runcinated-tesseract prism,
small-prismated-tesseract prism,
central segment of scant
- uniform relative:
- scant
- related segmentotera:
- squicuffip
- general polytopal classes:
- Wythoffian polytera segmentotera
links
| Acronym | sidpithip |
| Name |
small-disprismatotesseractihexadecachoron prism, runcinated-tesseract prism, small-prismated-tesseract prism, central segment of scant |
| Circumradius | sqrt[7+2 sqrt(2)]/2 = 1.567516 |
| Coordinates | ((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2) & all permutations in all but last coord., all changes of sign |
| Face vector | 128, 448, 608, 368, 82 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x x3o3o4x . . . . . | 128 | 1 3 3 | 3 3 3 6 3 | 3 6 3 1 3 3 1 | 1 3 3 1 1 ----------+-----+------------+------------------+----------------------+------------- x . . . . | 2 | 64 * * | 3 3 0 0 0 | 3 6 3 0 0 0 0 | 1 3 3 1 0 . x . . . | 2 | * 192 * | 1 0 2 2 0 | 2 2 0 1 2 1 0 | 1 2 1 0 1 . . . . x | 2 | * * 192 | 0 1 0 2 2 | 0 2 2 0 1 2 1 | 0 1 2 1 1 ----------+-----+------------+------------------+----------------------+------------- x x . . . | 4 | 2 2 0 | 96 * * * * | 2 2 0 0 0 0 0 | 1 2 1 0 0 x . . . x | 4 | 2 0 2 | * 96 * * * | 0 2 2 0 0 0 0 | 0 1 2 1 0 . x3o . . | 3 | 0 3 0 | * * 128 * * | 1 0 0 1 1 0 0 | 1 1 0 0 1 . x . . x | 4 | 0 2 2 | * * * 192 * | 0 1 0 0 1 1 0 | 0 1 1 0 1 . . . o4x | 4 | 0 0 4 | * * * * 96 | 0 0 1 0 0 1 1 | 0 0 1 1 1 ----------+-----+------------+------------------+----------------------+------------- x x3o . . ♦ 6 | 3 6 0 | 3 0 2 0 0 | 64 * * * * * * | 1 1 0 0 0 x x . . x ♦ 8 | 4 4 4 | 2 2 0 2 0 | * 96 * * * * * | 0 1 1 0 0 x . . o4x ♦ 8 | 4 0 8 | 0 4 0 0 2 | * * 48 * * * * | 0 0 1 1 0 . x3o3o . ♦ 4 | 0 6 0 | 0 0 4 0 0 | * * * 32 * * * | 1 0 0 0 1 . x3o . x ♦ 6 | 0 6 3 | 0 0 2 3 0 | * * * * 64 * * | 0 1 0 0 1 . x . o4x ♦ 8 | 0 4 8 | 0 0 0 4 2 | * * * * * 48 * | 0 0 1 0 1 . . o3o4x ♦ 8 | 0 0 12 | 0 0 0 0 6 | * * * * * * 16 | 0 0 0 1 1 ----------+-----+------------+------------------+----------------------+------------- x x3o3o . ♦ 8 | 4 12 0 | 6 0 8 0 0 | 4 0 0 2 0 0 0 | 16 * * * * x x3o . x ♦ 12 | 6 12 6 | 6 3 4 6 0 | 2 3 0 0 2 0 0 | * 32 * * * x x . o4x ♦ 16 | 8 8 16 | 4 8 0 8 4 | 0 4 2 0 0 2 0 | * * 24 * * x . o3o4x ♦ 16 | 8 0 24 | 0 12 0 0 12 | 0 0 6 0 0 0 2 | * * * 8 * . x3o3o4x ♦ 64 | 0 96 96 | 0 0 64 96 48 | 0 0 0 16 32 24 8 | * * * * 2 snubbed forms: s2x3o3o4s
((xo4xx ox4xx xx))&#zx → height = 0 (tegum sum of 2 interchanged ocubes) o.4o. o.4o. o. & | 128 | 1 1 2 1 2 | 2 1 2 1 1 2 3 4 2 | 1 2 1 2 1 1 3 3 2 4 | 1 1 1 3 1 2 -------------------------+-----+------------------+------------------------------+-------------------------------+--------------- x. .. .. .. .. & | 2 | 64 * * * * | 2 1 0 0 0 0 2 0 0 | 1 2 0 0 0 1 2 2 0 0 | 1 0 1 2 1 0 .. x. .. .. .. & | 2 | * 64 * * * | 0 0 2 1 0 0 0 2 0 | 0 0 1 2 0 0 1 0 2 2 | 0 1 0 1 1 2 .. .. .. x. .. & | 2 | * * 128 * * | 1 0 1 0 1 1 0 1 0 | 1 1 1 1 1 0 1 0 1 1 | 1 1 0 1 1 1 .. .. .. .. x. & | 2 | * * * 64 * | 0 1 0 1 0 2 0 0 2 | 0 2 0 2 1 0 0 3 0 4 | 1 1 1 3 0 2 oo4oo oo4oo oo &#x | 2 | * * * * 128 | 0 0 0 0 0 0 2 2 1 | 0 0 0 0 0 1 2 2 1 2 | 0 0 1 2 1 1 -------------------------+-----+------------------+------------------------------+-------------------------------+--------------- x. .. .. x. .. & | 4 | 2 0 2 0 0 | 64 * * * * * * * * | 1 1 0 0 0 0 1 0 0 0 | 1 0 0 1 1 0 x. .. .. .. x. & | 4 | 2 0 0 2 0 | * 32 * * * * * * * | 0 2 0 0 0 0 0 2 0 0 | 1 0 1 2 0 0 .. x. .. x. .. & | 4 | 0 2 2 0 0 | * * 64 * * * * * * | 0 0 1 1 0 0 0 0 1 0 | 0 1 0 0 1 1 .. x. .. .. x. & | 4 | 0 2 0 2 0 | * * * 32 * * * * * | 0 0 0 2 0 0 0 0 0 2 | 0 1 0 1 0 2 .. .. o.4x. .. & | 4 | 0 0 4 0 0 | * * * * 32 * * * * | 1 0 1 0 1 0 0 0 0 0 | 1 1 0 0 1 0 .. .. .. x. x. & | 4 | 0 0 2 2 0 | * * * * * 64 * * * | 0 1 0 1 1 0 0 0 0 1 | 1 1 0 1 0 1 xo .. .. .. .. &#x & | 3 | 1 0 0 0 2 | * * * * * * 128 * * | 0 0 0 0 0 1 1 1 0 0 | 0 0 1 1 1 0 .. xx .. .. .. &#x & | 4 | 0 1 1 0 2 | * * * * * * * 128 * | 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1 .. .. .. .. xx &#x | 4 | 0 0 0 2 2 | * * * * * * * * 64 | 0 0 0 0 0 0 0 2 0 2 | 0 0 1 2 0 1 -------------------------+-----+------------------+------------------------------+-------------------------------+--------------- x. .. o.4x. .. & ♦ 8 | 4 0 8 0 0 | 4 0 0 0 2 0 0 0 0 | 16 * * * * * * * * * | 1 0 0 0 1 0 x. .. .. x. x. & ♦ 8 | 4 0 4 4 0 | 2 2 0 0 0 2 0 0 0 | * 32 * * * * * * * * | 1 0 0 1 0 0 .. x. o.4x. .. & ♦ 8 | 0 4 8 0 0 | 0 0 4 0 2 0 0 0 0 | * * 16 * * * * * * * | 0 1 0 0 1 0 .. x. .. x. x. & ♦ 8 | 0 4 4 4 0 | 0 0 2 2 0 2 0 0 0 | * * * 32 * * * * * * | 0 1 0 0 0 1 .. .. o.4x. x. & ♦ 8 | 0 0 8 4 0 | 0 0 0 0 2 4 0 0 0 | * * * * 16 * * * * * | 1 1 0 0 0 0 xo .. ox .. .. &#x ♦ 4 | 2 0 0 0 4 | 0 0 0 0 0 0 4 0 0 | * * * * * 32 * * * * | 0 0 1 0 1 0 xo .. .. xx .. &#x & ♦ 6 | 2 1 2 0 4 | 1 0 0 0 0 0 2 2 0 | * * * * * * 64 * * * | 0 0 0 1 1 0 xo .. .. .. xx &#x & ♦ 6 | 2 0 0 3 4 | 0 1 0 0 0 0 2 0 2 | * * * * * * * 64 * * | 0 0 1 1 0 0 .. xx .. xx .. &#x ♦ 8 | 0 4 4 0 4 | 0 0 2 0 0 0 0 4 0 | * * * * * * * * 32 * | 0 0 0 0 1 1 .. xx .. .. xx &#x & ♦ 8 | 0 2 2 4 4 | 0 0 0 1 0 1 0 2 2 | * * * * * * * * * 64 | 0 0 0 1 0 1 -------------------------+-----+------------------+------------------------------+-------------------------------+--------------- x. .. o.4x. x. & ♦ 16 | 8 0 16 8 0 | 8 4 0 0 4 8 0 0 0 | 2 4 0 0 2 0 0 0 0 0 | 8 * * * * * .. x. o.4x. x. & ♦ 16 | 0 8 16 8 0 | 0 0 8 4 4 8 0 0 0 | 0 0 2 4 2 0 0 0 0 0 | * 8 * * * * xo .. ox .. xx &#x ♦ 8 | 4 0 0 4 8 | 0 2 0 0 0 0 8 0 4 | 0 0 0 0 0 2 0 4 0 0 | * * 16 * * * xo .. .. xx xx &#x & ♦ 12 | 4 2 4 6 8 | 2 2 0 1 0 2 4 4 4 | 0 1 0 0 0 0 2 2 0 2 | * * * 32 * * ((xo4xx ox4xx ..))&#zx ♦ 64 | 32 32 64 0 64 | 32 0 32 0 16 0 64 64 0 | 8 0 8 0 0 16 32 0 16 0 | * * * * 2 * .. xx .. xx xx &#x ♦ 16 | 0 8 8 8 8 | 0 0 4 4 0 4 0 8 4 | 0 0 0 2 0 0 0 0 2 4 | * * * * * 16
xx3oo3oo4xx&#x → height = 1
(sidpith || sidpith)
o.3o.3o.4o. | 64 * | 3 3 1 0 0 | 3 6 3 3 3 0 0 0 | 1 3 3 1 3 6 3 0 0 0 0 | 1 1 3 3 1 0
.o3.o3.o4.o | * 64 | 0 0 1 3 3 | 0 0 0 3 3 3 6 3 | 0 0 0 0 3 6 3 1 3 3 1 | 0 1 3 3 1 1
---------------+-------+----------------+-------------------------+--------------------------------+---------------
x. .. .. .. | 2 0 | 96 * * * * | 2 2 0 1 0 0 0 0 | 1 2 1 0 2 2 0 0 0 0 0 | 1 1 2 1 0 0
.. .. .. x. | 2 0 | * 96 * * * | 0 2 2 0 1 0 0 0 | 0 1 2 1 0 2 2 0 0 0 0 | 1 0 1 2 1 0
oo3oo3oo4oo&#x | 1 1 | * * 64 * * | 0 0 0 3 3 0 0 0 | 0 0 0 0 3 6 3 0 0 0 0 | 0 1 3 3 1 0
.x .. .. .. | 0 2 | * * * 96 * | 0 0 0 1 0 2 2 0 | 0 0 0 0 2 2 0 1 2 1 0 | 0 1 2 1 0 1
.. .. .. .x | 0 2 | * * * * 96 | 0 0 0 0 1 0 2 2 | 0 0 0 0 0 2 2 0 1 2 1 | 0 0 1 2 1 1
---------------+-------+----------------+-------------------------+--------------------------------+---------------
x.3o. .. .. | 3 0 | 3 0 0 0 0 | 64 * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 | 1 1 1 0 0 0
x. .. .. x. | 4 0 | 2 2 0 0 0 | * 96 * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 | 1 0 1 1 0 0
.. .. o.4x. | 4 0 | 0 4 0 0 0 | * * 48 * * * * * | 0 0 1 1 0 0 1 0 0 0 0 | 1 0 0 1 1 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * * 96 * * * * | 0 0 0 0 2 2 0 0 0 0 0 | 0 1 2 1 0 0
.. .. .. xx&#x | 2 2 | 0 1 2 0 1 | * * * * 96 * * * | 0 0 0 0 0 2 2 0 0 0 0 | 0 0 1 2 1 0
.x3.o .. .. | 0 3 | 0 0 0 3 0 | * * * * * 64 * * | 0 0 0 0 1 0 0 1 1 0 0 | 0 1 1 0 0 1
.x .. .. .x | 0 4 | 0 0 0 2 2 | * * * * * * 96 * | 0 0 0 0 0 1 0 0 1 1 0 | 0 0 1 1 0 1
.. .. .o4.x | 0 4 | 0 0 0 0 4 | * * * * * * * 48 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 0 1 1 1
---------------+-------+----------------+-------------------------+--------------------------------+---------------
x.3o.3o. .. ♦ 4 0 | 6 0 0 0 0 | 4 0 0 0 0 0 0 0 | 16 * * * * * * * * * * | 1 1 0 0 0 0
x.3o. .. x. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 | * 32 * * * * * * * * * | 1 0 1 0 0 0
x. .. o.4x. ♦ 8 0 | 4 8 0 0 0 | 0 4 2 0 0 0 0 0 | * * 24 * * * * * * * * | 1 0 0 1 0 0
.. o.3o.4x. ♦ 8 0 | 0 12 0 0 0 | 0 0 6 0 0 0 0 0 | * * * 8 * * * * * * * | 1 0 0 0 1 0
xx3oo .. ..&#x ♦ 3 3 | 3 0 3 3 0 | 1 0 0 3 0 1 0 0 | * * * * 64 * * * * * * | 0 1 1 0 0 0
xx .. .. xx&#x ♦ 4 4 | 2 2 4 2 2 | 0 1 0 2 2 0 1 0 | * * * * * 96 * * * * * | 0 0 1 1 0 0
.. .. oo4xx&#x ♦ 4 4 | 0 4 4 0 4 | 0 0 1 0 4 0 0 1 | * * * * * * 48 * * * * | 0 0 0 1 1 0
.x3.o3.o .. ♦ 0 4 | 0 0 0 6 0 | 0 0 0 0 0 4 0 0 | * * * * * * * 16 * * * | 0 1 0 0 0 1
.x3.o .. .x ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 2 3 0 | * * * * * * * * 32 * * | 0 0 1 0 0 1
.x .. .o4.x ♦ 0 8 | 0 0 0 4 8 | 0 0 0 0 0 0 4 2 | * * * * * * * * * 24 * | 0 0 0 1 0 1
.. .o3.o4.x ♦ 0 8 | 0 0 0 0 12 | 0 0 0 0 0 0 0 6 | * * * * * * * * * * 8 | 0 0 0 0 1 1
---------------+-------+----------------+-------------------------+--------------------------------+---------------
x.3o.3o.4x. ♦ 64 0 | 96 96 0 0 0 | 64 96 48 0 0 0 0 0 | 16 32 24 8 0 0 0 0 0 0 0 | 1 * * * * *
xx3oo3oo ..&#x ♦ 4 4 | 6 0 4 6 0 | 4 0 0 6 0 4 0 0 | 1 0 0 0 4 0 0 1 0 0 0 | * 16 * * * *
xx3oo .. xx&#x ♦ 6 6 | 6 3 6 6 3 | 2 3 0 6 3 2 3 0 | 0 1 0 0 2 3 0 0 1 0 0 | * * 32 * * *
xx .. oo4xx&#x ♦ 8 8 | 4 8 8 4 8 | 0 4 2 4 8 0 4 2 | 0 0 1 0 0 4 2 0 0 1 0 | * * * 24 * *
.. oo3oo4xx&#x ♦ 8 8 | 0 12 8 0 12 | 0 0 6 0 12 0 0 6 | 0 0 0 1 0 0 6 0 0 0 1 | * * * * 8 *
.x3.o3.o4.x ♦ 0 64 | 0 0 0 96 96 | 0 0 0 0 0 64 96 48 | 0 0 0 0 0 0 0 16 32 24 8 | * * * * * 1
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