| Acronym | skevatant |
| Name | small skewverted trispenteractitriacontaditeron |
| Circumradius | sqrt[11+2 sqrt(2)]/2 = 1.859330 |
| Coordinates | (1+sqrt(2), 1+sqrt(2), sqrt(2)-1, 1, 1)/2 & all permutations, all changes of sign |
| Colonel of regiment | skivbadant |
| Face vector | 960, 3840, 3200, 760, 62 |
| Confer |
|
As abstract polyteron skevatant is isomorph to gakevatant, thereby interchanging the roles of octagrams and octagons, resp. replacing tic by quith and interchanging the roles of socco and gocco, resp. replacing thatoth by thaquitoth and rawvatoth by wavitoth.
Incidence matrix according to Dynkin symbol
_x
_- /|
_3- 4/3 |
_- / |
o---3---x<---4---x 3
-_ \ |
3/2 4 |
-_ \|
-o
o3x4x4/3x3o3/2*b3*d *c4*e
. . . . . | 960 | 4 2 2 | 2 4 4 2 2 1 1 | 2 2 1 4 2 2 1 | 2 1 1 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 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2
. . . x . | 2 | * * 960 | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2
--------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3x . . . | 3 | 3 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x4x . . | 8 | 4 4 0 | * 480 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 {8}
. x . x . *b3*d | 6 | 3 0 3 | * * 640 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1
. x . . o3/2*b | 3 | 3 0 0 | * * * 640 * * * | 0 0 1 0 1 1 0 | 0 1 1 1
. . x4/3x . | 8 | 0 4 4 | * * * * 240 * * | 0 0 0 2 0 0 1 | 1 0 0 2 {8/3}
. . x . o *c4*e | 4 | 0 4 0 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2
. . . x3o | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 0 2 1 | 0 0 1 2
--------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3x4x . . ♦ 24 | 24 12 0 | 8 6 0 0 0 0 0 | 80 * * * * * * | 1 1 0 0
o3x . x . *b3*d ♦ 12 | 12 0 6 | 4 0 4 0 0 0 0 | * 160 * * * * * | 1 0 1 0
o3x . . o3/2*b ♦ 6 | 12 0 0 | 4 0 0 4 0 0 0 | * * 160 * * * * | 0 1 1 0
. x4x4/3x . *b3*d ♦ 48 | 24 24 24 | 0 6 8 0 6 0 0 | * * * 80 * * * | 1 0 0 1
. x4x . o3/2*b *c4*e ♦ 24 | 24 24 0 | 0 6 0 8 0 6 0 | * * * * 80 * * | 0 1 0 1
. x . x3o3/2*b3*d ♦ 12 | 12 0 12 | 0 0 4 4 0 0 4 | * * * * * 160 * | 0 0 1 1
. . x4/3x3o *c4*e ♦ 24 | 0 24 24 | 0 0 0 0 6 6 8 | * * * * * * 40 | 0 0 0 2
--------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3x4x4/3x . *b3*d ♦ 192 | 192 96 96 | 64 48 64 0 24 0 0 | 8 16 0 8 0 0 0 | 10 * * *
o3x4x . o3/2*b *c4*e ♦ 96 | 192 96 0 | 64 48 0 64 0 24 0 | 8 0 16 0 8 0 0 | * 10 * *
o3x . x3o3/2*b3*d ♦ 30 | 60 0 30 | 20 0 20 20 0 0 10 | 0 5 5 0 0 5 0 | * * 32 *
. x4x4/3x3o3/2*b3*d *c4*e ♦ 192 | 192 192 192 | 0 48 64 64 48 48 64 | 0 0 0 8 8 16 8 | * * * 10
_x
_- /|
_3- 4/3 |
_- / |
o---3---x<---4---x 3/2
-_ \ |
-3_ 4/3 |
-_ \|
-o
o3x4x4/3x3/2o3*b3*d *c4/3*e
. . . . . | 960 | 4 2 2 | 2 4 4 2 2 1 1 | 2 2 1 4 2 2 1 | 2 1 1 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 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2
. . . x . | 2 | * * 960 | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2
----------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3x . . . | 3 | 3 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x4x . . | 8 | 4 4 0 | * 480 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 {8}
. x . x . *b3*d | 6 | 3 0 3 | * * 640 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1
. x . . o3*b | 3 | 3 0 0 | * * * 640 * * * | 0 0 1 0 1 1 0 | 0 1 1 1
. . x4/3x . | 8 | 0 4 4 | * * * * 240 * * | 0 0 0 2 0 0 1 | 1 0 0 2 {8/3}
. . x . o *c4/3*e | 4 | 0 4 0 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2
. . . x3/2o | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 0 2 1 | 0 0 1 2
----------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3x4x . . ♦ 24 | 24 12 0 | 8 6 0 0 0 0 0 | 80 * * * * * * | 1 1 0 0
o3x . x . *b3*d ♦ 12 | 12 0 6 | 4 0 4 0 0 0 0 | * 160 * * * * * | 1 0 1 0
o3x . . o3*b ♦ 6 | 12 0 0 | 4 0 0 4 0 0 0 | * * 160 * * * * | 0 1 1 0
. x4x4/3x . *b3*d ♦ 48 | 24 24 24 | 0 6 8 0 6 0 0 | * * * 80 * * * | 1 0 0 1
. x4x . o3*b *c4/3*e ♦ 24 | 24 24 0 | 0 6 0 8 0 6 0 | * * * * 80 * * | 0 1 0 1
. x . x3/2o3*b3*d ♦ 12 | 12 0 12 | 0 0 4 4 0 0 4 | * * * * * 160 * | 0 0 1 1
. . x4/3x3/2o *c4/3*e ♦ 24 | 0 24 24 | 0 0 0 0 6 6 8 | * * * * * * 40 | 0 0 0 2
----------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3x4x4/3x . *b3*d ♦ 192 | 192 96 96 | 64 48 64 0 24 0 0 | 8 16 0 8 0 0 0 | 10 * * *
o3x4x . o3*b *c4/3*e ♦ 96 | 192 96 0 | 64 48 0 64 0 24 0 | 8 0 16 0 8 0 0 | * 10 * *
o3x . x3/2o3*b3*d ♦ 30 | 60 0 30 | 20 0 20 20 0 0 10 | 0 5 5 0 0 5 0 | * * 32 *
. x4x4/3x3/2o3*b3*d *c4/3*e ♦ 192 | 192 192 192 | 0 48 64 64 48 48 64 | 0 0 0 8 8 16 8 | * * * 10
_x
_- /|
_3- 4/3 |
_- / |
o--3/2--x<---4---x 3
-_ \ |
3/2 4 |
-_ \|
-o
o3/2x4x4/3x3o3/2*b3*d *c4*e
. . . . . | 960 | 4 2 2 | 2 4 4 2 2 1 1 | 2 2 1 4 2 2 1 | 2 1 1 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 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2
. . . x . | 2 | * * 960 | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2
----------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3/2x . . . | 3 | 3 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x4x . . | 8 | 4 4 0 | * 480 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 {8}
. x . x . *b3*d | 6 | 3 0 3 | * * 640 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1
. x . . o3/2*b | 3 | 3 0 0 | * * * 640 * * * | 0 0 1 0 1 1 0 | 0 1 1 1
. . x4/3x . | 8 | 0 4 4 | * * * * 240 * * | 0 0 0 2 0 0 1 | 1 0 0 2 {8/3}
. . x . o *c4*e | 4 | 0 4 0 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2
. . . x3o | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 0 2 1 | 0 0 1 2
----------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3/2x4x . . ♦ 24 | 24 12 0 | 8 6 0 0 0 0 0 | 80 * * * * * * | 1 1 0 0
o3/2x . x . *b3*d ♦ 12 | 12 0 6 | 4 0 4 0 0 0 0 | * 160 * * * * * | 1 0 1 0
o3/2x . . o3/2*b ♦ 6 | 12 0 0 | 4 0 0 4 0 0 0 | * * 160 * * * * | 0 1 1 0
. x4x4/3x . *b3*d ♦ 48 | 24 24 24 | 0 6 8 0 6 0 0 | * * * 80 * * * | 1 0 0 1
. x4x . o3/2*b *c4*e ♦ 24 | 24 24 0 | 0 6 0 8 0 6 0 | * * * * 80 * * | 0 1 0 1
. x . x3o3/2*b3*d ♦ 12 | 12 0 12 | 0 0 4 4 0 0 4 | * * * * * 160 * | 0 0 1 1
. . x4/3x3o *c4*e ♦ 24 | 0 24 24 | 0 0 0 0 6 6 8 | * * * * * * 40 | 0 0 0 2
----------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3/2x4x4/3x . *b3*d ♦ 192 | 192 96 96 | 64 48 64 0 24 0 0 | 8 16 0 8 0 0 0 | 10 * * *
o3/2x4x . o3/2*b *c4*e ♦ 96 | 192 96 0 | 64 48 0 64 0 24 0 | 8 0 16 0 8 0 0 | * 10 * *
o3/2x . x3o3/2*b3*d ♦ 30 | 60 0 30 | 20 0 20 20 0 0 10 | 0 5 5 0 0 5 0 | * * 32 *
. x4x4/3x3o3/2*b3*d *c4*e ♦ 192 | 192 192 192 | 0 48 64 64 48 48 64 | 0 0 0 8 8 16 8 | * * * 10
_x
_- /|
_3- 4/3 |
_- / |
o--3/2--x<---4---x 3/2
-_ \ |
-3_ 4/3 |
-_ \|
-o
o3/2x4x4/3x3/2o3*b3*d *c4/3*e
. . . . . | 960 | 4 2 2 | 2 4 4 2 2 1 1 | 2 2 1 4 2 2 1 | 2 1 1 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 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2
. . . x . | 2 | * * 960 | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2
------------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3/2x . . . | 3 | 3 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x4x . . | 8 | 4 4 0 | * 480 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 {8}
. x . x . *b3*d | 6 | 3 0 3 | * * 640 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1
. x . . o3*b | 3 | 3 0 0 | * * * 640 * * * | 0 0 1 0 1 1 0 | 0 1 1 1
. . x4/3x . | 8 | 0 4 4 | * * * * 240 * * | 0 0 0 2 0 0 1 | 1 0 0 2 {8/3}
. . x . o *c4/3*e | 4 | 0 4 0 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2
. . . x3/2o | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 0 2 1 | 0 0 1 2
------------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3/2x4x . . ♦ 24 | 24 12 0 | 8 6 0 0 0 0 0 | 80 * * * * * * | 1 1 0 0
o3/2x . x . *b3*d ♦ 12 | 12 0 6 | 4 0 4 0 0 0 0 | * 160 * * * * * | 1 0 1 0
o3/2x . . o3*b ♦ 6 | 12 0 0 | 4 0 0 4 0 0 0 | * * 160 * * * * | 0 1 1 0
. x4x4/3x . *b3*d ♦ 48 | 24 24 24 | 0 6 8 0 6 0 0 | * * * 80 * * * | 1 0 0 1
. x4x . o3*b *c4/3*e ♦ 24 | 24 24 0 | 0 6 0 8 0 6 0 | * * * * 80 * * | 0 1 0 1
. x . x3/2o3*b3*d ♦ 12 | 12 0 12 | 0 0 4 4 0 0 4 | * * * * * 160 * | 0 0 1 1
. . x4/3x3/2o *c4/3*e ♦ 24 | 0 24 24 | 0 0 0 0 6 6 8 | * * * * * * 40 | 0 0 0 2
------------------------------+-----+--------------+-----------------------------+-------------------------+------------
o3/2x4x4/3x . *b3*d ♦ 192 | 192 96 96 | 64 48 64 0 24 0 0 | 8 16 0 8 0 0 0 | 10 * * *
o3/2x4x . o3*b *c4/3*e ♦ 96 | 192 96 0 | 64 48 0 64 0 24 0 | 8 0 16 0 8 0 0 | * 10 * *
o3/2x . x3/2o3*b3*d ♦ 30 | 60 0 30 | 20 0 20 20 0 0 10 | 0 5 5 0 0 5 0 | * * 32 *
. x4x4/3x3/2o3*b3*d *c4/3*e ♦ 192 | 192 192 192 | 0 48 64 64 48 48 64 | 0 0 0 8 8 16 8 | * * * 10
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