prismatotruncated-tesseract prism,
runcitruncated-tesseract prism,
central segment of carnit
- uniform relative:
- carnit
- general polytopal classes:
- Wythoffian polytera segmentotera
links
| Acronym | prohp |
| Name |
prismatorhombated-hexadecachoron prism, prismatotruncated-tesseract prism, runcitruncated-tesseract prism, central segment of carnit |
| Circumradius | sqrt[17+8 sqrt(2)]/2 = 2.660531 |
| Coordinates | ((1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2) & all permutations in all but last coord., all changes of sign |
| Face vector | 384, 1152, 1216, 528, 82 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x x3o3x4x . . . . . | 384 | 1 2 2 1 | 2 2 1 1 2 2 1 2 | 1 2 2 1 2 1 1 2 1 | 1 1 2 1 1 ----------+-----+-----------------+-------------------------------+----------------------------+------------- x . . . . | 2 | 192 * * * | 2 2 1 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 | 1 1 2 1 0 . x . . . | 2 | * 384 * * | 1 0 0 1 1 1 0 0 | 1 1 1 0 0 1 1 1 0 | 1 1 1 0 1 . . . x . | 2 | * * 384 * | 0 1 0 0 1 0 1 1 | 0 1 0 1 1 1 0 1 1 | 1 0 1 1 1 . . . . x | 2 | * * * 192 | 0 0 1 0 0 2 0 2 | 0 0 2 0 2 0 1 2 1 | 0 1 2 1 1 ----------+-----+-----------------+-------------------------------+----------------------------+------------- x x . . . | 4 | 2 2 0 0 | 192 * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 x . . x . | 4 | 2 0 2 0 | * 192 * * * * * * | 0 1 0 1 1 0 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 2 | * * 96 * * * * * | 0 0 2 0 2 0 0 0 0 | 2 0 1 1 0 . x3o . . | 3 | 0 3 0 0 | * * * 128 * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . x . | 4 | 0 2 2 0 | * * * * 192 * * * | 0 1 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . x | 4 | 0 2 0 2 | * * * * * 192 * * | 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1 . . o3x . | 3 | 0 0 3 0 | * * * * * * 128 * | 0 0 0 1 0 1 0 0 1 | 1 0 0 1 1 . . . x4x | 8 | 0 0 4 4 | * * * * * * * 96 | 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 ----------+-----+-----------------+-------------------------------+----------------------------+------------- x x3o . . ♦ 6 | 3 6 0 0 | 3 0 0 2 0 0 0 0 | 64 * * * * * * * * | 1 1 0 0 0 x x . x . ♦ 8 | 4 4 4 0 | 2 2 0 0 2 0 0 0 | * 96 * * * * * * * | 1 0 1 0 0 x x . . x ♦ 8 | 4 4 0 4 | 2 0 2 0 0 2 0 0 | * * 96 * * * * * * | 0 1 1 0 0 x . o3x . ♦ 6 | 3 0 6 0 | 0 3 0 0 0 0 2 0 | * * * 64 * * * * * | 1 0 0 1 0 x . . x4x ♦ 16 | 8 0 8 8 | 0 4 4 0 0 0 0 2 | * * * * 48 * * * * | 0 0 1 1 0 . x3o3x . ♦ 12 | 0 12 12 0 | 0 0 0 4 6 0 4 0 | * * * * * 32 * * * | 1 0 0 0 1 . x3o . x ♦ 6 | 0 6 0 3 | 0 0 0 2 0 3 0 0 | * * * * * * 64 * * | 0 1 0 0 1 . x . x4x ♦ 16 | 0 8 8 8 | 0 0 0 0 4 4 0 2 | * * * * * * * 48 * | 0 0 1 0 1 . . o3x4x ♦ 24 | 0 0 24 12 | 0 0 0 0 0 0 8 6 | * * * * * * * * 16 | 0 0 0 1 1 ----------+-----+-----------------+-------------------------------+----------------------------+------------- x x3o3x . ♦ 24 | 12 24 24 0 | 12 12 0 8 12 0 8 0 | 4 6 0 4 0 2 0 0 0 | 16 * * * * x x3o . x ♦ 12 | 6 12 0 6 | 6 0 3 4 0 6 0 0 | 2 0 3 0 0 0 2 0 0 | * 32 * * * x x . x4x ♦ 32 | 16 16 16 16 | 8 8 8 0 8 8 0 4 | 0 4 4 0 2 0 0 2 0 | * * 24 * * x . o3x4x ♦ 48 | 24 0 48 24 | 0 24 12 0 0 0 16 12 | 0 0 0 8 6 0 0 0 2 | * * * 8 * . x3o3x4x ♦ 192 | 0 192 192 96 | 0 0 0 64 96 96 64 48 | 0 0 0 0 0 16 32 24 8 | * * * * 2
xx3oo3xx4xx&#x → height = 1
(proh || proh)
o.3o.3o.4o. | 192 * | 2 2 1 1 0 0 0 | 1 2 2 1 2 2 2 0 0 0 0 0 0 | 1 1 2 1 1 2 2 1 2 0 0 0 0 | 1 1 1 2 1 0
.o3.o3.o4.o | * 192 | 0 0 0 1 2 2 1 | 0 0 0 0 0 2 2 1 1 2 2 1 2 | 0 0 0 0 1 2 2 1 2 1 1 2 1 | 0 1 1 2 1 1
---------------+---------+---------------------------+------------------------------------------+--------------------------------------+---------------
x. .. .. .. | 2 0 | 192 * * * * * * | 1 1 1 0 0 1 0 0 0 0 0 0 0 | 1 1 1 0 1 1 1 0 0 0 0 0 0 | 1 1 1 1 0 0
.. .. x. .. | 2 0 | * 192 * * * * * | 0 1 0 1 1 0 1 0 0 0 0 0 0 | 1 0 1 1 0 1 0 1 1 0 0 0 0 | 1 1 0 1 1 0
.. .. .. x. | 2 0 | * * 96 * * * * | 0 0 2 0 2 0 0 1 0 0 0 0 0 | 0 1 2 1 0 0 2 0 2 0 0 0 0 | 1 0 1 2 1 0
oo3oo3oo4oo&#x | 1 1 | * * * 192 * * * | 0 0 0 0 0 2 2 1 0 0 0 0 0 | 0 0 0 0 1 2 2 1 2 0 0 0 0 | 0 1 1 2 1 0
.x .. .. .. | 0 2 | * * * * 192 * * | 0 0 0 0 0 1 0 0 1 1 1 0 0 | 0 0 0 0 1 1 1 0 0 1 1 1 0 | 0 1 1 1 0 1
.. .. .x .. | 0 2 | * * * * * 192 * | 0 0 0 0 0 0 1 0 0 1 0 1 1 | 0 0 0 0 0 1 0 1 1 1 0 1 1 | 0 1 0 1 1 1
.. .. .. .x | 0 2 | * * * * * * 96 | 0 0 0 0 0 0 0 1 0 0 2 0 2 | 0 0 0 0 0 0 2 0 2 0 1 2 1 | 0 0 1 2 1 1
---------------+---------+---------------------------+------------------------------------------+--------------------------------------+---------------
x.3o. .. .. | 3 0 | 3 0 0 0 0 0 0 | 64 * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 0 0 | * 96 * * * * * * * * * * * | 1 0 1 0 0 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
x. .. .. x. | 4 0 | 2 0 2 0 0 0 0 | * * 96 * * * * * * * * * * | 0 1 1 0 0 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
.. o.3x. .. | 3 0 | 0 3 0 0 0 0 0 | * * * 64 * * * * * * * * * | 1 0 0 1 0 0 0 1 0 0 0 0 0 | 1 1 0 0 1 0
.. .. x.4x. | 8 0 | 0 4 4 0 0 0 0 | * * * * 48 * * * * * * * * | 0 0 1 1 0 0 0 0 1 0 0 0 0 | 1 0 0 1 1 0
xx .. .. ..&#x | 2 2 | 1 0 0 2 1 0 0 | * * * * * 192 * * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
.. .. xx ..&#x | 2 2 | 0 1 0 2 0 1 0 | * * * * * * 192 * * * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 0 | 0 1 0 1 1 0
.. .. .. xx&#x | 2 2 | 0 0 1 2 0 0 1 | * * * * * * * 96 * * * * * | 0 0 0 0 0 0 2 0 2 0 0 0 0 | 0 0 1 2 1 0
.x3.o .. .. | 0 3 | 0 0 0 0 3 0 0 | * * * * * * * * 64 * * * * | 0 0 0 0 1 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
.x .. .x .. | 0 4 | 0 0 0 0 2 2 0 | * * * * * * * * * 96 * * * | 0 0 0 0 0 1 0 0 0 1 0 1 0 | 0 1 0 1 0 1
.x .. .. .x | 0 4 | 0 0 0 0 2 0 2 | * * * * * * * * * * 96 * * | 0 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 1 1 0 1
.. .o3.x .. | 0 3 | 0 0 0 0 0 3 0 | * * * * * * * * * * * 64 * | 0 0 0 0 0 0 0 1 0 1 0 0 1 | 0 1 0 0 1 1
.. .. .x4.x | 0 8 | 0 0 0 0 0 4 4 | * * * * * * * * * * * * 48 | 0 0 0 0 0 0 0 0 1 0 0 1 1 | 0 0 0 1 1 1
---------------+---------+---------------------------+------------------------------------------+--------------------------------------+---------------
x.3o.3x. .. ♦ 12 0 | 12 12 0 0 0 0 0 | 4 6 0 4 0 0 0 0 0 0 0 0 0 | 16 * * * * * * * * * * * * | 1 1 0 0 0 0
x.3o. .. x. ♦ 6 0 | 6 0 3 0 0 0 0 | 2 0 3 0 0 0 0 0 0 0 0 0 0 | * 32 * * * * * * * * * * * | 1 0 1 0 0 0
x. .. x.4x. ♦ 16 0 | 8 8 8 0 0 0 0 | 0 4 4 0 2 0 0 0 0 0 0 0 0 | * * 24 * * * * * * * * * * | 1 0 0 1 0 0
.. o.3x.4x. ♦ 24 0 | 0 24 12 0 0 0 0 | 0 0 0 8 6 0 0 0 0 0 0 0 0 | * * * 8 * * * * * * * * * | 1 0 0 0 1 0
xx3oo .. ..&#x ♦ 3 3 | 3 0 0 3 3 0 0 | 1 0 0 0 0 3 0 0 1 0 0 0 0 | * * * * 64 * * * * * * * * | 0 1 1 0 0 0
xx .. xx ..&#x ♦ 4 4 | 2 2 0 4 2 2 0 | 0 1 0 0 0 2 2 0 0 1 0 0 0 | * * * * * 96 * * * * * * * | 0 1 0 1 0 0
xx .. .. xx&#x ♦ 4 4 | 2 0 2 4 2 0 2 | 0 0 1 0 0 2 0 2 0 0 1 0 0 | * * * * * * 96 * * * * * * | 0 0 1 1 0 0
.. oo3xx ..&#x ♦ 3 3 | 0 3 0 3 0 3 0 | 0 0 0 1 0 0 3 0 0 0 0 1 0 | * * * * * * * 64 * * * * * | 0 1 0 0 1 0
.. .. xx4xx&#x ♦ 8 8 | 0 4 4 8 0 4 4 | 0 0 0 0 1 0 4 4 0 0 0 0 1 | * * * * * * * * 48 * * * * | 0 0 0 1 1 0
.x3.o3.x .. ♦ 0 12 | 0 0 0 0 12 12 0 | 0 0 0 0 0 0 0 0 4 6 0 4 0 | * * * * * * * * * 16 * * * | 0 1 0 0 0 1
.x3.o .. .x ♦ 0 6 | 0 0 0 0 6 0 3 | 0 0 0 0 0 0 0 0 2 0 3 0 0 | * * * * * * * * * * 32 * * | 0 0 1 0 0 1
.x .. .x4.x ♦ 0 16 | 0 0 0 0 8 8 8 | 0 0 0 0 0 0 0 0 0 4 4 0 2 | * * * * * * * * * * * 24 * | 0 0 0 1 0 1
.. .o3.x4.x ♦ 0 24 | 0 0 0 0 0 24 12 | 0 0 0 0 0 0 0 0 0 0 0 8 6 | * * * * * * * * * * * * 8 | 0 0 0 0 1 1
---------------+---------+---------------------------+------------------------------------------+--------------------------------------+---------------
x.3o.3x.4x. ♦ 192 0 | 192 192 96 0 0 0 0 | 64 96 96 64 48 0 0 0 0 0 0 0 0 | 16 32 24 8 0 0 0 0 0 0 0 0 0 | 1 * * * * *
xx3oo3xx ..&#x ♦ 12 12 | 12 12 0 12 12 12 0 | 4 6 0 4 0 12 12 0 4 6 0 4 0 | 1 0 0 0 4 6 0 4 0 1 0 0 0 | * 16 * * * *
xx3oo .. xx&#x ♦ 6 6 | 6 0 3 6 6 0 3 | 2 0 3 0 0 6 0 3 2 0 3 0 0 | 0 1 0 0 2 0 3 0 0 0 1 0 0 | * * 32 * * *
xx .. xx4xx&#x ♦ 16 16 | 8 8 8 16 8 8 8 | 0 4 4 0 2 8 8 8 0 4 4 0 2 | 0 0 1 0 0 4 4 0 2 0 0 1 0 | * * * 24 * *
.. oo3xx4xx&#x ♦ 24 24 | 0 24 12 24 0 24 12 | 0 0 0 8 6 0 24 12 0 0 0 8 6 | 0 0 0 1 0 0 0 8 6 0 0 0 1 | * * * * 8 *
.x3.o3.x4.x ♦ 0 192 | 0 0 0 0 192 192 96 | 0 0 0 0 0 0 0 0 64 96 96 64 48 | 0 0 0 0 0 0 0 0 0 16 32 24 8 | * * * * * 1
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