- general polytopal classes:
- Wythoffian polytera
links
| Acronym | roptit |
| Name | retoprismatotruncated triacontiditeron |
| Circumradius | sqrt(15/2) = 2.738613 |
| Colonel of regiment | pattit |
| Face vector | 960, 3360, 3360, 1120, 92 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
4 3 3
o---x---x---x
3 \ / 3/2
o
o4x3x3x *b3o3/2*c . . . . . | 960 | 4 2 1 | 2 4 4 2 2 1 | 2 2 1 4 2 2 1 | 2 1 1 2 ------------------+-----+--------------+-------------------------+--------------------------+------------ . x . . . | 2 | 1920 * * | 1 1 1 1 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 960 * | 0 2 0 0 1 1 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 480 | 0 0 4 0 2 0 | 0 2 0 4 0 2 1 | 2 0 1 2 ------------------+-----+--------------+-------------------------+--------------------------+------------ o4x . . . | 4 | 4 0 0 | 480 * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . *b3o | 3 | 3 0 0 | * * * 640 * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 | * * * * 320 * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . o3/2*c | 3 | 0 3 0 | * * * * * 320 | 0 0 0 0 2 0 1 | 0 1 0 2 ------------------+-----+--------------+-------------------------+--------------------------+------------ o4x3x . . ♦ 24 | 24 12 0 | 6 8 0 0 0 0 | 80 * * * * * * | 1 1 0 0 o4x . x . ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * 240 * * * * * | 1 0 1 0 o4x . . *b3o ♦ 12 | 24 0 0 | 6 0 0 8 0 0 | * * 80 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 | 0 4 6 0 4 0 | * * * 160 * * * | 1 0 0 1 . x3x . *b3o3/2*c ♦ 12 | 12 12 0 | 0 4 0 4 0 4 | * * * * 160 * * | 0 1 0 1 . x . x *b3o ♦ 6 | 6 0 3 | 0 0 3 2 0 0 | * * * * * 320 * | 0 0 1 1 . . x3x o3/2*c ♦ 12 | 0 12 6 | 0 0 0 0 4 4 | * * * * * * 80 | 0 0 0 2 ------------------+-----+--------------+-------------------------+--------------------------+------------ o4x3x3x . ♦ 192 | 192 96 96 | 48 64 96 0 32 0 | 8 24 0 16 0 0 0 | 10 * * * o4x3x . *b3o3/2*c ♦ 96 | 192 96 0 | 48 64 0 64 0 32 | 8 0 8 0 16 0 0 | * 10 * * o4x . x *b3o ♦ 24 | 48 0 12 | 12 0 24 16 0 0 | 0 6 2 0 0 8 0 | * * 40 * . x3x3x *b3o3/2*c ♦ 60 | 60 60 30 | 0 20 30 20 20 20 | 0 0 0 5 5 10 5 | * * * 32
4 3 3
o---x---x---x
3/2 \ / 3
o
o4x3x3x *b3/2o3*c . . . . . | 960 | 4 2 1 | 2 4 4 2 2 1 | 2 2 1 4 2 2 1 | 2 1 1 2 ------------------+-----+--------------+-------------------------+--------------------------+------------ . x . . . | 2 | 1920 * * | 1 1 1 1 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 960 * | 0 2 0 0 1 1 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 480 | 0 0 4 0 2 0 | 0 2 0 4 0 2 1 | 2 0 1 2 ------------------+-----+--------------+-------------------------+--------------------------+------------ o4x . . . | 4 | 4 0 0 | 480 * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . *b3/2o | 3 | 3 0 0 | * * * 640 * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 | * * * * 320 * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . o3*c | 3 | 0 3 0 | * * * * * 320 | 0 0 0 0 2 0 1 | 0 1 0 2 ------------------+-----+--------------+-------------------------+--------------------------+------------ o4x3x . . ♦ 24 | 24 12 0 | 6 8 0 0 0 0 | 80 * * * * * * | 1 1 0 0 o4x . x . ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * 240 * * * * * | 1 0 1 0 o4x . . *b3/2o ♦ 12 | 24 0 0 | 6 0 0 8 0 0 | * * 80 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 | 0 4 6 0 4 0 | * * * 160 * * * | 1 0 0 1 . x3x . *b3/2o3*c ♦ 12 | 12 12 0 | 0 4 0 4 0 4 | * * * * 160 * * | 0 1 0 1 . x . x *b3/2o ♦ 6 | 6 0 3 | 0 0 3 2 0 0 | * * * * * 320 * | 0 0 1 1 . . x3x o3*c ♦ 12 | 0 12 6 | 0 0 0 0 4 4 | * * * * * * 80 | 0 0 0 2 ------------------+-----+--------------+-------------------------+--------------------------+------------ o4x3x3x . ♦ 192 | 192 96 96 | 48 64 96 0 32 0 | 8 24 0 16 0 0 0 | 10 * * * o4x3x . *b3/2o3*c ♦ 96 | 192 96 0 | 48 64 0 64 0 32 | 8 0 8 0 16 0 0 | * 10 * * o4x . x *b3/2o ♦ 24 | 48 0 12 | 12 0 24 16 0 0 | 0 6 2 0 0 8 0 | * * 40 * . x3x3x *b3/2o3*c ♦ 60 | 60 60 30 | 0 20 30 20 20 20 | 0 0 0 5 5 10 5 | * * * 32
4/3 3 3
o---x---x---x
3 \ / 3/2
o
o4/3x3x3x *b3o3/2*c . . . . . | 960 | 4 2 1 | 2 4 4 2 2 1 | 2 2 1 4 2 2 1 | 2 1 1 2 --------------------+-----+--------------+-------------------------+--------------------------+------------ . x . . . | 2 | 1920 * * | 1 1 1 1 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 960 * | 0 2 0 0 1 1 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 480 | 0 0 4 0 2 0 | 0 2 0 4 0 2 1 | 2 0 1 2 --------------------+-----+--------------+-------------------------+--------------------------+------------ o4/3x . . . | 4 | 4 0 0 | 480 * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . *b3o | 3 | 3 0 0 | * * * 640 * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 | * * * * 320 * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . o3/2*c | 3 | 0 3 0 | * * * * * 320 | 0 0 0 0 2 0 1 | 0 1 0 2 --------------------+-----+--------------+-------------------------+--------------------------+------------ o4/3x3x . . ♦ 24 | 24 12 0 | 6 8 0 0 0 0 | 80 * * * * * * | 1 1 0 0 o4/3x . x . ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * 240 * * * * * | 1 0 1 0 o4/3x . . *b3o ♦ 12 | 24 0 0 | 6 0 0 8 0 0 | * * 80 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 | 0 4 6 0 4 0 | * * * 160 * * * | 1 0 0 1 . x3x . *b3o3/2*c ♦ 12 | 12 12 0 | 0 4 0 4 0 4 | * * * * 160 * * | 0 1 0 1 . x . x *b3o ♦ 6 | 6 0 3 | 0 0 3 2 0 0 | * * * * * 320 * | 0 0 1 1 . . x3x o3/2*c ♦ 12 | 0 12 6 | 0 0 0 0 4 4 | * * * * * * 80 | 0 0 0 2 --------------------+-----+--------------+-------------------------+--------------------------+------------ o4/3x3x3x . ♦ 192 | 192 96 96 | 48 64 96 0 32 0 | 8 24 0 16 0 0 0 | 10 * * * o4/3x3x . *b3o3/2*c ♦ 96 | 192 96 0 | 48 64 0 64 0 32 | 8 0 8 0 16 0 0 | * 10 * * o4/3x . x *b3o ♦ 24 | 48 0 12 | 12 0 24 16 0 0 | 0 6 2 0 0 8 0 | * * 40 * . x3x3x *b3o3/2*c ♦ 60 | 60 60 30 | 0 20 30 20 20 20 | 0 0 0 5 5 10 5 | * * * 32
4/3 3 3
o---x---x---x
3/2 \ / 3
o
o4/3x3x3x *b3/2o3*c . . . . . | 960 | 4 2 1 | 2 4 4 2 2 1 | 2 2 1 4 2 2 1 | 2 1 1 2 --------------------+-----+--------------+-------------------------+--------------------------+------------ . x . . . | 2 | 1920 * * | 1 1 1 1 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 960 * | 0 2 0 0 1 1 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 480 | 0 0 4 0 2 0 | 0 2 0 4 0 2 1 | 2 0 1 2 --------------------+-----+--------------+-------------------------+--------------------------+------------ o4/3x . . . | 4 | 4 0 0 | 480 * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . *b3/2o | 3 | 3 0 0 | * * * 640 * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 | * * * * 320 * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . o3*c | 3 | 0 3 0 | * * * * * 320 | 0 0 0 0 2 0 1 | 0 1 0 2 --------------------+-----+--------------+-------------------------+--------------------------+------------ o4/3x3x . . ♦ 24 | 24 12 0 | 6 8 0 0 0 0 | 80 * * * * * * | 1 1 0 0 o4/3x . x . ♦ 8 | 8 0 4 | 2 0 4 0 0 0 | * 240 * * * * * | 1 0 1 0 o4/3x . . *b3/2o ♦ 12 | 24 0 0 | 6 0 0 8 0 0 | * * 80 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 | 0 4 6 0 4 0 | * * * 160 * * * | 1 0 0 1 . x3x . *b3/2o3*c ♦ 12 | 12 12 0 | 0 4 0 4 0 4 | * * * * 160 * * | 0 1 0 1 . x . x *b3/2o ♦ 6 | 6 0 3 | 0 0 3 2 0 0 | * * * * * 320 * | 0 0 1 1 . . x3x o3*c ♦ 12 | 0 12 6 | 0 0 0 0 4 4 | * * * * * * 80 | 0 0 0 2 --------------------+-----+--------------+-------------------------+--------------------------+------------ o4/3x3x3x . ♦ 192 | 192 96 96 | 48 64 96 0 32 0 | 8 24 0 16 0 0 0 | 10 * * * o4/3x3x . *b3/2o3*c ♦ 96 | 192 96 0 | 48 64 0 64 0 32 | 8 0 8 0 16 0 0 | * 10 * * o4/3x . x *b3/2o ♦ 24 | 48 0 12 | 12 0 24 16 0 0 | 0 6 2 0 0 8 0 | * * 40 * . x3x3x *b3/2o3*c ♦ 60 | 60 60 30 | 0 20 30 20 20 20 | 0 0 0 5 5 10 5 | * * * 32
x
3 / 3
x---x
3 \ / \ 3
o---x
3/2 3
x3x3x3o3x3*b3/2*d . . . . . | 960 | 1 2 2 2 | 2 2 2 2 1 2 1 2 1 | 2 1 2 1 2 1 1 2 1 1 | 1 2 1 1 1 ------------------+-----+-----------------+-------------------------------------+----------------------------------+--------------- x . . . . | 2 | 480 * * * | 2 2 2 0 0 0 0 0 0 | 2 1 2 1 2 1 0 0 0 0 | 1 2 1 1 0 . x . . . | 2 | * 960 * * | 1 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 . . x . . | 2 | * * 960 * | 0 1 0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . . . . x | 2 | * * * 960 | 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 ------------------+-----+-----------------+-------------------------------------+----------------------------------+--------------- x3x . . . | 6 | 3 3 0 0 | 320 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 0 2 0 | * 480 * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 x . . . x | 4 | 2 0 0 2 | * * 480 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . x3x . . | 6 | 0 3 3 0 | * * * 320 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . o . *b3/2*d | 3 | 0 3 0 0 | * * * * 320 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . x3*b | 6 | 0 3 0 3 | * * * * * 320 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . x3o . | 3 | 0 0 3 0 | * * * * * * 320 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . . x . x | 4 | 0 0 2 2 | * * * * * * * 480 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . o3x | 3 | 0 0 0 3 | * * * * * * * * 320 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ------------------+-----+-----------------+-------------------------------------+----------------------------------+--------------- x3x3x . . ♦ 24 | 12 12 12 0 | 4 6 0 4 0 0 0 0 0 | 80 * * * * * * * * * | 1 1 0 0 0 x3x . o . *b3/2*d ♦ 12 | 6 12 0 0 | 4 0 0 0 4 0 0 0 0 | * 80 * * * * * * * * | 1 0 1 0 0 x3x . . x3*b ♦ 24 | 12 12 0 12 | 4 0 6 0 0 4 0 0 0 | * * 80 * * * * * * * | 0 1 1 0 0 x . x3o . ♦ 6 | 3 0 6 0 | 0 3 0 0 0 0 2 0 0 | * * * 160 * * * * * * | 1 0 0 1 0 x . x . x ♦ 8 | 4 0 4 4 | 0 2 2 0 0 0 0 2 0 | * * * * 240 * * * * * | 0 1 0 1 0 x . . o3x ♦ 6 | 3 0 0 6 | 0 0 3 0 0 0 0 0 2 | * * * * * 160 * * * * | 0 0 1 1 0 . x3x3o . *b3/2*d ♦ 12 | 0 12 12 0 | 0 0 0 4 4 0 4 0 0 | * * * * * * 80 * * * | 1 0 0 0 1 . x3x . x3*b ♦ 24 | 0 12 12 12 | 0 0 0 4 0 4 0 6 0 | * * * * * * * 80 * * | 0 1 0 0 1 . x . o3x3*b3/2*d ♦ 12 | 0 12 0 12 | 0 0 0 0 4 4 0 0 4 | * * * * * * * * 80 * | 0 0 1 0 1 . . x3o3x ♦ 12 | 0 0 12 12 | 0 0 0 0 0 0 4 6 4 | * * * * * * * * * 80 | 0 0 0 1 1 ------------------+-----+-----------------+-------------------------------------+----------------------------------+--------------- x3x3x3o . *b3/2*d ♦ 60 | 30 60 60 0 | 20 30 0 20 20 0 20 0 0 | 5 5 0 10 0 0 5 0 0 0 | 16 * * * * x3x3x . x3*b ♦ 192 | 96 96 96 96 | 32 48 48 32 0 32 0 48 0 | 8 0 8 0 24 0 0 8 0 0 | * 10 * * * x3x . o3x3*b3/2*d ♦ 60 | 30 60 0 60 | 20 0 30 0 20 20 0 0 20 | 0 5 5 0 0 10 0 0 5 0 | * * 16 * * x . x3o3x ♦ 24 | 12 0 24 24 | 0 12 12 0 0 0 8 12 8 | 0 0 0 4 6 4 0 0 0 2 | * * * 40 * . x3x3o3x3*b3/2*d ♦ 96 | 0 96 96 96 | 0 0 0 32 32 32 32 48 32 | 0 0 0 0 0 0 8 8 8 8 | * * * * 10
x
3 / 3
x---x
3/2 \ / \ 3
o---x
3 3/2
x3x3x3/2o3/2x3*b3*d . . . . . | 960 | 1 2 2 2 | 2 2 2 2 1 2 1 2 1 | 2 1 2 1 2 1 1 2 1 1 | 1 2 1 1 1 --------------------+-----+-----------------+-------------------------------------+----------------------------------+--------------- x . . . . | 2 | 480 * * * | 2 2 2 0 0 0 0 0 0 | 2 1 2 1 2 1 0 0 0 0 | 1 2 1 1 0 . x . . . | 2 | * 960 * * | 1 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 . . x . . | 2 | * * 960 * | 0 1 0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . . . . x | 2 | * * * 960 | 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 --------------------+-----+-----------------+-------------------------------------+----------------------------------+--------------- x3x . . . | 6 | 3 3 0 0 | 320 * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 0 2 0 | * 480 * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 x . . . x | 4 | 2 0 0 2 | * * 480 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . x3x . . | 6 | 0 3 3 0 | * * * 320 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . o . *b3*d | 3 | 0 3 0 0 | * * * * 320 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . x3*b | 6 | 0 3 0 3 | * * * * * 320 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . x3/2o . | 3 | 0 0 3 0 | * * * * * * 320 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . . x . x | 4 | 0 0 2 2 | * * * * * * * 480 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . o3/2x | 3 | 0 0 0 3 | * * * * * * * * 320 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 --------------------+-----+-----------------+-------------------------------------+----------------------------------+--------------- x3x3x . . ♦ 24 | 12 12 12 0 | 4 6 0 4 0 0 0 0 0 | 80 * * * * * * * * * | 1 1 0 0 0 x3x . o . *b3*d ♦ 12 | 6 12 0 0 | 4 0 0 0 4 0 0 0 0 | * 80 * * * * * * * * | 1 0 1 0 0 x3x . . x3*b ♦ 24 | 12 12 0 12 | 4 0 6 0 0 4 0 0 0 | * * 80 * * * * * * * | 0 1 1 0 0 x . x3/2o . ♦ 6 | 3 0 6 0 | 0 3 0 0 0 0 2 0 0 | * * * 160 * * * * * * | 1 0 0 1 0 x . x . x ♦ 8 | 4 0 4 4 | 0 2 2 0 0 0 0 2 0 | * * * * 240 * * * * * | 0 1 0 1 0 x . . o3/2x ♦ 6 | 3 0 0 6 | 0 0 3 0 0 0 0 0 2 | * * * * * 160 * * * * | 0 0 1 1 0 . x3x3/2o . *b3*d ♦ 12 | 0 12 12 0 | 0 0 0 4 4 0 4 0 0 | * * * * * * 80 * * * | 1 0 0 0 1 . x3x . x3*b ♦ 24 | 0 12 12 12 | 0 0 0 4 0 4 0 6 0 | * * * * * * * 80 * * | 0 1 0 0 1 . x . o3/2x3*b3*d ♦ 12 | 0 12 0 12 | 0 0 0 0 4 4 0 0 4 | * * * * * * * * 80 * | 0 0 1 0 1 . . x3/2o3/2x ♦ 12 | 0 0 12 12 | 0 0 0 0 0 0 4 6 4 | * * * * * * * * * 80 | 0 0 0 1 1 --------------------+-----+-----------------+-------------------------------------+----------------------------------+--------------- x3x3x3/2o . *b3*d ♦ 60 | 30 60 60 0 | 20 30 0 20 20 0 20 0 0 | 5 5 0 10 0 0 5 0 0 0 | 16 * * * * x3x3x . x3*b ♦ 192 | 96 96 96 96 | 32 48 48 32 0 32 0 48 0 | 8 0 8 0 24 0 0 8 0 0 | * 10 * * * x3x . o3/2x3*b3*d ♦ 60 | 30 60 0 60 | 20 0 30 0 20 20 0 0 20 | 0 5 5 0 0 10 0 0 5 0 | * * 16 * * x . x3/2o3/2x ♦ 24 | 12 0 24 24 | 0 12 12 0 0 0 8 12 8 | 0 0 0 4 6 4 0 0 0 2 | * * * 40 * . x3x3/2o3/2x3*b3*d ♦ 96 | 0 96 96 96 | 0 0 0 32 32 32 32 48 32 | 0 0 0 0 0 0 8 8 8 8 | * * * * 10
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