- general polytopal classes:
- Wythoffian polytera segmentotera lace simplices
links
| Acronym | thexip |
| Name | truncated-hexadecachoron prism |
| Circumradius | sqrt(11)/2 = 1.658312 |
| Coordinates | (sqrt(2), 1/sqrt(2), 0, 0) & all permutations in all but last coord., all changes of sign |
| Volume | 77/6 = 12.833333 |
| Face vector | 96, 288, 312, 144, 26 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x x3x3o4o . . . . . | 96 | 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1 ----------+----+-----------+--------------+-------------+------- x . . . . | 2 | 48 * * | 1 4 0 0 | 4 4 0 0 | 4 1 0 . x . . . | 2 | * 48 * | 1 0 4 0 | 4 0 4 0 | 4 0 1 . . x . . | 2 | * * 192 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------+----+-----------+--------------+-------------+------- x x . . . | 4 | 2 2 0 | 24 * * * | 4 0 0 0 | 4 0 0 x . x . . | 4 | 2 0 2 | * 96 * * | 1 2 0 0 | 2 1 0 . x3x . . | 6 | 0 3 3 | * * 64 * | 1 0 2 0 | 2 0 1 . . x3o . | 3 | 0 0 3 | * * * 128 | 0 1 1 1 | 1 1 1 ----------+----+-----------+--------------+-------------+------- x x3x . . ♦ 12 | 6 6 6 | 3 3 2 0 | 32 * * * | 2 0 0 x . x3o . ♦ 6 | 3 0 6 | 0 3 0 2 | * 64 * * | 1 1 0 . x3x3o . ♦ 12 | 0 6 12 | 0 0 4 4 | * * 32 * | 1 0 1 . . x3o4o ♦ 6 | 0 0 12 | 0 0 0 8 | * * * 16 | 0 1 1 ----------+----+-----------+--------------+-------------+------- x x3x3o . ♦ 24 | 12 12 24 | 6 12 8 8 | 4 4 2 0 | 16 * * x . x3o4o ♦ 12 | 6 0 24 | 0 12 0 16 | 0 8 0 2 | * 8 * . x3x3o4o ♦ 48 | 0 24 96 | 0 0 32 64 | 0 0 16 8 | * * 2
x x3x3o *c3o . . . . . | 96 | 1 1 4 | 1 4 4 2 2 | 4 2 2 2 2 1 | 2 2 1 1 -------------+----+-----------+----------------+-------------------+-------- x . . . . | 2 | 48 * * | 1 4 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0 . x . . . | 2 | * 48 * | 1 0 4 0 0 | 4 0 0 2 2 0 | 2 2 0 1 . . x . . | 2 | * * 192 | 0 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 -------------+----+-----------+----------------+-------------------+-------- x x . . . | 4 | 2 2 0 | 24 * * * * | 4 0 0 0 0 0 | 2 2 0 0 x . x . . | 4 | 2 0 2 | * 96 * * * | 1 1 1 0 0 0 | 1 1 1 0 . x3x . . | 6 | 0 3 3 | * * 64 * * | 1 0 0 1 1 0 | 1 1 0 1 . . x3o . | 3 | 0 0 3 | * * * 64 * | 0 1 0 1 0 1 | 1 0 1 1 . . x . *c3o | 3 | 0 0 3 | * * * * 64 | 0 0 1 0 1 1 | 0 1 1 1 -------------+----+-----------+----------------+-------------------+-------- x x3x . . ♦ 12 | 6 6 6 | 3 3 2 0 0 | 32 * * * * * | 1 1 0 0 x . x3o . ♦ 6 | 3 0 6 | 0 3 0 2 0 | * 32 * * * * | 1 0 1 0 x . x . *c3o ♦ 6 | 3 0 6 | 0 3 0 0 2 | * * 32 * * * | 0 1 1 0 . x3x3o . ♦ 12 | 0 6 12 | 0 0 4 4 0 | * * * 16 * * | 1 0 0 1 . x3x . *c3o ♦ 12 | 0 6 12 | 0 0 4 0 4 | * * * * 16 * | 0 1 0 1 . . x3o *c3o ♦ 6 | 0 0 12 | 0 0 0 4 4 | * * * * * 16 | 0 0 1 1 -------------+----+-----------+----------------+-------------------+-------- x x3x3o . ♦ 24 | 12 12 24 | 6 12 8 8 0 | 4 4 0 2 0 0 | 8 * * * x x3x . *c3o ♦ 24 | 12 12 24 | 6 12 8 0 8 | 4 0 4 0 2 0 | * 8 * * x . x3o *c3o ♦ 12 | 6 0 24 | 0 12 0 8 8 | 0 4 4 0 0 2 | * * 8 * . x3x3o *c3o ♦ 48 | 0 24 96 | 0 0 32 32 32 | 0 0 0 8 8 8 | * * * 2
x2o3x3o4s
demi( . . . . . ) | 96 | 1 4 1 | 4 2 2 1 4 | 2 2 1 2 4 2 | 1 2 1 2
------------------+----+-----------+----------------+-------------------+--------
demi( x . . . . ) | 2 | 48 * * | 4 0 0 1 0 | 2 2 0 0 4 0 | 1 2 0 2
demi( . . x . . ) | 2 | * 192 * | 1 1 1 0 1 | 1 1 1 1 1 1 | 1 1 1 1
. . . o4s | 2 | * * 48 | 0 0 0 1 4 | 0 0 0 2 4 2 | 0 2 1 2
------------------+----+-----------+----------------+-------------------+--------
demi( x . x . . ) | 4 | 2 2 0 | 96 * * * * | 1 1 0 0 1 0 | 1 1 0 1
demi( . o3x . . ) | 3 | 0 3 0 | * 64 * * * | 1 0 1 0 0 1 | 1 0 1 1
demi( . . x3o . ) | 3 | 0 3 0 | * * 64 * * | 0 1 1 1 0 0 | 1 1 1 0
x 2 . o4s | 4 | 2 0 2 | * * * 24 * | 0 0 0 0 4 0 | 0 2 0 2
sefa( . . x3o4s ) | 6 | 0 3 3 | * * * * 64 | 0 0 0 1 1 1 | 0 1 1 1
------------------+----+-----------+----------------+-------------------+--------
demi( x o3x . . ) ♦ 6 | 3 6 0 | 3 2 0 0 0 | 32 * * * * * | 1 0 0 1
demi( x . x3o . ) ♦ 6 | 3 6 0 | 3 0 2 0 0 | * 32 * * * * | 1 1 0 0
demi( . o3x3o . ) ♦ 6 | 0 12 0 | 0 4 4 0 0 | * * 16 * * * | 1 0 1 0
. . x3o4s ♦ 12 | 0 12 6 | 0 0 4 0 4 | * * * 16 * * | 0 1 1 0
sefa( x 2 x3o4s ) ♦ 12 | 6 6 6 | 3 0 0 3 2 | * * * * 32 * | 0 1 0 1
sefa( . o3x3o4s ) ♦ 12 | 0 12 6 | 0 4 0 0 4 | * * * * * 16 | 0 0 1 1
------------------+----+-----------+----------------+-------------------+--------
demi( x o3x3o . ) ♦ 12 | 6 24 0 | 12 8 8 0 0 | 4 4 2 0 0 0 | 8 * * *
x 2 x3o4s ♦ 24 | 12 24 12 | 12 0 8 6 8 | 0 4 0 2 4 0 | * 8 * *
. o3x3o4s ♦ 48 | 0 96 24 | 0 32 32 0 32 | 0 0 8 8 0 8 | * * 2 *
sefa( x2o3x3o4s ) ♦ 24 | 12 24 12 | 12 8 0 6 8 | 4 0 0 0 4 2 | * * * 8
starting figure: x o3x3o4x
xx3xx3oo4oo&#x → height = 1
(thex || thex)
o.3o.3o.4o. | 48 * | 1 4 1 0 0 | 4 4 1 4 0 0 | 4 1 4 4 0 0 | 1 4 1 0
.o3.o3.o4.o | * 48 | 0 0 1 1 4 | 0 0 1 4 4 4 | 0 0 4 4 4 1 | 0 4 1 1
---------------+-------+----------------+-------------------+-----------------+---------
x. .. .. .. | 2 0 | 24 * * * * | 4 0 1 0 0 0 | 4 0 4 0 0 0 | 1 4 0 0
.. x. .. .. | 2 0 | * 96 * * * | 1 2 0 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
oo3oo3oo4oo&#x | 1 1 | * * 48 * * | 0 0 1 4 0 0 | 0 0 4 4 0 0 | 0 4 1 0
.x .. .. .. | 0 2 | * * * 24 * | 0 0 1 0 4 0 | 0 0 4 0 4 0 | 0 4 0 1
.. .x .. .. | 0 2 | * * * * 96 | 0 0 0 1 1 2 | 0 0 1 2 2 1 | 0 2 1 1
---------------+-------+----------------+-------------------+-----------------+---------
x.3x. .. .. | 6 0 | 3 3 0 0 0 | 32 * * * * * | 2 0 1 0 0 0 | 1 2 0 0
.. x.3o. .. | 3 0 | 0 3 0 0 0 | * 64 * * * * | 1 1 0 1 0 0 | 1 1 1 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * 24 * * * | 0 0 4 0 0 0 | 0 4 0 0
.. xx .. ..&#x | 2 2 | 0 1 2 0 1 | * * * 96 * * | 0 0 1 2 0 0 | 0 2 1 0
.x3.x .. .. | 0 6 | 0 0 0 3 3 | * * * * 32 * | 0 0 1 0 2 0 | 0 2 0 1
.. .x3.o .. | 0 3 | 0 0 0 0 3 | * * * * * 64 | 0 0 0 1 1 1 | 0 1 1 1
---------------+-------+----------------+-------------------+-----------------+---------
x.3x.3o. .. ♦ 12 0 | 6 12 0 0 0 | 4 4 0 0 0 0 | 16 * * * * * | 1 1 0 0
.. x.3o.4o. ♦ 6 0 | 0 12 0 0 0 | 0 8 0 0 0 0 | * 8 * * * * | 1 0 1 0
xx3xx .. ..&#x ♦ 6 6 | 3 3 6 3 3 | 1 0 3 3 1 0 | * * 32 * * * | 0 2 0 0
.. xx3oo ..&#x ♦ 3 3 | 0 3 3 0 3 | 0 1 0 3 0 1 | * * * 64 * * | 0 1 1 0
.x3.x3.o .. ♦ 0 12 | 0 0 0 6 12 | 0 0 0 0 4 4 | * * * * 16 * | 0 1 0 1
.. .x3.o4.o ♦ 0 6 | 0 0 0 0 12 | 0 0 0 0 0 8 | * * * * * 8 | 0 0 1 1
---------------+-------+----------------+-------------------+-----------------+---------
x.3x.3o.4o. ♦ 48 0 | 24 96 0 0 0 | 32 64 0 0 0 0 | 16 8 0 0 0 0 | 1 * * *
xx3xx3oo ..&#x ♦ 12 12 | 6 12 12 6 12 | 4 4 6 12 4 4 | 1 0 4 4 1 0 | * 16 * *
.. xx3oo4oo&#x ♦ 6 6 | 0 12 6 0 12 | 0 8 0 12 0 8 | 0 1 0 8 0 1 | * * 8 *
.x3.x3.o4.o ♦ 0 48 | 0 0 0 24 96 | 0 0 0 0 32 64 | 0 0 0 0 16 8 | * * * 1
xx3xx3oo *b3oo&#x → height = 1
(thex || thex)
o.3o.3o. *b3o. | 48 * | 1 4 1 0 0 | 4 2 2 1 4 0 0 0 | 2 2 1 4 2 2 0 0 0 | 1 2 2 1 0
.o3.o3.o *b3.o | * 48 | 0 0 1 1 4 | 0 0 0 1 4 4 2 2 | 0 0 0 4 2 2 2 2 1 | 0 2 2 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x. .. .. .. | 2 0 | 24 * * * * | 4 0 0 1 0 0 0 0 | 2 2 0 4 0 0 0 0 0 | 1 2 2 0 0
.. x. .. .. | 2 0 | * 96 * * * | 1 1 1 0 1 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
oo3oo3oo *b3oo&#x | 1 1 | * * 48 * * | 0 0 0 1 4 0 0 0 | 0 0 0 4 2 2 0 0 0 | 0 2 2 1 0
.x .. .. .. | 0 2 | * * * 24 * | 0 0 0 1 0 4 0 0 | 0 0 0 4 0 0 2 2 0 | 0 2 2 0 1
.. .x .. .. | 0 2 | * * * * 96 | 0 0 0 0 1 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x.3x. .. .. | 6 0 | 3 3 0 0 0 | 32 * * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
.. x.3o. .. | 3 0 | 0 3 0 0 0 | * 32 * * * * * * | 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
.. x. .. *b3o. | 3 0 | 0 3 0 0 0 | * * 32 * * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
xx .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * * 24 * * * * | 0 0 0 4 0 0 0 0 0 | 0 2 2 0 0
.. xx .. ..&#x | 2 2 | 0 1 2 0 1 | * * * * 96 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.x3.x .. .. | 0 6 | 0 0 0 3 3 | * * * * * 32 * * | 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1
.. .x3.o .. | 0 3 | 0 0 0 0 3 | * * * * * * 32 * | 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
.. .x .. *b3.o | 0 3 | 0 0 0 0 3 | * * * * * * * 32 | 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x.3x.3o. .. ♦ 12 0 | 6 12 0 0 0 | 4 4 0 0 0 0 0 0 | 8 * * * * * * * * | 1 1 0 0 0
x.3x. .. *b3o. ♦ 12 0 | 6 12 0 0 0 | 4 0 4 0 0 0 0 0 | * 8 * * * * * * * | 1 0 1 0 0
.. x.3o. *b3o. ♦ 6 0 | 0 12 0 0 0 | 0 4 4 0 0 0 0 0 | * * 8 * * * * * * | 1 0 0 1 0
xx3xx .. ..&#x ♦ 6 6 | 3 3 6 3 3 | 1 0 0 3 3 1 0 0 | * * * 32 * * * * * | 0 1 1 0 0
.. xx3oo ..&#x ♦ 3 3 | 0 3 3 0 3 | 0 1 0 0 3 0 1 0 | * * * * 32 * * * * | 0 1 0 1 0
.. xx .. *b3oo&#x ♦ 3 3 | 0 3 3 0 3 | 0 0 1 0 3 0 0 1 | * * * * * 32 * * * | 0 0 1 1 0
.x3.x3.o .. ♦ 0 12 | 0 0 0 6 12 | 0 0 0 0 0 4 4 0 | * * * * * * 8 * * | 0 1 0 0 1
.x3.x .. *b3.o ♦ 0 12 | 0 0 0 6 12 | 0 0 0 0 0 4 0 4 | * * * * * * * 8 * | 0 0 1 0 1
.. .x3.o *b3.o ♦ 0 6 | 0 0 0 0 12 | 0 0 0 0 0 0 4 4 | * * * * * * * * 8 | 0 0 0 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x.3x.3o. *b3o. ♦ 48 0 | 24 96 0 0 0 | 32 32 32 0 0 0 0 0 | 8 8 8 0 0 0 0 0 0 | 1 * * * *
xx3xx3oo ..&#x ♦ 12 12 | 6 12 12 6 12 | 4 4 0 6 12 4 4 0 | 1 0 0 4 4 0 1 0 0 | * 8 * * *
xx3xx .. *b3oo&#x ♦ 12 12 | 6 12 12 6 12 | 4 0 4 6 12 4 0 4 | 0 1 0 4 0 4 0 1 0 | * * 8 * *
.. xx3oo *b3oo&#x ♦ 6 6 | 0 12 6 0 12 | 0 4 4 0 12 0 4 4 | 0 0 1 0 4 4 0 0 1 | * * * 8 *
.x3.x3.o *b3.o ♦ 0 48 | 0 0 0 24 96 | 0 0 0 0 0 32 32 32 | 0 0 0 0 0 0 8 8 8 | * * * * 1
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