| Acronym | ratkus |
| Name | retroteriskewed hepteract |
| Circumradius | sqrt(11)/2 = 1.658312 |
| Face vector | 5376, 40320, 106400, 143360, 101752, 32032, 1752 |
| Confer |
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As abstract polytope ratkus is isomorphic to takus, thereby replacing octagons by octagrams, resp. op by stop and socco by gocco, resp. todip by tistodip, soccope by goccope, and steth by gittith, resp otet by stotet, trasocco by tragocco, stethip by gittithip, and sinnont by ginnont, resp. quitoxog by stoxog, open by stopen, tetsocco by tetgocco, trasteth by tragittith, sinnontip by ginnontip, and soxaxog by goxaxog.
Incidence matrix according to Dynkin symbol
x3o3o3o3o3x4x4/3*e . . . . . . . | 5376 | 5 5 5 | 10 20 20 10 10 5 | 10 30 30 30 30 20 10 10 10 | 5 20 20 30 30 30 20 20 30 5 5 10 | 1 5 5 10 10 20 10 10 30 5 5 20 1 1 5 | 1 1 5 10 10 5 1 -------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------- x . . . . . . | 2 | 13440 * * | 4 4 4 0 0 0 | 6 12 12 6 6 4 0 0 0 | 4 12 12 12 12 12 4 4 6 0 0 0 | 1 4 4 6 6 12 4 4 12 1 1 4 0 0 0 | 1 1 4 6 4 1 0 . . . . . x . | 2 | * 13440 * | 0 4 0 4 0 1 | 0 6 0 12 0 4 6 0 4 | 0 4 0 12 0 6 12 0 12 4 0 6 | 0 1 0 4 0 4 6 0 12 4 0 12 1 0 4 | 1 0 1 4 6 4 1 . . . . . . x | 2 | * * 13440 | 0 0 4 0 4 1 | 0 0 6 0 12 4 0 6 4 | 0 0 4 0 12 6 0 12 12 0 4 6 | 0 0 1 0 4 4 0 6 12 0 4 12 0 1 4 | 0 1 1 4 6 4 1 -------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------- x3o . . . . . | 3 | 3 0 0 | 17920 * * * * * | 3 3 3 0 0 0 0 0 0 | 3 6 6 3 3 3 0 0 0 0 0 0 | 1 3 3 3 3 6 1 1 3 0 0 0 0 0 0 | 1 1 3 3 1 0 0 x . . . . x . | 4 | 2 2 0 | * 26880 * * * * | 0 3 0 3 0 1 0 0 0 | 0 3 0 6 0 3 3 0 3 0 0 0 | 0 1 0 3 0 3 3 0 6 1 0 3 0 0 0 | 1 0 1 3 3 1 0 x . . . . . x | 4 | 2 0 2 | * * 26880 * * * | 0 0 3 0 3 1 0 0 0 | 0 0 3 0 6 3 0 3 3 0 0 0 | 0 0 1 0 3 3 0 3 6 0 1 3 0 0 0 | 0 1 1 3 3 1 0 . . . . o3x . | 3 | 0 3 0 | * * * 17920 * * | 0 0 0 3 0 0 3 0 1 | 0 0 0 3 0 0 6 0 3 3 0 3 | 0 0 0 1 0 0 3 0 3 3 0 6 1 0 3 | 1 0 0 1 3 3 1 . . . . o . x4/3*e | 4 | 0 0 4 | * * * * 13440 * | 0 0 0 0 3 0 0 3 1 | 0 0 0 0 3 0 0 6 3 0 3 3 | 0 0 0 0 1 0 0 3 3 0 3 6 0 1 3 | 0 1 0 1 3 3 1 . . . . . x4x | 8 | 0 4 4 | * * * * * 3360 | 0 0 0 0 0 4 0 0 4 | 0 0 0 0 0 6 0 0 12 0 0 6 | 0 0 0 0 0 4 0 0 12 0 0 12 0 0 4 | 0 0 1 4 6 4 1 -------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------- x3o3o . . . . ♦ 4 | 6 0 0 | 4 0 0 0 0 0 | 13440 * * * * * * * * | 2 2 2 0 0 0 0 0 0 0 0 0 | 1 2 2 1 1 2 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0 x3o . . . x . ♦ 6 | 6 3 0 | 2 3 0 0 0 0 | * 26880 * * * * * * * | 0 2 0 2 0 1 0 0 0 0 0 0 | 0 1 0 2 0 2 1 0 2 0 0 0 0 0 0 | 1 0 1 2 1 0 0 x3o . . . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * * 26880 * * * * * * | 0 0 2 0 2 1 0 0 0 0 0 0 | 0 0 1 0 2 2 0 1 2 0 0 0 0 0 0 | 0 1 1 2 1 0 0 x . . . o3x . ♦ 6 | 3 6 0 | 0 3 0 2 0 0 | * * * 26880 * * * * * | 0 0 0 2 0 0 2 0 1 0 0 0 | 0 0 0 1 0 0 2 0 2 1 0 2 0 0 0 | 1 0 0 1 2 1 0 x . . . o . x4/3*e ♦ 8 | 4 0 8 | 0 0 4 0 2 0 | * * * * 20160 * * * * | 0 0 0 0 2 0 0 2 1 0 0 0 | 0 0 0 0 1 0 0 2 2 0 1 2 0 0 0 | 0 1 0 1 2 1 0 x . . . . x4x ♦ 16 | 8 8 8 | 0 4 4 0 0 2 | * * * * * 6720 * * * | 0 0 0 0 0 3 0 0 3 0 0 0 | 0 0 0 0 0 3 0 0 6 0 0 3 0 0 0 | 0 0 1 3 3 1 0 . . . o3o3x . ♦ 4 | 0 6 0 | 0 0 0 4 0 0 | * * * * * * 13440 * * | 0 0 0 0 0 0 2 0 0 2 0 1 | 0 0 0 0 0 0 1 0 0 2 0 2 1 0 2 | 1 0 0 0 1 2 1 . . . o3o . x4/3*e ♦ 8 | 0 0 12 | 0 0 0 0 6 0 | * * * * * * * 6720 * | 0 0 0 0 0 0 0 2 0 0 2 1 | 0 0 0 0 0 0 0 1 0 0 2 2 0 1 2 | 0 1 0 0 1 2 1 . . . . o3x4x4/3*e ♦ 24 | 0 24 24 | 0 0 0 8 6 6 | * * * * * * * * 2240 | 0 0 0 0 0 0 0 0 3 0 0 3 | 0 0 0 0 0 0 0 0 3 0 0 6 0 0 3 | 0 0 0 1 3 3 1 -------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------- x3o3o3o . . . ♦ 5 | 10 0 0 | 10 0 0 0 0 0 | 5 0 0 0 0 0 0 0 0 | 5376 * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 x3o3o . . x . ♦ 8 | 12 4 0 | 8 6 0 0 0 0 | 2 4 0 0 0 0 0 0 0 | * 13440 * * * * * * * * * * | 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 0 x3o3o . . . x ♦ 8 | 12 0 4 | 8 0 6 0 0 0 | 2 0 4 0 0 0 0 0 0 | * * 13440 * * * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 x3o . . o3x . ♦ 9 | 9 9 0 | 3 9 0 3 0 0 | 0 3 0 3 0 0 0 0 0 | * * * 17920 * * * * * * * * | 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 | 1 0 0 1 1 0 0 x3o . . o . x4/3*e ♦ 12 | 12 0 12 | 4 0 12 0 3 0 | 0 0 4 0 3 0 0 0 0 | * * * * 13440 * * * * * * * | 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 | 0 1 0 1 1 0 0 x3o . . . x4x ♦ 24 | 24 12 12 | 8 12 12 0 0 3 | 0 4 4 0 0 3 0 0 0 | * * * * * 6720 * * * * * * | 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 | 0 0 1 2 1 0 0 x . . o3o3x . ♦ 8 | 4 12 0 | 0 6 0 8 0 0 | 0 0 0 4 0 0 2 0 0 | * * * * * * 13440 * * * * * | 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 | 1 0 0 0 1 1 0 x . . o3o . x4/3*e ♦ 16 | 8 0 24 | 0 0 12 0 12 0 | 0 0 0 0 6 0 0 2 0 | * * * * * * * 6720 * * * * | 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 | 0 1 0 0 1 1 0 x . . . o3x4x4/3*e ♦ 48 | 24 48 48 | 0 24 24 16 12 12 | 0 0 0 8 6 6 0 0 2 | * * * * * * * * 3360 * * * | 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 | 0 0 0 1 2 1 0 . . o3o3o3x . ♦ 5 | 0 10 0 | 0 0 0 10 0 0 | 0 0 0 0 0 0 5 0 0 | * * * * * * * * * 5376 * * | 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 | 1 0 0 0 0 1 1 . . o3o3o . x4/3*e ♦ 16 | 0 0 32 | 0 0 0 0 24 0 | 0 0 0 0 0 0 0 8 0 | * * * * * * * * * * 1680 * | 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 | 0 1 0 0 0 1 1 . . . o3o3x4x4/3*e ♦ 64 | 0 96 96 | 0 0 0 64 48 24 | 0 0 0 0 0 0 16 8 8 | * * * * * * * * * * * 840 | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 | 0 0 0 0 1 2 1 -------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------- x3o3o3o3o . . ♦ 6 | 15 0 0 | 20 0 0 0 0 0 | 15 0 0 0 0 0 0 0 0 | 6 0 0 0 0 0 0 0 0 0 0 0 | 896 * * * * * * * * * * * * * * | 1 1 0 0 0 0 0 x3o3o3o . x . ♦ 10 | 20 5 0 | 20 10 0 0 0 0 | 10 10 0 0 0 0 0 0 0 | 2 5 0 0 0 0 0 0 0 0 0 0 | * 2688 * * * * * * * * * * * * * | 1 0 1 0 0 0 0 x3o3o3o . . x ♦ 10 | 20 0 5 | 20 0 10 0 0 0 | 10 0 10 0 0 0 0 0 0 | 2 0 5 0 0 0 0 0 0 0 0 0 | * * 2688 * * * * * * * * * * * * | 0 1 1 0 0 0 0 x3o3o . o3x . ♦ 12 | 18 12 0 | 12 18 0 4 0 0 | 3 12 0 6 0 0 0 0 0 | 0 3 0 4 0 0 0 0 0 0 0 0 | * * * 4480 * * * * * * * * * * * | 1 0 0 1 0 0 0 x3o3o . o . x4/3*e ♦ 16 | 24 0 16 | 16 0 24 0 4 0 | 4 0 16 0 6 0 0 0 0 | 0 0 4 0 4 0 0 0 0 0 0 0 | * * * * 3360 * * * * * * * * * * | 0 1 0 1 0 0 0 x3o3o . . x4x ♦ 32 | 48 16 16 | 32 24 24 0 0 4 | 8 16 16 0 0 6 0 0 0 | 0 4 4 0 0 4 0 0 0 0 0 0 | * * * * * 3360 * * * * * * * * * | 0 0 1 1 0 0 0 x3o . o3o3x . ♦ 12 | 12 18 0 | 4 18 0 12 0 0 | 0 6 0 12 0 0 3 0 0 | 0 0 0 4 0 0 3 0 0 0 0 0 | * * * * * * 4480 * * * * * * * * | 1 0 0 0 1 0 0 x3o . o3o . x4/3*e ♦ 24 | 24 0 36 | 8 0 36 0 18 0 | 0 0 12 0 18 0 0 3 0 | 0 0 0 0 6 0 0 3 0 0 0 0 | * * * * * * * 2240 * * * * * * * | 0 1 0 0 1 0 0 x3o . . o3x4x4/3*e ♦ 72 | 72 72 72 | 24 72 72 24 18 18 | 0 24 24 24 18 18 0 0 3 | 0 0 0 8 6 6 0 0 3 0 0 0 | * * * * * * * * 2240 * * * * * * | 0 0 0 1 1 0 0 x . o3o3o3x . ♦ 10 | 5 20 0 | 0 10 0 20 0 0 | 0 0 0 10 0 0 10 0 0 | 0 0 0 0 0 0 5 0 0 2 0 0 | * * * * * * * * * 2688 * * * * * | 1 0 0 0 0 1 0 x . o3o3o . x4/3*e ♦ 32 | 16 0 64 | 0 0 32 0 48 0 | 0 0 0 0 24 0 0 16 0 | 0 0 0 0 0 0 0 8 0 0 2 0 | * * * * * * * * * * 840 * * * * | 0 1 0 0 0 1 0 x . . o3o3x4x4/3*e ♦ 128 | 64 192 192 | 0 96 96 128 96 48 | 0 0 0 64 48 24 32 16 16 | 0 0 0 0 0 0 16 8 8 0 0 2 | * * * * * * * * * * * 840 * * * | 0 0 0 0 1 1 0 . o3o3o3o3x . ♦ 6 | 0 15 0 | 0 0 0 20 0 0 | 0 0 0 0 0 0 15 0 0 | 0 0 0 0 0 0 0 0 0 6 0 0 | * * * * * * * * * * * * 896 * * | 1 0 0 0 0 0 1 . o3o3o3o . x4/3*e ♦ 32 | 0 0 80 | 0 0 0 0 80 0 | 0 0 0 0 0 0 0 40 0 | 0 0 0 0 0 0 0 0 0 0 10 0 | * * * * * * * * * * * * * 168 * | 0 1 0 0 0 0 1 . . o3o3o3x4x4/3*e ♦ 160 | 0 320 320 | 0 0 0 320 240 80 | 0 0 0 0 0 0 160 80 40 | 0 0 0 0 0 0 0 0 0 32 10 10 | * * * * * * * * * * * * * * 168 | 0 0 0 0 0 1 1 -------------------+------+-------------------+------------------------------------+----------------------------------------------------+-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------- x3o3o3o3o3x . ♦ 42 | 105 105 0 | 140 210 0 140 0 0 | 105 210 0 210 0 0 105 0 0 | 42 105 0 140 0 0 105 0 0 42 0 0 | 7 21 0 35 0 0 35 0 0 21 0 0 7 0 0 | 128 * * * * * * x3o3o3o3o . x4/3*e ♦ 384 | 960 0 960 | 1280 0 1920 0 960 0 | 960 0 1920 0 1440 0 0 480 0 | 384 0 960 0 960 0 0 480 0 0 120 0 | 64 0 192 0 240 0 0 160 0 0 60 0 0 12 0 | * 14 * * * * * x3o3o3o . x4x ♦ 40 | 80 20 20 | 80 40 40 0 0 5 | 40 40 40 0 0 10 0 0 0 | 8 20 20 0 0 10 0 0 0 0 0 0 | 0 4 4 0 0 5 0 0 0 0 0 0 0 0 0 | * * 672 * * * * x3o3o . o3x4x4/3*e ♦ 96 | 144 96 96 | 96 144 144 32 24 24 | 24 96 96 48 36 36 0 0 4 | 0 24 24 32 24 24 0 0 6 0 0 0 | 0 0 0 8 6 6 0 0 4 0 0 0 0 0 0 | * * * 560 * * * x3o . o3o3x4x4/3*e ♦ 192 | 192 288 288 | 64 288 288 192 144 72 | 0 96 96 192 144 72 48 24 24 | 0 0 0 64 48 24 48 24 24 0 0 3 | 0 0 0 0 0 0 16 8 8 0 0 3 0 0 0 | * * * * 280 * * x . o3o3o3x4x4/3*e ♦ 320 | 160 640 640 | 0 320 320 640 480 160 | 0 0 0 320 240 80 320 160 80 | 0 0 0 0 0 0 160 80 40 64 20 20 | 0 0 0 0 0 0 0 0 0 32 10 10 0 0 2 | * * * * * 84 * . o3o3o3o3x4x4/3*e ♦ 384 | 0 960 960 | 0 0 0 1280 960 240 | 0 0 0 0 0 0 960 480 160 | 0 0 0 0 0 0 0 0 0 384 120 60 | 0 0 0 0 0 0 0 0 0 0 0 0 64 12 12 | * * * * * * 14
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