 168 0 56 | 28 0 56 0 28 0 0 | 8 0 8 0 0 0 | 17280N * * * * | 1 1 0 o3o3o3x3o3o . . *c3o ♦ 4032 | 60480 | 120960 40320 | 60480 60480 30240 10080 | 12096 24192 7560 12096 12096 0 | 4032 756 4032 1512 0 2016 0 | 576 56 0 126 0 0 | * 120N * * * | 0 2 0 . o3o3x3o3o3o3o . ♦ 56 | 420 | 280 560 | 70 280 0 420 | 0 56 0 168 0 168 | 0 0 28 0 56 0 28 | 0 0 8 0 8 0 | * * 17280N * * | 1 0 1 . o3o3x3o3o3o . *c3o ♦ 560 | 6720 | 8960 6720 | 2240 6720 2240 3360 | 0 1344 280 2688 1344 672 | 0 0 448 84 448 448 0 | 0 0 64 14 0 64 | * * * 2160N * | 0 1 1 . . o3x3o3o3o3o *c3o ♦ 56 | 420 | 280 560 | 0 280 70 420 | 0 0 0 168 56 168 | 0 0 0 0 56 28 28 | 0 0 0 0 8 8 | * * * * 8640N | 0 0 2 ---------------------+--------+----------+-------------------+------------------------------------+--------------------------------------------------+------------------------------------------------------+-------------------------------------------+--------------------------------+------------- o3o3o3x3o3o3o3o . ♦ 126 | 1260 | 1260 1680 | 630 1260 0 1260 | 126 504 0 756 0 504 | 84 0 252 0 252 0 84 | 36 0 72 0 36 0 | 9 0 9 0 0 | 1920N * * o3o3o3x3o3o3o . *c3o ♦ 241920 | 4838400 | 9676800 4838400 | 4838400 7257600 2419200 2419200 | 967680 2903040 604800 2903040 1451520 483840 | 483840 60480 967680 181440 483840 483840 0 | 138240 6720 138240 30240 0 69120 | 17280 240 0 2160 0 | * N * . o3o3x3o3o3o3o *c3o ♦ 1792 | 26880 | 35840 35840 | 8960 35840 8960 26880 | 0 7168 1120 21504 7168 10752 | 0 0 3584 448 7168 3584 1792 | 0 0 1024 112 1024 1024 | 0 0 128 16 128 | * * 135N
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