- general polytopal classes:
- Wythoffian polytera segmentotera lace simplices
links
| Acronym | ticope |
| Name | truncated-icositetrachoron prism |
| Circumradius | sqrt(29)/2 = 2.692582 |
| Coordinates | (3/sqrt(2), sqrt(2), 1/sqrt(2), 0, 1/2) & all permutations in all but last coord., all changes of sign |
| Face vector | 384, 960, 864, 336, 50 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x x3x4o3o . . . . . | 384 | 1 1 3 | 1 3 3 3 | 3 3 3 1 | 3 1 1 ----------+-----+-------------+----------------+--------------+-------- x . . . . | 2 | 192 * * | 1 3 0 0 | 3 3 0 0 | 3 1 0 . x . . . | 2 | * 192 * | 1 0 3 0 | 3 0 3 0 | 3 0 1 . . x . . | 2 | * * 576 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------+-----+-------------+----------------+--------------+-------- x x . . . | 4 | 2 2 0 | 96 * * * | 3 0 0 0 | 3 0 0 x . x . . | 4 | 2 0 2 | * 288 * * | 1 2 0 0 | 2 1 0 . x3x . . | 6 | 0 3 3 | * * 192 * | 1 0 2 0 | 2 0 1 . . x4o . | 4 | 0 0 4 | * * * 288 | 0 1 1 1 | 1 1 1 ----------+-----+-------------+----------------+--------------+-------- x x3x . . ♦ 12 | 6 6 6 | 3 3 2 0 | 96 * * * | 2 0 0 x . x4o . ♦ 8 | 4 0 8 | 0 4 0 2 | * 144 * * | 1 1 0 . x3x4o . ♦ 24 | 0 12 24 | 0 0 8 6 | * * 48 * | 1 0 1 . . x4o3o ♦ 8 | 0 0 12 | 0 0 0 6 | * * * 48 | 0 1 1 ----------+-----+-------------+----------------+--------------+-------- x x3x4o . ♦ 48 | 24 24 48 | 12 24 16 12 | 8 6 2 0 | 24 * * x . x4o3o ♦ 16 | 8 0 24 | 0 12 0 12 | 0 6 0 2 | * 24 * . x3x4o3o ♦ 192 | 0 96 288 | 0 0 96 144 | 0 0 24 24 | * * 2
x x3x3x4o . . . . . | 384 | 1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1 ----------+-----+-----------------+-------------------------+----------------------+---------- x . . . . | 2 | 192 * * * | 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 . x . . . | 2 | * 192 * * | 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 . . x . . | 2 | * * 192 * | 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1 . . . x . | 2 | * * * 384 | 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 ----------+-----+-----------------+-------------------------+----------------------+---------- x x . . . | 4 | 2 2 0 0 | 96 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 x . x . . | 4 | 2 0 2 0 | * 96 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 x . . x . | 4 | 2 0 0 2 | * * 192 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 . x3x . . | 6 | 0 3 3 0 | * * * 64 * * * | 1 0 0 0 2 0 0 | 2 0 0 1 . x . x . | 4 | 0 2 0 2 | * * * * 192 * * | 0 1 0 0 1 1 0 | 1 1 0 1 . . x3x . | 6 | 0 0 3 3 | * * * * * 128 * | 0 0 1 0 1 0 1 | 1 0 1 1 . . . x4o | 4 | 0 0 0 4 | * * * * * * 96 | 0 0 0 1 0 1 1 | 0 1 1 1 ----------+-----+-----------------+-------------------------+----------------------+---------- x x3x . . ♦ 12 | 6 6 6 0 | 3 3 0 2 0 0 0 | 32 * * * * * * | 2 0 0 0 x x . x . ♦ 8 | 4 4 0 4 | 2 0 2 0 2 0 0 | * 96 * * * * * | 1 1 0 0 x . x3x . ♦ 12 | 6 0 6 6 | 0 3 3 0 0 2 0 | * * 64 * * * * | 1 0 1 0 x . . x4o ♦ 8 | 4 0 0 8 | 0 0 4 0 0 0 2 | * * * 48 * * * | 0 1 1 0 . x3x3x . ♦ 24 | 0 12 12 12 | 0 0 0 4 6 4 0 | * * * * 32 * * | 1 0 0 1 . x . x4o ♦ 8 | 0 4 0 8 | 0 0 0 0 4 0 2 | * * * * * 48 * | 0 1 0 1 . . x3x4o ♦ 24 | 0 0 12 24 | 0 0 0 0 0 8 6 | * * * * * * 16 | 0 0 1 1 ----------+-----+-----------------+-------------------------+----------------------+---------- x x3x3x . ♦ 48 | 24 24 24 24 | 12 12 12 8 12 8 0 | 4 6 4 0 2 0 0 | 16 * * * x x . x4o ♦ 16 | 8 8 0 16 | 4 0 8 0 8 0 4 | 0 4 0 2 0 2 0 | * 24 * * x . x3x4o ♦ 48 | 24 0 24 48 | 0 12 24 0 0 16 12 | 0 0 8 6 0 0 2 | * * 8 * . x3x3x4o ♦ 192 | 0 96 96 192 | 0 0 0 32 96 64 48 | 0 0 0 0 16 24 8 | * * * 2
x x3x3x *c3x . . . . . | 384 | 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 -------------+-----+---------------------+-------------------------------+-------------------------------+----------- x . . . . | 2 | 192 * * * * | 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0 . x . . . | 2 | * 192 * * * | 1 0 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 | * * 192 * * | 0 1 0 0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . . . x . | 2 | * * * 192 * | 0 0 1 0 0 1 0 1 0 1 | 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1 . . . . x | 2 | * * * * 192 | 0 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 -------------+-----+---------------------+-------------------------------+-------------------------------+----------- x x . . . | 4 | 2 2 0 0 0 | 96 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 0 2 0 0 | * 96 * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 0 2 0 | * * 96 * * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 0 2 | * * * 96 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . x3x . . | 6 | 0 3 3 0 0 | * * * * 64 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . x . | 4 | 0 2 0 2 0 | * * * * * 96 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . x | 4 | 0 2 0 0 2 | * * * * * * 96 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . x3x . | 6 | 0 0 3 3 0 | * * * * * * * 64 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . . x . *c3x | 6 | 0 0 3 0 3 | * * * * * * * * 64 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . x x | 4 | 0 0 0 2 2 | * * * * * * * * * 96 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 -------------+-----+---------------------+-------------------------------+-------------------------------+----------- x x3x . . ♦ 12 | 6 6 6 0 0 | 3 3 0 0 2 0 0 0 0 0 | 32 * * * * * * * * * | 1 1 0 0 0 x x . x . ♦ 8 | 4 4 0 4 0 | 2 0 2 0 0 2 0 0 0 0 | * 48 * * * * * * * * | 1 0 1 0 0 x x . . x ♦ 8 | 4 4 0 0 4 | 2 0 0 2 0 0 2 0 0 0 | * * 48 * * * * * * * | 0 1 1 0 0 x . x3x . ♦ 12 | 6 0 6 6 0 | 0 3 3 0 0 0 0 2 0 0 | * * * 32 * * * * * * | 1 0 0 1 0 x . x . *c3x ♦ 12 | 6 0 6 0 6 | 0 3 0 3 0 0 0 0 2 0 | * * * * 32 * * * * * | 0 1 0 1 0 x . . x x ♦ 8 | 4 0 0 4 4 | 0 0 2 2 0 0 0 0 0 2 | * * * * * 48 * * * * | 0 0 1 1 0 . x3x3x . ♦ 24 | 0 12 12 12 0 | 0 0 0 0 4 6 0 4 0 0 | * * * * * * 16 * * * | 1 0 0 0 1 . x3x . *c3x ♦ 24 | 0 12 12 0 12 | 0 0 0 0 4 0 6 0 4 0 | * * * * * * * 16 * * | 0 1 0 0 1 . x . x x ♦ 8 | 0 4 0 4 4 | 0 0 0 0 0 2 2 0 0 2 | * * * * * * * * 48 * | 0 0 1 0 1 . . x3x *c3x ♦ 24 | 0 0 12 12 12 | 0 0 0 0 0 0 0 4 4 6 | * * * * * * * * * 16 | 0 0 0 1 1 -------------+-----+---------------------+-------------------------------+-------------------------------+----------- x x3x3x . ♦ 48 | 24 24 24 24 0 | 12 12 12 0 8 12 0 8 0 0 | 4 6 0 4 0 0 2 0 0 0 | 8 * * * * x x3x . *c3x ♦ 48 | 24 24 24 0 24 | 12 12 0 12 8 0 12 0 8 0 | 4 0 6 0 4 0 0 2 0 0 | * 8 * * * x x . x x ♦ 16 | 8 8 0 8 8 | 4 0 4 4 0 4 4 0 0 4 | 0 2 2 0 0 2 0 0 2 0 | * * 24 * * x . x3x *c3x ♦ 48 | 24 0 24 24 24 | 0 12 12 12 0 0 0 8 8 12 | 0 0 0 4 4 6 0 0 0 2 | * * * 8 * . x3x3x *c3x ♦ 192 | 0 96 96 96 96 | 0 0 0 0 32 48 48 32 32 48 | 0 0 0 0 0 0 8 8 24 8 | * * * * 2
xx3xx4oo3oo&#x → height = 1
(tico || tico)
...
xx3xx3xx4oo&#x → height = 1
(tico || tico)
...
xx3xx3xx *b3xx&#x → height = 1
(tico || tico)
o.3o.3o. *b3o. | 192 * | 1 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 1 0
.o3.o3.o *b3.o | * 192 | 0 0 0 0 1 1 1 1 1 | 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 | 0 0 0 0 1 1 1 1 1 1 1 1 1 1 | 0 1 1 1 1 1
------------------+---------+-----------------------------+-------------------------------------------------+-------------------------------------+-------------
x. .. .. .. | 2 0 | 96 * * * * * * * * | 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 1 0 0
.. x. .. .. | 2 0 | * 96 * * * * * * * | 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 1 0 1 1 0 0 1 1 0 0 0 0 0 | 1 1 1 0 1 0
.. .. x. .. | 2 0 | * * 96 * * * * * * | 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 | 1 0 1 1 0 1 0 1 0 1 0 0 0 0 | 1 1 0 1 1 0
.. .. .. x. | 2 0 | * * * 96 * * * * * | 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 | 0 1 1 1 0 0 1 0 1 1 0 0 0 0 | 1 0 1 1 1 0
oo3oo3oo *b3oo&#x | 1 1 | * * * * 192 * * * * | 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 | 0 0 0 0 1 1 1 1 1 1 0 0 0 0 | 0 1 1 1 1 0
.x .. .. .. | 0 2 | * * * * * 96 * * * | 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 | 0 0 0 0 1 1 1 0 0 0 1 1 1 0 | 0 1 1 1 0 1
.. .x .. .. | 0 2 | * * * * * * 96 * * | 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 | 0 0 0 0 1 0 0 1 1 0 1 1 0 1 | 0 1 1 0 1 1
.. .. .x .. | 0 2 | * * * * * * * 96 * | 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 | 0 0 0 0 0 1 0 1 0 1 1 0 1 1 | 0 1 0 1 1 1
.. .. .. .x | 0 2 | * * * * * * * * 96 | 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 | 0 0 0 0 0 0 1 0 1 1 0 1 1 1 | 0 0 1 1 1 1
------------------+---------+-----------------------------+-------------------------------------------------+-------------------------------------+-------------
x.3x. .. .. | 6 0 | 3 3 0 0 0 0 0 0 0 | 32 * * * * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
x. .. x. .. | 4 0 | 2 0 2 0 0 0 0 0 0 | * 48 * * * * * * * * * * * * * * | 1 0 1 0 0 1 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
x. .. .. x. | 4 0 | 2 0 0 2 0 0 0 0 0 | * * 48 * * * * * * * * * * * * * | 0 1 1 0 0 0 1 0 0 0 0 0 0 0 | 1 0 1 1 0 0
.. x.3x. .. | 6 0 | 0 3 3 0 0 0 0 0 0 | * * * 32 * * * * * * * * * * * * | 1 0 0 1 0 0 0 1 0 0 0 0 0 0 | 1 1 0 0 1 0
.. x. .. *b3x. | 6 0 | 0 3 0 3 0 0 0 0 0 | * * * * 32 * * * * * * * * * * * | 0 1 0 1 0 0 0 0 1 0 0 0 0 0 | 1 0 1 0 1 0
.. .. x. x. | 4 0 | 0 0 2 2 0 0 0 0 0 | * * * * * 48 * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 1 0 0 0 0 | 1 0 0 1 1 0
xx .. .. ..&#x | 2 2 | 1 0 0 0 2 1 0 0 0 | * * * * * * 96 * * * * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0
.. xx .. ..&#x | 2 2 | 0 1 0 0 2 0 1 0 0 | * * * * * * * 96 * * * * * * * * | 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 1 1 0 1 0
.. .. xx ..&#x | 2 2 | 0 0 1 0 2 0 0 1 0 | * * * * * * * * 96 * * * * * * * | 0 0 0 0 0 1 0 1 0 1 0 0 0 0 | 0 1 0 1 1 0
.. .. .. xx&#x | 2 2 | 0 0 0 1 2 0 0 0 1 | * * * * * * * * * 96 * * * * * * | 0 0 0 0 0 0 1 0 1 1 0 0 0 0 | 0 0 1 1 1 0
.x3.x .. .. | 0 6 | 0 0 0 0 0 3 3 0 0 | * * * * * * * * * * 32 * * * * * | 0 0 0 0 1 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.x .. .x .. | 0 4 | 0 0 0 0 0 2 0 2 0 | * * * * * * * * * * * 48 * * * * | 0 0 0 0 0 1 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
.x .. .. .x | 0 4 | 0 0 0 0 0 2 0 0 2 | * * * * * * * * * * * * 48 * * * | 0 0 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 1 1 0 1
.. .x3.x .. | 0 6 | 0 0 0 0 0 0 3 3 0 | * * * * * * * * * * * * * 32 * * | 0 0 0 0 0 0 0 1 0 0 1 0 0 1 | 0 1 0 0 1 1
.. .x .. *b3.x | 0 6 | 0 0 0 0 0 0 3 0 3 | * * * * * * * * * * * * * * 32 * | 0 0 0 0 0 0 0 0 1 0 0 1 0 1 | 0 0 1 0 1 1
.. .. .x .x | 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * * 48 | 0 0 0 0 0 0 0 0 0 1 0 0 1 1 | 0 0 0 1 1 1
------------------+---------+-----------------------------+-------------------------------------------------+-------------------------------------+-------------
x.3x.3x. .. ♦ 24 0 | 12 12 12 0 0 0 0 0 0 | 4 6 0 4 0 0 0 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * * * * | 1 1 0 0 0 0
x.3x. .. *b3x. ♦ 24 0 | 12 12 0 12 0 0 0 0 0 | 4 0 6 0 4 0 0 0 0 0 0 0 0 0 0 0 | * 8 * * * * * * * * * * * * | 1 0 1 0 0 0
x. .. x. x. ♦ 8 0 | 4 0 4 4 0 0 0 0 0 | 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 | * * 24 * * * * * * * * * * * | 1 0 0 1 0 0
.. x.3x. *b3x. ♦ 24 0 | 0 12 12 12 0 0 0 0 0 | 0 0 0 4 4 6 0 0 0 0 0 0 0 0 0 0 | * * * 8 * * * * * * * * * * | 1 0 0 0 1 0
xx3xx .. ..&#x ♦ 6 6 | 3 3 0 0 6 3 3 0 0 | 1 0 0 0 0 0 3 3 0 0 1 0 0 0 0 0 | * * * * 32 * * * * * * * * * | 0 1 1 0 0 0
xx .. xx ..&#x ♦ 4 4 | 2 0 2 0 4 2 0 2 0 | 0 1 0 0 0 0 2 0 2 0 0 1 0 0 0 0 | * * * * * 48 * * * * * * * * | 0 1 0 1 0 0
xx .. .. xx&#x ♦ 4 4 | 2 0 0 2 4 2 0 0 2 | 0 0 1 0 0 0 2 0 0 2 0 0 1 0 0 0 | * * * * * * 48 * * * * * * * | 0 0 1 1 0 0
.. xx3xx ..&#x ♦ 6 6 | 0 3 3 0 6 0 3 3 0 | 0 0 0 1 0 0 0 3 3 0 0 0 0 1 0 0 | * * * * * * * 32 * * * * * * | 0 1 0 0 1 0
.. xx .. *b3xx&#x ♦ 6 6 | 0 3 0 3 6 0 3 0 3 | 0 0 0 0 1 0 0 3 0 3 0 0 0 0 1 0 | * * * * * * * * 32 * * * * * | 0 0 1 0 1 0
.. .. xx xx&#x ♦ 4 4 | 0 0 2 2 4 0 0 2 2 | 0 0 0 0 0 1 0 0 2 2 0 0 0 0 0 1 | * * * * * * * * * 48 * * * * | 0 0 0 1 1 0
.x3.x3.x .. ♦ 0 24 | 0 0 0 0 0 12 12 12 0 | 0 0 0 0 0 0 0 0 0 0 4 6 0 4 0 0 | * * * * * * * * * * 8 * * * | 0 1 0 0 0 1
.x3.x .. *b3.x ♦ 0 24 | 0 0 0 0 0 12 12 0 12 | 0 0 0 0 0 0 0 0 0 0 4 0 6 0 4 0 | * * * * * * * * * * * 8 * * | 0 0 1 0 0 1
.x .. .x .x ♦ 0 8 | 0 0 0 0 0 4 0 4 4 | 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 | * * * * * * * * * * * * 24 * | 0 0 0 1 0 1
.. .x3.x *b3.x ♦ 0 24 | 0 0 0 0 0 0 12 12 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 6 | * * * * * * * * * * * * * 8 | 0 0 0 0 1 1
------------------+---------+-----------------------------+-------------------------------------------------+-------------------------------------+-------------
x.3x.3x. *b3x. ♦ 192 0 | 96 96 96 96 0 0 0 0 0 | 32 48 48 32 32 48 0 0 0 0 0 0 0 0 0 0 | 8 8 24 8 0 0 0 0 0 0 0 0 0 0 | 1 * * * * *
xx3xx3xx ..&#x ♦ 24 24 | 12 12 12 0 24 12 12 12 0 | 4 6 0 4 0 0 12 12 12 0 4 6 0 4 0 0 | 1 0 0 0 4 6 0 4 0 0 1 0 0 0 | * 8 * * * *
xx3xx .. *b3xx&#x ♦ 24 24 | 12 12 0 12 24 12 12 0 12 | 4 0 6 0 4 0 12 12 0 12 4 0 6 0 4 0 | 0 1 0 0 4 0 6 0 4 0 0 1 0 0 | * * 8 * * *
xx .. xx xx&#x ♦ 8 8 | 4 0 4 4 8 4 0 4 4 | 0 2 2 0 0 2 4 0 4 4 0 2 2 0 0 2 | 0 0 1 0 0 2 2 0 0 2 0 0 1 0 | * * * 24 * *
.. xx3xx *b3xx&#x ♦ 24 24 | 0 12 12 12 24 0 12 12 12 | 0 0 0 4 4 6 0 12 12 12 0 0 0 4 4 6 | 0 0 0 1 0 0 0 4 4 6 0 0 0 1 | * * * * 8 *
.x3.x3.x *b3.x ♦ 0 192 | 0 0 0 0 0 96 96 96 96 | 0 0 0 0 0 0 0 0 0 0 32 48 48 32 32 48 | 0 0 0 0 0 0 0 0 0 0 8 8 24 8 | * * * * * 1
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