| Acronym | gaquacox |
| Name | great quasicellated hexeract |
| Circumradius | sqrt[(49-14 sqrt(2))/2] = 3.821061 |
| Coordinates | ((4 sqrt(2)-1)/2, (4 sqrt(2)-1)/2, (3 sqrt(2)-1)/2, (2 sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2) & all permutations, all changes of sign |
| Face vector | 23040, 69120, 77760, 40320, 9308, 668 |
| Confer |
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As abstract polypeton gaquacox is isomorphic to gocax, thereby replacing the octagrams by octagons, resp. replacing quitco by girco and stop by op, resp. replacing gaquidpoth by gidpith, histodip by hodip, quitcope by gircope, and tistodip by todip, resp. replacing gaquacint by gacnet, traquitco by tragirco, and stotut by otut.
Incidence matrix according to Dynkin symbol
o3x3x3x3x4/3x
. . . . . . | 23040 | 2 1 1 1 1 | 1 2 2 2 2 1 1 1 1 1 1 | 1 1 1 1 2 2 2 2 2 2 1 1 1 1 | 1 1 1 1 1 1 2 2 2 2 1 | 1 1 1 1 2
--------------+-------+-------------------------------+-----------------------------------------------------------+---------------------------------------------------------------------+----------------------------------------------+------------------
. x . . . . | 2 | 23040 * * * * | 1 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 | 1 1 1 1 1
. . x . . . | 2 | * 11520 * * * | 0 2 0 0 0 1 1 1 0 0 0 | 1 0 0 0 2 2 2 0 0 0 1 1 1 0 | 1 1 1 0 0 0 2 2 2 0 1 | 1 1 1 0 2
. . . x . . | 2 | * * 11520 * * | 0 0 2 0 0 1 0 0 1 1 0 | 0 1 0 0 2 0 0 2 2 0 1 1 0 1 | 1 0 0 1 1 0 2 2 0 2 1 | 1 1 0 1 2
. . . . x . | 2 | * * * 11520 * | 0 0 0 2 0 0 1 0 1 0 1 | 0 0 1 0 0 2 0 2 0 2 1 0 1 1 | 0 1 0 1 0 1 2 0 2 2 1 | 1 0 1 1 2
. . . . . x | 2 | * * * * 11520 | 0 0 0 0 2 0 0 1 0 1 1 | 0 0 0 1 0 0 2 0 2 2 0 1 1 1 | 0 0 1 0 1 1 0 2 2 2 1 | 0 1 1 1 2
--------------+-------+-------------------------------+-----------------------------------------------------------+---------------------------------------------------------------------+----------------------------------------------+------------------
o3x . . . . | 3 | 3 0 0 0 0 | 7680 * * * * * * * * * * | 1 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 | 1 1 1 1 0
. x3x . . . | 6 | 3 3 0 0 0 | * 7680 * * * * * * * * * | 1 0 0 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0 1 1 1 0 0 | 1 1 1 0 1
. x . x . . | 4 | 2 0 2 0 0 | * * 11520 * * * * * * * * | 0 1 0 0 1 0 0 1 1 0 0 0 0 0 | 1 0 0 1 1 0 1 1 0 1 0 | 1 1 0 1 1
. x . . x . | 4 | 2 0 0 2 0 | * * * 11520 * * * * * * * | 0 0 1 0 0 1 0 1 0 1 0 0 0 0 | 0 1 0 1 0 1 1 0 1 1 0 | 1 0 1 1 1
. x . . . x | 4 | 2 0 0 0 2 | * * * * 11520 * * * * * * | 0 0 0 1 0 0 1 0 1 1 0 0 0 0 | 0 0 1 0 1 1 0 1 1 1 0 | 0 1 1 1 1
. . x3x . . | 6 | 0 3 3 0 0 | * * * * * 3840 * * * * * | 0 0 0 0 2 0 0 0 0 0 1 1 0 0 | 1 0 0 0 0 0 2 2 0 0 1 | 1 1 0 0 2
. . x . x . | 4 | 0 2 0 2 0 | * * * * * * 5760 * * * * | 0 0 0 0 0 2 0 0 0 0 1 0 1 0 | 0 1 0 0 0 0 2 0 2 0 1 | 1 0 1 0 2
. . x . . x | 4 | 0 2 0 0 2 | * * * * * * * 5760 * * * | 0 0 0 0 0 0 2 0 0 0 0 1 1 0 | 0 0 1 0 0 0 0 2 2 0 1 | 0 1 1 0 2
. . . x3x . | 6 | 0 0 3 3 0 | * * * * * * * * 3840 * * | 0 0 0 0 0 0 0 2 0 0 1 0 0 1 | 0 0 0 1 0 0 2 0 0 2 1 | 1 0 0 1 2
. . . x . x | 4 | 0 0 2 0 2 | * * * * * * * * * 5760 * | 0 0 0 0 0 0 0 0 2 0 0 1 0 1 | 0 0 0 0 1 0 0 2 0 2 1 | 0 1 0 1 2
. . . . x4/3x | 8 | 0 0 0 4 4 | * * * * * * * * * * 2880 | 0 0 0 0 0 0 0 0 0 2 0 0 1 1 | 0 0 0 0 0 1 0 0 2 2 1 | 0 0 1 1 2 {8/3}
--------------+-------+-------------------------------+-----------------------------------------------------------+---------------------------------------------------------------------+----------------------------------------------+------------------
o3x3x . . . ♦ 12 | 12 6 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 | 1920 * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0
o3x . x . . ♦ 6 | 6 0 3 0 0 | 2 0 3 0 0 0 0 0 0 0 0 | * 3840 * * * * * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 0 | 1 1 0 1 0
o3x . . x . ♦ 6 | 6 0 0 3 0 | 2 0 0 3 0 0 0 0 0 0 0 | * * 3840 * * * * * * * * * * * | 0 1 0 1 0 1 0 0 0 0 0 | 1 0 1 1 0
o3x . . . x ♦ 6 | 6 0 0 0 3 | 2 0 0 0 3 0 0 0 0 0 0 | * * * 3840 * * * * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 | 0 1 1 1 0
. x3x3x . . ♦ 24 | 12 12 12 0 0 | 0 4 6 0 0 4 0 0 0 0 0 | * * * * 1920 * * * * * * * * * | 1 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 1
. x3x . x . ♦ 12 | 6 6 0 6 0 | 0 2 0 3 0 0 3 0 0 0 0 | * * * * * 3840 * * * * * * * * | 0 1 0 0 0 0 1 0 1 0 0 | 1 0 1 0 1
. x3x . . x ♦ 12 | 6 6 0 0 6 | 0 2 0 0 3 0 0 3 0 0 0 | * * * * * * 3840 * * * * * * * | 0 0 1 0 0 0 0 1 1 0 0 | 0 1 1 0 1
. x . x3x . ♦ 12 | 6 0 6 6 0 | 0 0 3 3 0 0 0 0 2 0 0 | * * * * * * * 3840 * * * * * * | 0 0 0 1 0 0 1 0 0 1 0 | 1 0 0 1 1
. x . x . x ♦ 8 | 4 0 4 0 4 | 0 0 2 0 2 0 0 0 0 2 0 | * * * * * * * * 5760 * * * * * | 0 0 0 0 1 0 0 1 0 1 0 | 0 1 0 1 1
. x . . x4/3x ♦ 16 | 8 0 0 8 8 | 0 0 0 4 4 0 0 0 0 0 2 | * * * * * * * * * 2880 * * * * | 0 0 0 0 0 1 0 0 1 1 0 | 0 0 1 1 1
. . x3x3x . ♦ 24 | 0 12 12 12 0 | 0 0 0 0 0 4 6 0 4 0 0 | * * * * * * * * * * 960 * * * | 0 0 0 0 0 0 2 0 0 0 1 | 1 0 0 0 2
. . x3x . x ♦ 12 | 0 6 6 0 6 | 0 0 0 0 0 2 0 3 0 3 0 | * * * * * * * * * * * 1920 * * | 0 0 0 0 0 0 0 2 0 0 1 | 0 1 0 0 2
. . x . x4/3x ♦ 16 | 0 8 0 8 8 | 0 0 0 0 0 0 4 4 0 0 2 | * * * * * * * * * * * * 1440 * | 0 0 0 0 0 0 0 0 2 0 1 | 0 0 1 0 2
. . . x3x4/3x ♦ 48 | 0 0 24 24 24 | 0 0 0 0 0 0 0 0 8 12 6 | * * * * * * * * * * * * * 480 | 0 0 0 0 0 0 0 0 0 2 1 | 0 0 0 1 2
--------------+-------+-------------------------------+-----------------------------------------------------------+---------------------------------------------------------------------+----------------------------------------------+------------------
o3x3x3x . . ♦ 60 | 60 30 30 0 0 | 20 20 30 0 0 10 0 0 0 0 0 | 5 10 0 0 5 0 0 0 0 0 0 0 0 0 | 384 * * * * * * * * * * | 1 1 0 0 0
o3x3x . x . ♦ 24 | 24 12 0 12 0 | 8 8 0 12 0 0 6 0 0 0 0 | 2 0 4 0 0 4 0 0 0 0 0 0 0 0 | * 960 * * * * * * * * * | 1 0 1 0 0
o3x3x . . x ♦ 24 | 24 12 0 0 12 | 8 8 0 0 12 0 0 6 0 0 0 | 2 0 0 4 0 0 4 0 0 0 0 0 0 0 | * * 960 * * * * * * * * | 0 1 1 0 0
o3x . x3x . ♦ 18 | 18 0 9 9 0 | 6 0 9 9 0 0 0 0 3 0 0 | 0 3 3 0 0 0 0 3 0 0 0 0 0 0 | * * * 1280 * * * * * * * | 1 0 0 1 0
o3x . x . x ♦ 12 | 12 0 6 0 6 | 4 0 6 0 6 0 0 0 0 3 0 | 0 2 0 2 0 0 0 0 3 0 0 0 0 0 | * * * * 1920 * * * * * * | 0 1 0 1 0
o3x . . x4/3x ♦ 24 | 24 0 0 12 12 | 8 0 0 12 12 0 0 0 0 0 3 | 0 0 4 4 0 0 0 0 0 3 0 0 0 0 | * * * * * 960 * * * * * | 0 0 1 1 0
. x3x3x3x . ♦ 120 | 60 60 60 60 0 | 0 20 30 30 0 20 30 0 20 0 0 | 0 0 0 0 5 10 0 10 0 0 5 0 0 0 | * * * * * * 384 * * * * | 1 0 0 0 1
. x3x3x . x ♦ 48 | 24 24 24 0 24 | 0 8 12 0 12 8 0 12 0 12 0 | 0 0 0 0 2 0 4 0 6 0 0 4 0 0 | * * * * * * * 960 * * * | 0 1 0 0 1
. x3x . x4/3x ♦ 48 | 24 24 0 24 24 | 0 8 0 12 12 0 12 12 0 0 6 | 0 0 0 0 0 4 4 0 0 3 0 0 3 0 | * * * * * * * * 960 * * | 0 0 1 0 1
. x . x3x4/3x ♦ 96 | 48 0 48 48 48 | 0 0 24 24 24 0 0 0 16 24 12 | 0 0 0 0 0 0 0 8 12 6 0 0 0 2 | * * * * * * * * * 480 * | 0 0 0 1 1
. . x3x3x4/3x ♦ 384 | 0 192 192 192 192 | 0 0 0 0 0 64 96 96 64 96 48 | 0 0 0 0 0 0 0 0 0 0 16 32 24 8 | * * * * * * * * * * 60 | 0 0 0 0 2
--------------+-------+-------------------------------+-----------------------------------------------------------+---------------------------------------------------------------------+----------------------------------------------+------------------
o3x3x3x3x . ♦ 360 | 360 180 180 180 0 | 120 120 180 180 0 60 90 0 60 0 0 | 30 60 60 0 30 60 0 60 0 0 15 0 0 0 | 6 15 0 20 0 0 6 0 0 0 0 | 64 * * * *
o3x3x3x . x ♦ 120 | 120 60 60 0 60 | 40 40 60 0 60 20 0 30 0 30 0 | 10 20 0 20 10 0 20 0 30 0 0 10 0 0 | 2 0 5 0 10 0 0 5 0 0 0 | * 192 * * *
o3x3x . x4/3x ♦ 96 | 96 48 0 48 48 | 32 32 0 48 48 0 24 24 0 0 12 | 8 0 16 16 0 16 16 0 0 12 0 0 6 0 | 0 4 4 0 0 4 0 0 4 0 0 | * * 240 * *
o3x . x3x4/3x ♦ 144 | 144 0 72 72 72 | 48 0 72 72 72 0 0 0 24 36 18 | 0 24 24 24 0 0 0 24 36 18 0 0 0 3 | 0 0 0 8 12 6 0 0 0 3 0 | * * * 160 *
. x3x3x3x4/3x ♦ 3840 | 1920 1920 1920 1920 1920 | 0 640 960 960 960 640 960 960 640 960 480 | 0 0 0 0 160 320 320 320 480 240 160 320 240 80 | 0 0 0 0 0 0 32 80 80 40 10 | * * * * 12
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