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| Acronym | sircarn |
| Name | small retrocellirhombated penteract |
| Circumradius | sqrt[17+8 sqrt(2)]/2 = 2.660531 |
| Coordinates | (1+2 sqrt(2), 1+sqrt(2), 1+sqrt(2), 1, 1)/2 & all permutations, all changes of sign |
| General of army | carnit |
| Colonel of regiment | carnit |
| Face vector | 960, 3840, 4400, 1760, 212 |
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As abstract polytope sircarn is isomorph to qracorn, thereby replacing sirco by querco, resp. prit by paqrit and srit by qrit.
Incidence matrix according to Dynkin symbol
3 3 4
x---x---o---x
3 \ / 3/2
o
x4o3x3x3o3/2*c . . . . . | 960 | 2 4 2 | 1 4 4 2 4 2 1 | 2 2 4 2 2 2 1 2 | 2 1 1 2 1 ---------------+-----+--------------+-----------------------------+--------------------------------+--------------- x . . . . | 2 | 960 * * | 1 2 2 0 0 0 0 | 2 2 2 1 1 0 0 0 | 2 1 1 1 0 . . x . . | 2 | * 1920 * | 0 1 0 1 1 1 0 | 1 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . x . | 2 | * * 960 | 0 0 2 0 2 0 1 | 0 1 2 0 2 1 0 2 | 1 0 1 2 1 ---------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4o . . . | 4 | 4 0 0 | 240 * * * * * * | 2 2 0 0 0 0 0 0 | 2 1 1 0 0 x . x . . | 4 | 2 2 0 | * 960 * * * * * | 1 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 2 | * * 960 * * * * | 0 1 1 0 1 0 0 0 | 1 0 1 1 0 . o3x . . | 3 | 0 3 0 | * * * 640 * * * | 1 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3x . | 6 | 0 3 3 | * * * * 640 * * | 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . o3/2*c | 3 | 0 3 0 | * * * * * 640 * | 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x3o | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 2 0 0 2 | 0 0 1 2 1 ---------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4o3x . . ♦ 24 | 24 24 0 | 6 12 0 8 0 0 0 | 80 * * * * * * * | 1 1 0 0 0 x4o . x . ♦ 8 | 8 0 4 | 2 0 4 0 0 0 0 | * 240 * * * * * * | 1 0 1 0 0 x . x3x . ♦ 12 | 6 6 6 | 0 3 3 0 2 0 0 | * * 320 * * * * * | 1 0 0 1 0 x . x . o3/2*c ♦ 6 | 3 6 0 | 0 3 0 0 0 2 0 | * * * 320 * * * * | 0 1 0 1 0 x . . x3o ♦ 6 | 3 0 6 | 0 0 3 0 0 0 2 | * * * * 320 * * * | 0 0 1 1 0 . o3x3x . ♦ 12 | 0 12 6 | 0 0 0 4 4 0 0 | * * * * * 160 * * | 1 0 0 0 1 . o3x . o3/2*c ♦ 6 | 0 12 0 | 0 0 0 4 0 4 0 | * * * * * * 160 * | 0 1 0 0 1 . . x3x3o3/2*c ♦ 12 | 0 12 12 | 0 0 0 0 4 4 4 | * * * * * * * 160 | 0 0 0 1 1 ---------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4o3x3x . ♦ 192 | 192 192 96 | 48 96 96 64 64 0 0 | 8 24 32 0 0 16 0 0 | 10 * * * * x4o3x . o3/2*c ♦ 96 | 96 192 0 | 24 96 0 64 0 64 0 | 8 0 0 32 0 0 16 0 | * 10 * * * x4o . x3o ♦ 12 | 12 0 12 | 3 0 12 0 0 0 4 | 0 3 0 0 4 0 0 0 | * * 80 * * x . x3x3o3/2*c ♦ 24 | 12 24 24 | 0 12 12 0 8 8 8 | 0 0 4 4 4 0 0 2 | * * * 80 * . o3x3x3o3/2*c ♦ 30 | 0 60 30 | 0 0 0 20 20 20 10 | 0 0 0 0 0 5 5 5 | * * * * 32
4 3 3
x---o---x---x
3 \ / 3/2
o
x4o3x3x3/2o3/2*c . . . . . | 960 | 2 4 2 | 1 4 4 2 4 2 1 | 2 2 4 2 2 2 1 2 | 2 1 1 2 1 ---------------+-----+--------------+-----------------------------+--------------------------------+--------------- x . . . . | 2 | 960 * * | 1 2 2 0 0 0 0 | 2 2 2 1 1 0 0 0 | 2 1 1 1 0 . . x . . | 2 | * 1920 * | 0 1 0 1 1 1 0 | 1 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . x . | 2 | * * 960 | 0 0 2 0 2 0 1 | 0 1 2 0 2 1 0 2 | 1 0 1 2 1 ---------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4o . . . | 4 | 4 0 0 | 240 * * * * * * | 2 2 0 0 0 0 0 0 | 2 1 1 0 0 x . x . . | 4 | 2 2 0 | * 960 * * * * * | 1 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 2 | * * 960 * * * * | 0 1 1 0 1 0 0 0 | 1 0 1 1 0 . o3x . . | 3 | 0 3 0 | * * * 640 * * * | 1 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3x . | 6 | 0 3 3 | * * * * 640 * * | 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . o3*c | 3 | 0 3 0 | * * * * * 640 * | 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x3/2o | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 2 0 0 2 | 0 0 1 2 1 ---------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4o3x . . ♦ 24 | 24 24 0 | 6 12 0 8 0 0 0 | 80 * * * * * * * | 1 1 0 0 0 x4o . x . ♦ 8 | 8 0 4 | 2 0 4 0 0 0 0 | * 240 * * * * * * | 1 0 1 0 0 x . x3x . ♦ 12 | 6 6 6 | 0 3 3 0 2 0 0 | * * 320 * * * * * | 1 0 0 1 0 x . x . o3*c ♦ 6 | 3 6 0 | 0 3 0 0 0 2 0 | * * * 320 * * * * | 0 1 0 1 0 x . . x3/2o ♦ 6 | 3 0 6 | 0 0 3 0 0 0 2 | * * * * 320 * * * | 0 0 1 1 0 . o3x3x . ♦ 12 | 0 12 6 | 0 0 0 4 4 0 0 | * * * * * 160 * * | 1 0 0 0 1 . o3x . o3*c ♦ 6 | 0 12 0 | 0 0 0 4 0 4 0 | * * * * * * 160 * | 0 1 0 0 1 . . x3x3/2o3*c ♦ 12 | 0 12 12 | 0 0 0 0 4 4 4 | * * * * * * * 160 | 0 0 0 1 1 ---------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4o3x3x . ♦ 192 | 192 192 96 | 48 96 96 64 64 0 0 | 8 24 32 0 0 16 0 0 | 10 * * * * x4o3x . o3*c ♦ 96 | 96 192 0 | 24 96 0 64 0 64 0 | 8 0 0 32 0 0 16 0 | * 10 * * * x4o . x3/2o ♦ 12 | 12 0 12 | 3 0 12 0 0 0 4 | 0 3 0 0 4 0 0 0 | * * 80 * * x . x3x3/2o3*c ♦ 24 | 12 24 24 | 0 12 12 0 8 8 8 | 0 0 4 4 4 0 0 2 | * * * 80 * . o3x3x3/2o3*c ♦ 30 | 0 60 30 | 0 0 0 20 20 20 10 | 0 0 0 0 0 5 5 5 | * * * * 32
3 3/2 4/3
x---x---o---x
3 \ / 3/2
o
x4/3o3x3x3o3/2*c . . . . . | 960 | 2 4 2 | 1 4 4 2 4 2 1 | 2 2 4 2 2 2 1 2 | 2 1 1 2 1 -------------------+-----+--------------+-----------------------------+--------------------------------+--------------- x . . . . | 2 | 960 * * | 1 2 2 0 0 0 0 | 2 2 2 1 1 0 0 0 | 2 1 1 1 0 . . x . . | 2 | * 1920 * | 0 1 0 1 1 1 0 | 1 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . x . | 2 | * * 960 | 0 0 2 0 2 0 1 | 0 1 2 0 2 1 0 2 | 1 0 1 2 1 -------------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4/3o . . . | 4 | 4 0 0 | 240 * * * * * * | 2 2 0 0 0 0 0 0 | 2 1 1 0 0 x . x . . | 4 | 2 2 0 | * 960 * * * * * | 1 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 2 | * * 960 * * * * | 0 1 1 0 1 0 0 0 | 1 0 1 1 0 . o3/2x . . | 3 | 0 3 0 | * * * 640 * * * | 1 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3x . | 6 | 0 3 3 | * * * * 640 * * | 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . o3/2*c | 3 | 0 3 0 | * * * * * 640 * | 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x3o | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 2 0 0 2 | 0 0 1 2 1 -------------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4/3o3/2x . . ♦ 24 | 24 24 0 | 6 12 0 8 0 0 0 | 80 * * * * * * * | 1 1 0 0 0 x4/3o . x . ♦ 8 | 8 0 4 | 2 0 4 0 0 0 0 | * 240 * * * * * * | 1 0 1 0 0 x . x3x . ♦ 12 | 6 6 6 | 0 3 3 0 2 0 0 | * * 320 * * * * * | 1 0 0 1 0 x . x . o3/2*c ♦ 6 | 3 6 0 | 0 3 0 0 0 2 0 | * * * 320 * * * * | 0 1 0 1 0 x . . x3o ♦ 6 | 3 0 6 | 0 0 3 0 0 0 2 | * * * * 320 * * * | 0 0 1 1 0 . o3/2x3x . ♦ 12 | 0 12 6 | 0 0 0 4 4 0 0 | * * * * * 160 * * | 1 0 0 0 1 . o3/2x . o3/2*c ♦ 6 | 0 12 0 | 0 0 0 4 0 4 0 | * * * * * * 160 * | 0 1 0 0 1 . . x3x3o3/2*c ♦ 12 | 0 12 12 | 0 0 0 0 4 4 4 | * * * * * * * 160 | 0 0 0 1 1 -------------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4/3o3/2x3x . ♦ 192 | 192 192 96 | 48 96 96 64 64 0 0 | 8 24 32 0 0 16 0 0 | 10 * * * * x4/3o3/2x . o3/2*c ♦ 96 | 96 192 0 | 24 96 0 64 0 64 0 | 8 0 0 32 0 0 16 0 | * 10 * * * x4/3o . x3o ♦ 12 | 12 0 12 | 3 0 12 0 0 0 4 | 0 3 0 0 4 0 0 0 | * * 80 * * x . x3x3o3/2*c ♦ 24 | 12 24 24 | 0 12 12 0 8 8 8 | 0 0 4 4 4 0 0 2 | * * * 80 * . o3/2x3x3o3/2*c ♦ 30 | 0 60 30 | 0 0 0 20 20 20 10 | 0 0 0 0 0 5 5 5 | * * * * 32
4/3 3/2 3
x---o---x---x
3 \ / 3/2
o
x4/3o3/2x3x3/2o3/2*c . . . . . | 960 | 2 4 2 | 1 4 4 2 4 2 1 | 2 2 4 2 2 2 1 2 | 2 1 1 2 1 -------------------+-----+--------------+-----------------------------+--------------------------------+--------------- x . . . . | 2 | 960 * * | 1 2 2 0 0 0 0 | 2 2 2 1 1 0 0 0 | 2 1 1 1 0 . . x . . | 2 | * 1920 * | 0 1 0 1 1 1 0 | 1 0 1 1 0 1 1 1 | 1 1 0 1 1 . . . x . | 2 | * * 960 | 0 0 2 0 2 0 1 | 0 1 2 0 2 1 0 2 | 1 0 1 2 1 -------------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4/3o . . . | 4 | 4 0 0 | 240 * * * * * * | 2 2 0 0 0 0 0 0 | 2 1 1 0 0 x . x . . | 4 | 2 2 0 | * 960 * * * * * | 1 0 1 1 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 2 | * * 960 * * * * | 0 1 1 0 1 0 0 0 | 1 0 1 1 0 . o3/2x . . | 3 | 0 3 0 | * * * 640 * * * | 1 0 0 0 0 1 1 0 | 1 1 0 0 1 . . x3x . | 6 | 0 3 3 | * * * * 640 * * | 0 0 1 0 0 1 0 1 | 1 0 0 1 1 . . x . o3*c | 3 | 0 3 0 | * * * * * 640 * | 0 0 0 1 0 0 1 1 | 0 1 0 1 1 . . . x3/2o | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 2 0 0 2 | 0 0 1 2 1 -------------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4/3o3/2x . . ♦ 24 | 24 24 0 | 6 12 0 8 0 0 0 | 80 * * * * * * * | 1 1 0 0 0 x4/3o . x . ♦ 8 | 8 0 4 | 2 0 4 0 0 0 0 | * 240 * * * * * * | 1 0 1 0 0 x . x3x . ♦ 12 | 6 6 6 | 0 3 3 0 2 0 0 | * * 320 * * * * * | 1 0 0 1 0 x . x . o3*c ♦ 6 | 3 6 0 | 0 3 0 0 0 2 0 | * * * 320 * * * * | 0 1 0 1 0 x . . x3/2o ♦ 6 | 3 0 6 | 0 0 3 0 0 0 2 | * * * * 320 * * * | 0 0 1 1 0 . o3/2x3x . ♦ 12 | 0 12 6 | 0 0 0 4 4 0 0 | * * * * * 160 * * | 1 0 0 0 1 . o3/2x . o3*c ♦ 6 | 0 12 0 | 0 0 0 4 0 4 0 | * * * * * * 160 * | 0 1 0 0 1 . . x3x3/2o3*c ♦ 12 | 0 12 12 | 0 0 0 0 4 4 4 | * * * * * * * 160 | 0 0 0 1 1 -------------------+-----+--------------+-----------------------------+--------------------------------+--------------- x4/3o3/2x3x . ♦ 192 | 192 192 96 | 48 96 96 64 64 0 0 | 8 24 32 0 0 16 0 0 | 10 * * * * x4/3o3/2x . o3*c ♦ 96 | 96 192 0 | 24 96 0 64 0 64 0 | 8 0 0 32 0 0 16 0 | * 10 * * * x4/3o . x3/2o ♦ 12 | 12 0 12 | 3 0 12 0 0 0 4 | 0 3 0 0 4 0 0 0 | * * 80 * * x . x3x3/2o3*c ♦ 24 | 12 24 24 | 0 12 12 0 8 8 8 | 0 0 4 4 4 0 0 2 | * * * 80 * . o3/2x3x3/2o3*c ♦ 30 | 0 60 30 | 0 0 0 20 20 20 10 | 0 0 0 0 0 5 5 5 | * * * * 32
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