| Acronym | gacdincat |
| Name | great cellidispenteracticellitriacontaditeron |
| Circumradius | sqrt[17-4 sqrt(2)]/2 = 1.683979 |
| Coordinates | (1+sqrt(2), sqrt(2)-1, 2 sqrt(2)-1, 1, 1)/2 & all permutations, all changes of sign |
| Colonel of regiment | gidacadint |
| Face vector | 1920, 6720, 6880, 2320, 172 |
| Confer |
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As abstract polytope gacdincat is isomorphic to scadnicat, thereby interchanging the roles of sirco and querco, resp. replacing paqrit by prit, and sircope by quercope.
Incidence matrix according to Dynkin symbol
4/3 3 3
x---o---x---x
3/2 \ / 3
x
x4/3o3x3x *b3/2x3*c . . . . . | 1920 | 2 2 1 2 | 1 2 2 2 1 1 2 2 2 | 1 1 1 2 2 2 1 1 1 2 | 1 1 1 2 1 --------------------+------+--------------------+-------------------------------------+---------------------------------------+--------------- x . . . . | 2 | 1920 * * * | 1 1 1 1 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0 . . x . . | 2 | * 1920 * * | 0 1 0 0 1 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . . . x . | 2 | * * 960 * | 0 0 2 0 0 0 2 0 2 | 0 1 0 2 0 2 1 0 1 2 | 1 0 1 2 1 . . . . x | 2 | * * * 1920 | 0 0 0 1 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 --------------------+------+--------------------+-------------------------------------+---------------------------------------+--------------- x4/3o . . . | 4 | 4 0 0 0 | 480 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 2 0 0 | * 960 * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 2 0 | * * 960 * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 2 | * * * 960 * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . o3x . . | 3 | 0 3 0 0 | * * * * 640 * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . o . . *b3/2x | 3 | 0 0 0 3 | * * * * * 640 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . x3x . | 6 | 0 3 3 0 | * * * * * * 640 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . . x . x3*c | 6 | 0 3 0 3 | * * * * * * * 640 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . x x | 4 | 0 0 2 2 | * * * * * * * * 960 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 --------------------+------+--------------------+-------------------------------------+---------------------------------------+--------------- x4/3o3x . . ♦ 24 | 24 24 0 0 | 6 12 0 0 8 0 0 0 0 | 80 * * * * * * * * * | 1 1 0 0 0 x4/3o . x . ♦ 8 | 8 0 4 0 | 2 0 4 0 0 0 0 0 0 | * 240 * * * * * * * * | 1 0 1 0 0 x4/3o . . *b3/2x ♦ 24 | 24 0 0 24 | 6 0 0 12 0 8 0 0 0 | * * 80 * * * * * * * | 0 1 1 0 0 x . x3x . ♦ 12 | 6 6 6 0 | 0 3 3 0 0 0 2 0 0 | * * * 320 * * * * * * | 1 0 0 1 0 x . x . x3*c ♦ 12 | 6 6 0 6 | 0 3 0 3 0 0 0 2 0 | * * * * 320 * * * * * | 0 1 0 1 0 x . . x x ♦ 8 | 4 0 4 4 | 0 0 2 2 0 0 0 0 2 | * * * * * 480 * * * * | 0 0 1 1 0 . o3x3x . ♦ 12 | 0 12 6 0 | 0 0 0 0 4 0 4 0 0 | * * * * * * 160 * * * | 1 0 0 0 1 . o3x . *b3/2x3*c ♦ 12 | 0 12 0 12 | 0 0 0 0 4 4 0 4 0 | * * * * * * * 160 * * | 0 1 0 0 1 . o . x *b3/2x ♦ 6 | 0 0 3 6 | 0 0 0 0 0 2 0 0 3 | * * * * * * * * 320 * | 0 0 1 0 1 . . x3x x3*c ♦ 24 | 0 12 12 12 | 0 0 0 0 0 0 4 4 6 | * * * * * * * * * 160 | 0 0 0 1 1 --------------------+------+--------------------+-------------------------------------+---------------------------------------+--------------- x4/3o3x3x . ♦ 192 | 192 192 96 0 | 48 96 96 0 64 0 64 0 0 | 8 24 0 32 0 0 16 0 0 0 | 10 * * * * x4/3o3x . *b3/2x3*c ♦ 192 | 192 192 0 192 | 48 96 0 96 64 64 0 64 0 | 8 0 8 0 32 0 0 16 0 0 | * 10 * * * x4/3o . x *b3/2x ♦ 48 | 48 0 24 48 | 12 0 24 24 0 16 0 0 24 | 0 6 2 0 0 12 0 0 8 0 | * * 40 * * x . x3x x3*c ♦ 48 | 24 24 24 24 | 0 12 12 12 0 0 8 8 12 | 0 0 0 4 4 6 0 0 0 2 | * * * 80 * . o3x3x *b3/2x3*c ♦ 60 | 0 60 30 60 | 0 0 0 0 20 20 20 20 30 | 0 0 0 0 0 0 5 5 10 5 | * * * * 32
4 3/2 3
x---o---x---x
3 \ / 3
x
x4o3/2x3x *b3x3*c . . . . . | 1920 | 2 2 1 2 | 1 2 2 2 1 1 2 2 2 | 1 1 1 2 2 2 1 1 1 2 | 1 1 1 2 1 ------------------+------+--------------------+-------------------------------------+---------------------------------------+--------------- x . . . . | 2 | 1920 * * * | 1 1 1 1 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0 . . x . . | 2 | * 1920 * * | 0 1 0 0 1 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . . . x . | 2 | * * 960 * | 0 0 2 0 0 0 2 0 2 | 0 1 0 2 0 2 1 0 1 2 | 1 0 1 2 1 . . . . x | 2 | * * * 1920 | 0 0 0 1 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 ------------------+------+--------------------+-------------------------------------+---------------------------------------+--------------- x4o . . . | 4 | 4 0 0 0 | 480 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 2 0 0 | * 960 * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 2 0 | * * 960 * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 2 | * * * 960 * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . o3/2x . . | 3 | 0 3 0 0 | * * * * 640 * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . o . . *b3x | 3 | 0 0 0 3 | * * * * * 640 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . x3x . | 6 | 0 3 3 0 | * * * * * * 640 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . . x . x3*c | 6 | 0 3 0 3 | * * * * * * * 640 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . x x | 4 | 0 0 2 2 | * * * * * * * * 960 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ------------------+------+--------------------+-------------------------------------+---------------------------------------+--------------- x4o3/2x . . ♦ 24 | 24 24 0 0 | 6 12 0 0 8 0 0 0 0 | 80 * * * * * * * * * | 1 1 0 0 0 x4o . x . ♦ 8 | 8 0 4 0 | 2 0 4 0 0 0 0 0 0 | * 240 * * * * * * * * | 1 0 1 0 0 x4o . . *b3x ♦ 24 | 24 0 0 24 | 6 0 0 12 0 8 0 0 0 | * * 80 * * * * * * * | 0 1 1 0 0 x . x3x . ♦ 12 | 6 6 6 0 | 0 3 3 0 0 0 2 0 0 | * * * 320 * * * * * * | 1 0 0 1 0 x . x . x3*c ♦ 12 | 6 6 0 6 | 0 3 0 3 0 0 0 2 0 | * * * * 320 * * * * * | 0 1 0 1 0 x . . x x ♦ 8 | 4 0 4 4 | 0 0 2 2 0 0 0 0 2 | * * * * * 480 * * * * | 0 0 1 1 0 . o3/2x3x . ♦ 12 | 0 12 6 0 | 0 0 0 0 4 0 4 0 0 | * * * * * * 160 * * * | 1 0 0 0 1 . o3/2x . *b3x3*c ♦ 12 | 0 12 0 12 | 0 0 0 0 4 4 0 4 0 | * * * * * * * 160 * * | 0 1 0 0 1 . o . x *b3x ♦ 6 | 0 0 3 6 | 0 0 0 0 0 2 0 0 3 | * * * * * * * * 320 * | 0 0 1 0 1 . . x3x x3*c ♦ 24 | 0 12 12 12 | 0 0 0 0 0 0 4 4 6 | * * * * * * * * * 160 | 0 0 0 1 1 ------------------+------+--------------------+-------------------------------------+---------------------------------------+--------------- x4o3/2x3x . ♦ 192 | 192 192 96 0 | 48 96 96 0 64 0 64 0 0 | 8 24 0 32 0 0 16 0 0 0 | 10 * * * * x4o3/2x . *b3x3*c ♦ 192 | 192 192 0 192 | 48 96 0 96 64 64 0 64 0 | 8 0 8 0 32 0 0 16 0 0 | * 10 * * * x4o . x *b3x ♦ 48 | 48 0 24 48 | 12 0 24 24 0 16 0 0 24 | 0 6 2 0 0 12 0 0 8 0 | * * 40 * * x . x3x x3*c ♦ 48 | 24 24 24 24 | 0 12 12 12 0 0 8 8 12 | 0 0 0 4 4 6 0 0 0 2 | * * * 80 * . o3/2x3x *b3x3*c ♦ 60 | 0 60 30 60 | 0 0 0 0 20 20 20 20 30 | 0 0 0 0 0 0 5 5 10 5 | * * * * 32
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