- general polytopal classes:
- Wythoffian polytera
links
| Acronym | gakvebidant (old: gikkivbadant) |
| Name | great skewverted biprismatodispenteractitriacontaditeron |
| Circumradius | sqrt[11-2 sqrt(2)]/2 = 1.429298 |
| Coordinates | (1+sqrt(2), sqrt(2)-1, sqrt(2)-1, 1, 1)/2 & all permutations, all changes of sign |
| Colonel of regiment | gikvacadint |
| Face vector | 960, 3840, 4000, 1320, 132 |
| Confer |
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External links |
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As abstract polytope gakvebidant is isomorphic to skivbadant, thereby replacing octagons by octagrams, resp. querco by sirco, op by stop, and socco by gocco, resp. qrit by srit, todip by tistodip and gikviphado by skiviphado. – As such gakvebidant is a lieutenant.
Incidence matrix according to Dynkin symbol
3 3 3
x---o---x---o
4 \ / 4/3
x
o3x3o3x4x4/3*c
. . . . . | 960 | 4 2 2 | 2 2 4 4 1 1 2 | 1 2 2 2 2 4 1 | 1 1 2 2
---------------+-----+--------------+-----------------------------+---------------------------+------------
. x . . . | 2 | 1920 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1
. . . x . | 2 | * 960 * | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2
. . . . x | 2 | * * 960 | 0 0 0 2 0 1 1 | 0 0 1 0 2 2 1 | 0 1 1 2
---------------+-----+--------------+-----------------------------+---------------------------+------------
o3x . . . | 3 | 3 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x3o . . | 3 | 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1
. x . x . | 4 | 2 2 0 | * * 960 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1
. x . . x | 4 | 2 0 2 | * * * 960 * * * | 0 0 1 0 1 1 0 | 0 1 1 1
. . o3x . | 3 | 0 3 0 | * * * * 320 * * | 0 0 0 2 0 0 1 | 1 0 0 2
. . o . x4/3*c | 4 | 0 0 4 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2
. . . x4x | 8 | 0 4 4 | * * * * * * 240 | 0 0 0 0 0 2 1 | 0 0 1 2 {8}
---------------+-----+--------------+-----------------------------+---------------------------+------------
o3x3o . . ♦ 6 | 12 0 0 | 4 4 0 0 0 0 0 | 160 * * * * * * | 1 1 0 0
o3x . x . ♦ 6 | 6 3 0 | 2 0 3 0 0 0 0 | * 320 * * * * * | 1 0 1 0
o3x . . x ♦ 6 | 6 0 3 | 2 0 0 3 0 0 0 | * * 320 * * * * | 0 1 1 0
. x3o3x . ♦ 12 | 12 12 0 | 0 4 6 0 4 0 0 | * * * 160 * * * | 1 0 0 1
. x3o . x4/3*c ♦ 24 | 24 0 24 | 0 8 0 12 0 6 0 | * * * * 80 * * | 0 1 0 1
. x . x4x ♦ 16 | 8 8 8 | 0 0 4 4 0 0 2 | * * * * * 240 * | 0 0 1 1
. . o3x4x4/3*c ♦ 24 | 0 24 24 | 0 0 0 0 8 6 6 | * * * * * * 40 | 0 0 0 2
---------------+-----+--------------+-----------------------------+---------------------------+------------
o3x3o3x . ♦ 30 | 60 30 0 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 32 * * *
o3x3o . x4/3*c ♦ 96 | 192 0 96 | 64 64 0 96 0 24 0 | 16 0 32 0 8 0 0 | * 10 * *
o3x . x4x ♦ 24 | 24 12 12 | 8 0 12 12 0 0 3 | 0 4 4 0 0 3 0 | * * 80 *
. x3o3x4x4/3*c ♦ 192 | 192 192 192 | 0 64 96 96 64 48 48 | 0 0 0 16 8 24 8 | * * * 10
3/2 3/2 3
x---o---x---o
4 \ / 4
x
o3x3/2o3/2x4x4*c
. . . . . | 960 | 4 2 2 | 2 2 4 4 1 1 2 | 1 2 2 2 2 4 1 | 1 1 2 2
-----------------+-----+--------------+-----------------------------+---------------------------+------------
. x . . . | 2 | 1920 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1
. . . x . | 2 | * 960 * | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2
. . . . x | 2 | * * 960 | 0 0 0 2 0 1 1 | 0 0 1 0 2 2 1 | 0 1 1 2
-----------------+-----+--------------+-----------------------------+---------------------------+------------
o3x . . . | 3 | 3 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x3/2o . . | 3 | 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1
. x . x . | 4 | 2 2 0 | * * 960 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1
. x . . x | 4 | 2 0 2 | * * * 960 * * * | 0 0 1 0 1 1 0 | 0 1 1 1
. . o3/2x . | 3 | 0 3 0 | * * * * 320 * * | 0 0 0 2 0 0 1 | 1 0 0 2
. . o . x4*c | 4 | 0 0 4 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2
. . . x4x | 8 | 0 4 4 | * * * * * * 240 | 0 0 0 0 0 2 1 | 0 0 1 2 {8}
-----------------+-----+--------------+-----------------------------+---------------------------+------------
o3x3/2o . . ♦ 6 | 12 0 0 | 4 4 0 0 0 0 0 | 160 * * * * * * | 1 1 0 0
o3x . x . ♦ 6 | 6 3 0 | 2 0 3 0 0 0 0 | * 320 * * * * * | 1 0 1 0
o3x . . x ♦ 6 | 6 0 3 | 2 0 0 3 0 0 0 | * * 320 * * * * | 0 1 1 0
. x3/2o3/2x . ♦ 12 | 12 12 0 | 0 4 6 0 4 0 0 | * * * 160 * * * | 1 0 0 1
. x3/2o . x4*c ♦ 24 | 24 0 24 | 0 8 0 12 0 6 0 | * * * * 80 * * | 0 1 0 1
. x . x4x ♦ 16 | 8 8 8 | 0 0 4 4 0 0 2 | * * * * * 240 * | 0 0 1 1
. . o3/2x4x4*c ♦ 24 | 0 24 24 | 0 0 0 0 8 6 6 | * * * * * * 40 | 0 0 0 2
-----------------+-----+--------------+-----------------------------+---------------------------+------------
o3x3/2o3/2x . ♦ 30 | 60 30 0 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 32 * * *
o3x3/2o . x4*c ♦ 96 | 192 0 96 | 64 64 0 96 0 24 0 | 16 0 32 0 8 0 0 | * 10 * *
o3x . x4x ♦ 24 | 24 12 12 | 8 0 12 12 0 0 3 | 0 4 4 0 0 3 0 | * * 80 *
. x3/2o3/2x4x4*c ♦ 192 | 192 192 192 | 0 64 96 96 64 48 48 | 0 0 0 16 8 24 8 | * * * 10
3 3 3/2
x---o---x---o
4 \ / 4/3
x
o3/2x3o3x4x4/3*c
. . . . . | 960 | 4 2 2 | 2 2 4 4 1 1 2 | 1 2 2 2 2 4 1 | 1 1 2 2
-----------------+-----+--------------+-----------------------------+---------------------------+------------
. x . . . | 2 | 1920 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1
. . . x . | 2 | * 960 * | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2
. . . . x | 2 | * * 960 | 0 0 0 2 0 1 1 | 0 0 1 0 2 2 1 | 0 1 1 2
-----------------+-----+--------------+-----------------------------+---------------------------+------------
o3/2x . . . | 3 | 3 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x3o . . | 3 | 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1
. x . x . | 4 | 2 2 0 | * * 960 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1
. x . . x | 4 | 2 0 2 | * * * 960 * * * | 0 0 1 0 1 1 0 | 0 1 1 1
. . o3x . | 3 | 0 3 0 | * * * * 320 * * | 0 0 0 2 0 0 1 | 1 0 0 2
. . o . x4/3*c | 4 | 0 0 4 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2
. . . x4x | 8 | 0 4 4 | * * * * * * 240 | 0 0 0 0 0 2 1 | 0 0 1 2 {8}
-----------------+-----+--------------+-----------------------------+---------------------------+------------
o3/2x3o . . ♦ 6 | 12 0 0 | 4 4 0 0 0 0 0 | 160 * * * * * * | 1 1 0 0
o3/2x . x . ♦ 6 | 6 3 0 | 2 0 3 0 0 0 0 | * 320 * * * * * | 1 0 1 0
o3/2x . . x ♦ 6 | 6 0 3 | 2 0 0 3 0 0 0 | * * 320 * * * * | 0 1 1 0
. x3o3x . ♦ 12 | 12 12 0 | 0 4 6 0 4 0 0 | * * * 160 * * * | 1 0 0 1
. x3o . x4/3*c ♦ 24 | 24 0 24 | 0 8 0 12 0 6 0 | * * * * 80 * * | 0 1 0 1
. x . x4x ♦ 16 | 8 8 8 | 0 0 4 4 0 0 2 | * * * * * 240 * | 0 0 1 1
. . o3x4x4/3*c ♦ 24 | 0 24 24 | 0 0 0 0 8 6 6 | * * * * * * 40 | 0 0 0 2
-----------------+-----+--------------+-----------------------------+---------------------------+------------
o3/2x3o3x . ♦ 30 | 60 30 0 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 32 * * *
o3/2x3o . x4/3*c ♦ 96 | 192 0 96 | 64 64 0 96 0 24 0 | 16 0 32 0 8 0 0 | * 10 * *
o3/2x . x4x ♦ 24 | 24 12 12 | 8 0 12 12 0 0 3 | 0 4 4 0 0 3 0 | * * 80 *
. x3o3x4x4/3*c ♦ 192 | 192 192 192 | 0 64 96 96 64 48 48 | 0 0 0 16 8 24 8 | * * * 10
3/2 3/2 3/2
x---o---x---o
4 \ / 4
x
o/23x3/2o3/2x4x4*c
. . . . . | 960 | 4 2 2 | 2 2 4 4 1 1 2 | 1 2 2 2 2 4 1 | 1 1 2 2
-------------------+-----+--------------+-----------------------------+---------------------------+------------
. x . . . | 2 | 1920 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1
. . . x . | 2 | * 960 * | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2
. . . . x | 2 | * * 960 | 0 0 0 2 0 1 1 | 0 0 1 0 2 2 1 | 0 1 1 2
-------------------+-----+--------------+-----------------------------+---------------------------+------------
o3/2x . . . | 3 | 3 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x3/2o . . | 3 | 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1
. x . x . | 4 | 2 2 0 | * * 960 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1
. x . . x | 4 | 2 0 2 | * * * 960 * * * | 0 0 1 0 1 1 0 | 0 1 1 1
. . o3/2x . | 3 | 0 3 0 | * * * * 320 * * | 0 0 0 2 0 0 1 | 1 0 0 2
. . o . x4*c | 4 | 0 0 4 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2
. . . x4x | 8 | 0 4 4 | * * * * * * 240 | 0 0 0 0 0 2 1 | 0 0 1 2 {8}
-------------------+-----+--------------+-----------------------------+---------------------------+------------
o3/2x3/2o . . ♦ 6 | 12 0 0 | 4 4 0 0 0 0 0 | 160 * * * * * * | 1 1 0 0
o3/2x . x . ♦ 6 | 6 3 0 | 2 0 3 0 0 0 0 | * 320 * * * * * | 1 0 1 0
o3/2x . . x ♦ 6 | 6 0 3 | 2 0 0 3 0 0 0 | * * 320 * * * * | 0 1 1 0
. x3/2o3/2x . ♦ 12 | 12 12 0 | 0 4 6 0 4 0 0 | * * * 160 * * * | 1 0 0 1
. x3/2o . x4*c ♦ 24 | 24 0 24 | 0 8 0 12 0 6 0 | * * * * 80 * * | 0 1 0 1
. x . x4x ♦ 16 | 8 8 8 | 0 0 4 4 0 0 2 | * * * * * 240 * | 0 0 1 1
. . o3/2x4x4*c ♦ 24 | 0 24 24 | 0 0 0 0 8 6 6 | * * * * * * 40 | 0 0 0 2
-------------------+-----+--------------+-----------------------------+---------------------------+------------
o3/2x3/2o3/2x . ♦ 30 | 60 30 0 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 32 * * *
o3/2x3/2o . x4*c ♦ 96 | 192 0 96 | 64 64 0 96 0 24 0 | 16 0 32 0 8 0 0 | * 10 * *
o3/2x . x4x ♦ 24 | 24 12 12 | 8 0 12 12 0 0 3 | 0 4 4 0 0 3 0 | * * 80 *
. x3/2o3/2x4x4*c ♦ 192 | 192 192 192 | 0 64 96 96 64 48 48 | 0 0 0 16 8 24 8 | * * * 10
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