| Acronym | groptin |
| Name | great retroprismatotruncated penteract |
| Circumradius | sqrt[25-12 sqrt(2)]/2 = 1.416813 |
| Coordinates | (2 sqrt(2)-1, 2 sqrt(2)-1, sqrt(2)-1, sqrt(2)-1, 1)/2 & all permutations, all changes of sign |
| Colonel of regiment | quiptin |
| Face vector | 960, 3360, 3440, 1240, 132 |
| Confer |
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As abstract polyteron groptin is isomorphic to sroptin, thereby replacing octagrams by octagons, resp. quitco by girco and quith by tic, resp. gaqrit by grit and giphado by siphado.
Incidence matrix according to Dynkin symbol
4/3 3 3
x---x---x---o
3 \ / 3/2
o
x4/3x3x3o *b3o3/2*c
. . . . . | 960 | 1 2 4 | 2 4 4 1 2 2 | 4 1 2 2 2 2 1 | 2 2 1 1
--------------------+-----+--------------+-------------------------+---------------------------+------------
x . . . . | 2 | 480 * * | 2 4 0 0 0 0 | 4 1 2 2 0 0 0 | 2 2 1 0
. x . . . | 2 | * 960 * | 1 0 2 1 0 0 | 2 1 0 0 1 2 0 | 1 2 0 1
. . x . . | 2 | * * 1920 | 0 1 1 0 1 1 | 1 0 1 1 1 1 1 | 1 1 1 1
--------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x . . . | 8 | 4 4 0 | 240 * * * * * | 2 1 0 0 0 0 0 | 1 2 0 0 {8/3}
x . x . . | 4 | 2 0 2 | * 960 * * * * | 1 0 1 1 0 0 0 | 1 1 1 0
. x3x . . | 6 | 0 3 3 | * * 640 * * * | 1 0 0 0 1 1 0 | 1 1 0 1
. x . . *b3o | 3 | 0 3 0 | * * * 320 * * | 0 1 0 0 0 2 0 | 0 2 0 1
. . x3o . | 3 | 0 0 3 | * * * * 640 * | 0 0 1 0 1 0 1 | 1 0 1 1
. . x . o3/2*c | 3 | 0 0 3 | * * * * * 640 | 0 0 0 1 0 1 1 | 0 1 1 1
--------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x3x . . ♦ 48 | 24 24 24 | 6 12 8 0 0 0 | 80 * * * * * * | 1 1 0 0
x4/3x . . *b3o ♦ 24 | 12 24 0 | 6 0 0 8 0 0 | * 40 * * * * * | 0 2 0 0
x . x3o . ♦ 6 | 3 0 6 | 0 3 0 0 2 0 | * * 320 * * * * | 1 0 1 0
x . x . o3/2*c ♦ 6 | 3 0 6 | 0 3 0 0 0 2 | * * * 320 * * * | 0 1 1 0
. x3x3o . ♦ 12 | 0 6 12 | 0 0 4 0 4 0 | * * * * 160 * * | 1 0 0 1
. x3x . *b3o3/2*c ♦ 12 | 0 12 12 | 0 0 4 4 0 4 | * * * * * 160 * | 0 1 0 1
. . x3o o3/2*c ♦ 6 | 0 0 12 | 0 0 0 0 4 4 | * * * * * * 160 | 0 0 1 1
--------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x3x3o . ♦ 192 | 96 96 192 | 24 96 64 0 64 0 | 8 0 32 0 16 0 0 | 10 * * *
x4/3x3x . *b3o3/2*c ♦ 192 | 96 192 192 | 48 96 64 64 0 64 | 8 8 0 32 0 16 0 | * 10 * *
x . x3o o3/2*c ♦ 12 | 6 0 24 | 0 12 0 0 8 8 | 0 0 4 4 0 0 2 | * * 80 *
. x3x3o *b3o3/2*c ♦ 30 | 0 30 60 | 0 0 20 10 20 20 | 0 0 0 0 5 5 5 | * * * 32
4/3 3 3
x---x---x---o
3/2 \ / 3
o
x4/3x3x3o *b3/2o3*c
. . . . . | 960 | 1 2 4 | 2 4 4 1 2 2 | 4 1 2 2 2 2 1 | 2 2 1 1
--------------------+-----+--------------+-------------------------+---------------------------+------------
x . . . . | 2 | 480 * * | 2 4 0 0 0 0 | 4 1 2 2 0 0 0 | 2 2 1 0
. x . . . | 2 | * 960 * | 1 0 2 1 0 0 | 2 1 0 0 1 2 0 | 1 2 0 1
. . x . . | 2 | * * 1920 | 0 1 1 0 1 1 | 1 0 1 1 1 1 1 | 1 1 1 1
--------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x . . . | 8 | 4 4 0 | 240 * * * * * | 2 1 0 0 0 0 0 | 1 2 0 0 {8/3}
x . x . . | 4 | 2 0 2 | * 960 * * * * | 1 0 1 1 0 0 0 | 1 1 1 0
. x3x . . | 6 | 0 3 3 | * * 640 * * * | 1 0 0 0 1 1 0 | 1 1 0 1
. x . . *b3/2o | 3 | 0 3 0 | * * * 320 * * | 0 1 0 0 0 2 0 | 0 2 0 1
. . x3o . | 3 | 0 0 3 | * * * * 640 * | 0 0 1 0 1 0 1 | 1 0 1 1
. . x . o3*c | 3 | 0 0 3 | * * * * * 640 | 0 0 0 1 0 1 1 | 0 1 1 1
--------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x3x . . ♦ 48 | 24 24 24 | 6 12 8 0 0 0 | 80 * * * * * * | 1 1 0 0
x4/3x . . *b3/2o ♦ 24 | 12 24 0 | 6 0 0 8 0 0 | * 40 * * * * * | 0 2 0 0
x . x3o . ♦ 6 | 3 0 6 | 0 3 0 0 2 0 | * * 320 * * * * | 1 0 1 0
x . x . o3*c ♦ 6 | 3 0 6 | 0 3 0 0 0 2 | * * * 320 * * * | 0 1 1 0
. x3x3o . ♦ 12 | 0 6 12 | 0 0 4 0 4 0 | * * * * 160 * * | 1 0 0 1
. x3x . *b3/2o3*c ♦ 12 | 0 12 12 | 0 0 4 4 0 4 | * * * * * 160 * | 0 1 0 1
. . x3o o3*c ♦ 6 | 0 0 12 | 0 0 0 0 4 4 | * * * * * * 160 | 0 0 1 1
--------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x3x3o . ♦ 192 | 96 96 192 | 24 96 64 0 64 0 | 8 0 32 0 16 0 0 | 10 * * *
x4/3x3x . *b3/2o3*c ♦ 192 | 96 192 192 | 48 96 64 64 0 64 | 8 8 0 32 0 16 0 | * 10 * *
x . x3o o3*c ♦ 12 | 6 0 24 | 0 12 0 0 8 8 | 0 0 4 4 0 0 2 | * * 80 *
. x3x3o *b3/2o3*c ♦ 30 | 0 30 60 | 0 0 20 10 20 20 | 0 0 0 0 5 5 5 | * * * 32
4/3 3 3/2
x---x---x---o
3 \ / 3/2
o
x4/3x3x3/2o *b3o3/2*c
. . . . . | 960 | 1 2 4 | 2 4 4 1 2 2 | 4 1 2 2 2 2 1 | 2 2 1 1
----------------------+-----+--------------+-------------------------+---------------------------+------------
x . . . . | 2 | 480 * * | 2 4 0 0 0 0 | 4 1 2 2 0 0 0 | 2 2 1 0
. x . . . | 2 | * 960 * | 1 0 2 1 0 0 | 2 1 0 0 1 2 0 | 1 2 0 1
. . x . . | 2 | * * 1920 | 0 1 1 0 1 1 | 1 0 1 1 1 1 1 | 1 1 1 1
----------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x . . . | 8 | 4 4 0 | 240 * * * * * | 2 1 0 0 0 0 0 | 1 2 0 0 {8/3}
x . x . . | 4 | 2 0 2 | * 960 * * * * | 1 0 1 1 0 0 0 | 1 1 1 0
. x3x . . | 6 | 0 3 3 | * * 640 * * * | 1 0 0 0 1 1 0 | 1 1 0 1
. x . . *b3o | 3 | 0 3 0 | * * * 320 * * | 0 1 0 0 0 2 0 | 0 2 0 1
. . x3/2o . | 3 | 0 0 3 | * * * * 640 * | 0 0 1 0 1 0 1 | 1 0 1 1
. . x . o3/2*c | 3 | 0 0 3 | * * * * * 640 | 0 0 0 1 0 1 1 | 0 1 1 1
----------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x3x . . ♦ 48 | 24 24 24 | 6 12 8 0 0 0 | 80 * * * * * * | 1 1 0 0
x4/3x . . *b3o ♦ 24 | 12 24 0 | 6 0 0 8 0 0 | * 40 * * * * * | 0 2 0 0
x . x3/2o . ♦ 6 | 3 0 6 | 0 3 0 0 2 0 | * * 320 * * * * | 1 0 1 0
x . x . o3/2*c ♦ 6 | 3 0 6 | 0 3 0 0 0 2 | * * * 320 * * * | 0 1 1 0
. x3x3/2o . ♦ 12 | 0 6 12 | 0 0 4 0 4 0 | * * * * 160 * * | 1 0 0 1
. x3x . *b3o3/2*c ♦ 12 | 0 12 12 | 0 0 4 4 0 4 | * * * * * 160 * | 0 1 0 1
. . x3/2o o3/2*c ♦ 6 | 0 0 12 | 0 0 0 0 4 4 | * * * * * * 160 | 0 0 1 1
----------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x3x3/2o . ♦ 192 | 96 96 192 | 24 96 64 0 64 0 | 8 0 32 0 16 0 0 | 10 * * *
x4/3x3x . *b3o3/2*c ♦ 192 | 96 192 192 | 48 96 64 64 0 64 | 8 8 0 32 0 16 0 | * 10 * *
x . x3/2o o3/2*c ♦ 12 | 6 0 24 | 0 12 0 0 8 8 | 0 0 4 4 0 0 2 | * * 80 *
. x3x3/2o *b3o3/2*c ♦ 30 | 0 30 60 | 0 0 20 10 20 20 | 0 0 0 0 5 5 5 | * * * 32
4/3 3 3/2
x---x---x---o
3/2 \ / 3
o
x4/3x3x3/2o *b3/2o3*c
. . . . . | 960 | 1 2 4 | 2 4 4 1 2 2 | 4 1 2 2 2 2 1 | 2 2 1 1
----------------------+-----+--------------+-------------------------+---------------------------+------------
x . . . . | 2 | 480 * * | 2 4 0 0 0 0 | 4 1 2 2 0 0 0 | 2 2 1 0
. x . . . | 2 | * 960 * | 1 0 2 1 0 0 | 2 1 0 0 1 2 0 | 1 2 0 1
. . x . . | 2 | * * 1920 | 0 1 1 0 1 1 | 1 0 1 1 1 1 1 | 1 1 1 1
----------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x . . . | 8 | 4 4 0 | 240 * * * * * | 2 1 0 0 0 0 0 | 1 2 0 0 {8/3}
x . x . . | 4 | 2 0 2 | * 960 * * * * | 1 0 1 1 0 0 0 | 1 1 1 0
. x3x . . | 6 | 0 3 3 | * * 640 * * * | 1 0 0 0 1 1 0 | 1 1 0 1
. x . . *b3/2o | 3 | 0 3 0 | * * * 320 * * | 0 1 0 0 0 2 0 | 0 2 0 1
. . x3/2o . | 3 | 0 0 3 | * * * * 640 * | 0 0 1 0 1 0 1 | 1 0 1 1
. . x . o3*c | 3 | 0 0 3 | * * * * * 640 | 0 0 0 1 0 1 1 | 0 1 1 1
----------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x3x . . ♦ 48 | 24 24 24 | 6 12 8 0 0 0 | 80 * * * * * * | 1 1 0 0
x4/3x . . *b3/2o ♦ 24 | 12 24 0 | 6 0 0 8 0 0 | * 40 * * * * * | 0 2 0 0
x . x3/2o . ♦ 6 | 3 0 6 | 0 3 0 0 2 0 | * * 320 * * * * | 1 0 1 0
x . x . o3*c ♦ 6 | 3 0 6 | 0 3 0 0 0 2 | * * * 320 * * * | 0 1 1 0
. x3x3/2o . ♦ 12 | 0 6 12 | 0 0 4 0 4 0 | * * * * 160 * * | 1 0 0 1
. x3x . *b3/2o3*c ♦ 12 | 0 12 12 | 0 0 4 4 0 4 | * * * * * 160 * | 0 1 0 1
. . x3/2o o3*c ♦ 6 | 0 0 12 | 0 0 0 0 4 4 | * * * * * * 160 | 0 0 1 1
----------------------+-----+--------------+-------------------------+---------------------------+------------
x4/3x3x3/2o . ♦ 192 | 96 96 192 | 24 96 64 0 64 0 | 8 0 32 0 16 0 0 | 10 * * *
x4/3x3x . *b3/2o3*c ♦ 192 | 96 192 192 | 48 96 64 64 0 64 | 8 8 0 32 0 16 0 | * 10 * *
x . x3/2o o3*c ♦ 12 | 6 0 24 | 0 12 0 0 8 8 | 0 0 4 4 0 0 2 | * * 80 *
. x3x3/2o *b3/2o3*c ♦ 30 | 0 30 60 | 0 0 20 10 20 20 | 0 0 0 0 5 5 5 | * * * 32
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