vertex figure of barz
- more general:
- n,hex-dip
- general polytopal classes:
- Wythoffian polypeta lace simplices
links
| Acronym | trahex |
| Name |
triangle - hexadecachoron duoprism, vertex figure of barz |
| Circumradius | sqrt(5/6) = 0.912871 |
| Volume | sqrt(3)/24 = 0.072169 |
| Face vector | 24, 96, 176, 168, 83, 19 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o x3o3o4o . . . . . . | 24 | 2 6 | 1 12 12 | 6 12 8 | 12 16 1 | 8 2 ------------+----+-------+---------+----------+---------+----- x . . . . . | 2 | 24 * | 1 6 0 | 6 12 0 | 12 8 0 | 8 1 . . x . . . | 2 | * 72 | 0 2 4 | 1 8 4 | 4 8 1 | 4 2 ------------+----+-------+---------+----------+---------+----- x3o . . . . | 3 | 3 0 | 8 * * ♦ 6 0 0 | 12 0 0 | 8 0 x . x . . . | 4 | 2 2 | * 72 * | 1 4 0 | 4 4 0 | 4 1 . . x3o . . | 3 | 0 3 | * * 96 | 0 2 2 | 1 4 1 | 2 2 ------------+----+-------+---------+----------+---------+----- x3o x . . . ♦ 6 | 6 3 | 2 3 0 | 24 * * | 4 0 0 | 4 0 x . x3o . . ♦ 6 | 3 6 | 0 3 2 | * 96 * | 1 2 0 | 2 1 . . x3o3o . ♦ 4 | 0 6 | 0 0 4 | * * 48 | 0 2 1 | 1 2 ------------+----+-------+---------+----------+---------+----- x3o x3o . . ♦ 9 | 9 9 | 3 9 3 | 3 3 0 | 32 * * | 2 0 x . x3o3o . ♦ 8 | 4 12 | 0 6 8 | 0 4 2 | * 48 * | 1 1 . . x3o3o4o ♦ 8 | 0 24 | 0 0 32 | 0 0 16 | * * 3 | 0 2 ------------+----+-------+---------+----------+---------+----- x3o x3o3o . ♦ 12 | 12 18 | 4 18 12 | 6 12 3 | 4 3 0 | 16 * x . x3o3o4o ♦ 16 | 8 48 | 0 24 64 | 0 32 32 | 0 16 2 | * 3
x3o x3o3o *d3o . . . . . . | 24 | 2 6 | 1 12 12 | 6 12 4 4 | 12 8 8 1 | 4 4 2 ---------------+----+-------+---------+-------------+------------+------ x . . . . . | 2 | 24 * | 1 6 0 | 6 12 0 0 | 12 4 4 0 | 4 4 1 . . x . . . | 2 | * 72 | 0 2 4 | 1 8 2 2 | 4 4 4 1 | 2 2 2 ---------------+----+-------+---------+-------------+------------+------ x3o . . . . | 3 | 3 0 | 8 * * ♦ 6 0 0 0 | 12 0 0 0 | 4 4 0 x . x . . . | 4 | 2 2 | * 72 * | 1 4 0 0 | 4 2 2 0 | 2 2 1 . . x3o . . | 3 | 0 3 | * * 96 | 0 2 1 1 | 1 2 2 1 | 1 1 2 ---------------+----+-------+---------+-------------+------------+------ x3o x . . . ♦ 6 | 6 3 | 2 3 0 | 24 * * * | 4 0 0 0 | 2 2 0 x . x3o . . ♦ 6 | 3 6 | 0 3 2 | * 96 * * | 1 1 1 0 | 1 1 1 . . x3o3o . ♦ 4 | 0 6 | 0 0 4 | * * 24 * | 0 2 0 1 | 1 0 2 . . x3o . *d3o ♦ 4 | 0 6 | 0 0 4 | * * * 24 | 0 0 2 1 | 0 1 2 ---------------+----+-------+---------+-------------+------------+------ x3o x3o . . ♦ 9 | 9 9 | 3 9 3 | 3 3 0 0 | 32 * * * | 1 1 0 x . x3o3o . ♦ 8 | 4 12 | 0 6 8 | 0 4 2 0 | * 24 * * | 1 0 1 x . x3o . *d3o ♦ 8 | 4 12 | 0 6 8 | 0 4 0 2 | * * 24 * | 0 1 1 . . x3o3o *d3o ♦ 8 | 0 24 | 0 0 32 | 0 0 8 8 | * * * 3 | 0 0 2 ---------------+----+-------+---------+-------------+------------+------ x3o x3o3o . ♦ 12 | 12 18 | 4 18 12 | 6 12 3 0 | 4 3 0 0 | 8 * * x3o x3o . *d3o ♦ 12 | 12 18 | 4 18 12 | 6 12 0 3 | 4 0 3 0 | * 8 * x . x3o3o *d3o ♦ 16 | 8 48 | 0 24 64 | 0 32 16 16 | 0 8 8 2 | * * 3
ox xx3oo3oo4oo&#x → height = 1/2
(hex || hexip)
o. o.3o.3o.4o. | 8 * | 6 2 0 0 | 12 1 12 0 0 | 8 6 24 0 0 | 1 12 16 0 0 | 8 2 0
.o .o3.o3.o4.o | * 16 | 0 1 1 6 | 0 1 6 6 12 | 0 6 12 12 8 | 0 12 8 8 1 | 8 1 1
------------------+------+------------+---------------+----------------+--------------+-------
.. x. .. .. .. | 2 0 | 24 * * * | 4 0 2 0 0 | 4 1 8 0 0 | 1 4 8 0 0 | 4 2 0
oo oo3oo3oo4oo&#x | 1 1 | * 16 * * | 0 1 6 0 0 | 0 6 12 0 0 | 0 12 8 0 0 | 8 1 0
.x .. .. .. .. | 0 2 | * * 8 * | 0 1 0 6 0 | 0 6 0 12 0 | 0 12 0 8 0 | 8 0 1
.. .x .. .. .. | 0 2 | * * * 48 | 0 0 1 1 4 | 0 1 4 4 4 | 0 4 4 4 1 | 4 1 1
------------------+------+------------+---------------+----------------+--------------+-------
.. x.3o. .. .. | 3 0 | 3 0 0 0 | 32 * * * * | 2 0 2 0 0 | 1 1 4 0 0 | 2 2 0
ox .. .. .. ..&#x | 1 2 | 0 2 1 0 | * 8 * * * ♦ 0 6 0 0 0 | 0 12 0 0 0 | 8 0 0
.. xx .. .. ..&#x | 2 2 | 1 2 0 1 | * * 48 * * | 0 1 4 0 0 | 0 4 4 0 0 | 4 1 0
.x .x .. .. .. | 0 4 | 0 0 2 2 | * * * 24 * | 0 1 0 4 0 | 0 4 0 4 0 | 4 0 1
.. .x3.o .. .. | 0 3 | 0 0 0 3 | * * * * 64 | 0 0 1 1 2 | 0 1 2 2 1 | 2 1 1
------------------+------+------------+---------------+----------------+--------------+-------
.. x.3o.3o. .. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 | 16 * * * * | 1 0 2 0 0 | 1 2 0
ox xx .. .. ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 1 0 | * 24 * * * | 0 4 0 0 0 | 4 0 0
.. xx3oo .. ..&#x ♦ 3 3 | 3 3 0 3 | 1 0 3 0 1 | * * 64 * * | 0 1 2 0 0 | 2 1 0
.x .x3.o .. .. ♦ 0 6 | 0 0 3 6 | 0 0 0 3 2 | * * * 32 * | 0 1 0 2 0 | 2 0 1
.. .x3.o3.o .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * 32 | 0 0 1 1 1 | 1 1 1
------------------+------+------------+---------------+----------------+--------------+-------
.. x.3o.3o.4o. ♦ 8 0 | 24 0 0 0 | 32 0 0 0 0 | 16 0 0 0 0 | 1 * * * * | 0 2 0
ox xx3oo .. ..&#x ♦ 3 6 | 3 6 3 6 | 1 3 6 3 2 | 0 3 2 1 0 | * 32 * * * | 2 0 0
.. xx3oo3oo ..&#x ♦ 4 4 | 6 4 0 6 | 4 0 6 0 4 | 1 0 4 0 1 | * * 32 * * | 1 1 0
.x .x3.o3.o .. ♦ 0 8 | 0 0 4 12 | 0 0 0 6 8 | 0 0 0 4 2 | * * * 16 * | 1 0 1
.. .x3.o3.o4.o ♦ 0 8 | 0 0 0 24 | 0 0 0 0 32 | 0 0 0 0 16 | * * * * 2 | 0 1 1
------------------+------+------------+---------------+----------------+--------------+-------
ox xx3oo3oo ..&#x ♦ 4 8 | 6 8 4 12 | 4 4 12 6 8 | 1 6 8 4 2 | 0 4 2 1 0 | 16 * *
.. xx3oo3oo4oo&#x ♦ 8 8 | 24 8 0 24 | 32 0 24 0 32 | 16 0 32 0 16 | 1 0 16 0 1 | * 2 *
.x .x3.o3.o4.o ♦ 0 16 | 0 0 8 48 | 0 0 0 24 64 | 0 0 0 32 32 | 0 0 0 16 2 | * * 1
xx3oo xo3oo3ox&#x → height = 1/sqrt(2) = 0.707107
(shallower version of: tratet || para-dual tratet)
o.3o. o.3o.3o. | 12 * | 2 3 3 0 0 | 1 6 3 6 6 3 0 0 0 | 3 6 1 3 12 6 3 3 1 0 0 0 | 3 2 6 3 6 6 2 1 0 0 | 1 3 3 1 2 0
.o3.o .o3.o3.o | * 12 | 0 0 3 2 3 | 0 0 0 6 3 6 1 6 3 | 0 0 0 3 6 12 1 3 3 3 6 1 | 0 0 3 6 2 6 6 1 3 2 | 0 1 3 3 2 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x. .. .. .. .. | 2 0 | 12 * * * * | 1 3 0 3 0 0 0 0 0 | 3 3 0 3 6 3 0 0 0 0 0 0 | 3 1 6 3 3 3 1 0 0 0 | 1 3 3 1 1 0
.. .. x. .. .. | 2 0 | * 18 * * * | 0 2 2 0 2 0 0 0 0 | 1 4 1 0 4 0 2 1 0 0 0 0 | 2 2 2 0 4 2 0 1 0 0 | 1 2 1 0 2 0
oo3oo oo3oo3oo&#x | 1 1 | * * 36 * * | 0 0 0 2 2 2 0 0 0 | 0 0 0 1 4 4 1 2 1 0 0 0 | 0 0 2 2 2 4 2 1 0 0 | 0 1 2 1 2 0
.x .. .. .. .. | 0 2 | * * * 12 * | 0 0 0 3 0 0 1 3 0 | 0 0 0 3 3 6 0 0 0 3 3 0 | 0 0 3 6 1 3 3 0 3 1 | 0 1 3 3 1 1
.. .. .. .. .x | 0 2 | * * * * 18 | 0 0 0 0 0 2 0 2 2 | 0 0 0 0 0 4 0 1 2 1 4 1 | 0 0 0 2 0 2 4 1 2 2 | 0 0 1 2 2 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x.3o. .. .. .. | 3 0 | 3 0 0 0 0 | 4 * * * * * * * * ♦ 3 0 0 3 0 0 0 0 0 0 0 0 | 3 0 6 3 0 0 0 0 0 0 | 1 3 3 1 0 0
x. .. x. .. .. | 4 0 | 2 2 0 0 0 | * 18 * * * * * * * | 1 2 0 0 2 0 0 0 0 0 0 0 | 2 1 2 0 2 1 0 0 0 0 | 1 2 1 0 1 0
.. .. x.3o. .. | 3 0 | 0 3 0 0 0 | * * 12 * * * * * * | 0 2 1 0 0 0 1 0 0 0 0 0 | 1 2 0 0 2 0 0 1 0 0 | 1 1 0 0 2 0
xx .. .. .. ..&#x | 2 2 | 1 0 2 1 0 | * * * 36 * * * * * | 0 0 0 1 2 2 0 0 0 0 0 0 | 0 0 2 2 1 2 1 0 0 0 | 0 1 2 1 1 0
.. .. xo .. ..&#x | 2 1 | 0 1 2 0 0 | * * * * 36 * * * * | 0 0 0 0 2 0 1 1 0 0 0 0 | 0 0 1 0 2 2 0 1 0 0 | 0 1 1 0 2 0
.. .. .. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * * * 36 * * * | 0 0 0 0 0 2 0 1 1 0 0 0 | 0 0 0 1 0 2 2 1 0 0 | 0 0 1 1 2 0
.x3.o .. .. .. | 0 3 | 0 0 0 3 0 | * * * * * * 4 * * ♦ 0 0 0 3 0 0 0 0 0 3 0 0 | 0 0 3 6 0 0 0 0 3 0 | 0 1 3 3 0 1
.x .. .. .. .x | 0 4 | 0 0 0 2 2 | * * * * * * * 18 * | 0 0 0 0 0 2 0 0 0 1 2 0 | 0 0 0 2 0 1 2 0 2 1 | 0 0 1 2 1 1
.. .. .. .o3.x | 0 3 | 0 0 0 0 3 | * * * * * * * * 12 | 0 0 0 0 0 0 0 0 1 0 2 1 | 0 0 0 0 0 0 2 1 1 2 | 0 0 0 1 2 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x.3o. x. .. .. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 0 | 6 * * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 | 1 2 1 0 0 0
x. .. x.3o. .. ♦ 6 0 | 3 6 0 0 0 | 0 3 2 0 0 0 0 0 0 | * 12 * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 | 1 1 0 0 1 0
.. .. x.3o.3o. ♦ 4 0 | 0 6 0 0 0 | 0 0 4 0 0 0 0 0 0 | * * 3 * * * * * * * * * | 0 2 0 0 0 0 0 1 0 0 | 1 0 0 0 2 0
xx3oo .. .. ..&#x ♦ 3 3 | 3 0 3 3 0 | 1 0 0 3 0 0 1 0 0 | * * * 12 * * * * * * * * | 0 0 2 2 0 0 0 0 0 0 | 0 1 2 1 0 0
xx .. xo .. ..&#x ♦ 4 2 | 2 2 4 1 0 | 0 1 0 2 2 0 0 0 0 | * * * * 36 * * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 0 1 0
xx .. .. .. ox&#x ♦ 2 4 | 1 0 4 2 2 | 0 0 0 2 0 2 0 1 0 | * * * * * 36 * * * * * * | 0 0 0 1 0 1 1 0 0 0 | 0 0 1 1 1 0
.. .. xo3oo ..&#x ♦ 3 1 | 0 3 3 0 0 | 0 0 1 0 3 0 0 0 0 | * * * * * * 12 * * * * * | 0 0 0 0 2 0 0 1 0 0 | 0 1 0 0 2 0
.. .. xo .. ox&#x ♦ 2 2 | 0 1 4 0 1 | 0 0 0 0 2 2 0 0 0 | * * * * * * * 18 * * * * | 0 0 0 0 0 2 0 1 0 0 | 0 0 1 0 2 0
.. .. .. oo3ox&#x ♦ 1 3 | 0 0 3 0 3 | 0 0 0 0 0 3 0 0 1 | * * * * * * * * 12 * * * | 0 0 0 0 0 0 2 1 0 0 | 0 0 0 1 2 0
.x3.o .. .. .x ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 2 3 0 | * * * * * * * * * 6 * * | 0 0 0 2 0 0 0 0 2 0 | 0 0 1 2 0 1
.x .. .. .o3.x ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * 12 * | 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1
.. .. .o3.o3.x ♦ 0 4 | 0 0 0 0 6 | 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 1 0 2 | 0 0 0 0 2 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x.3o. x.3o. .. ♦ 9 0 | 9 9 0 0 0 | 3 9 3 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 0 0 | 4 * * * * * * * * * | 1 1 0 0 0 0
x. .. x.3o.3o. ♦ 8 0 | 4 12 0 0 0 | 0 6 8 0 0 0 0 0 0 | 0 4 2 0 0 0 0 0 0 0 0 0 | * 3 * * * * * * * * | 1 0 0 0 1 0
xx3oo xo .. ..&#x ♦ 6 3 | 6 3 6 3 0 | 2 3 0 6 3 0 1 0 0 | 1 0 0 2 3 0 0 0 0 0 0 0 | * * 12 * * * * * * * | 0 1 1 0 0 0
xx3oo .. .. ox&#x ♦ 3 6 | 3 0 6 6 3 | 1 0 0 6 0 3 2 3 0 | 0 0 0 2 0 3 0 0 0 1 0 0 | * * * 12 * * * * * * | 0 0 1 1 0 0
xx .. xo3oo ..&#x ♦ 6 2 | 3 6 6 1 0 | 0 3 2 3 6 0 0 0 0 | 0 1 0 0 3 0 2 0 0 0 0 0 | * * * * 12 * * * * * | 0 1 0 0 1 0
xx .. xo .. ox&#x ♦ 4 4 | 2 2 8 2 2 | 0 1 0 4 4 4 0 1 0 | 0 0 0 0 2 2 0 2 0 0 0 0 | * * * * * 18 * * * * | 0 0 1 0 1 0
xx .. .. oo3ox&#x ♦ 2 6 | 1 0 6 3 6 | 0 0 0 3 0 6 0 3 2 | 0 0 0 0 0 3 0 0 2 0 1 0 | * * * * * * 12 * * * | 0 0 0 1 1 0
.. .. xo3oo3ox&#x ♦ 4 4 | 0 6 12 0 6 | 0 0 4 0 12 12 0 0 4 | 0 0 1 0 0 0 4 6 4 0 0 1 | * * * * * * * 3 * * | 0 0 0 0 2 0
.x3.o .. .o3.x ♦ 0 9 | 0 0 0 9 9 | 0 0 0 0 0 0 3 9 3 | 0 0 0 0 0 0 0 0 0 3 3 0 | * * * * * * * * 4 * | 0 0 0 1 0 1
.x .. .o3.o3.x ♦ 0 8 | 0 0 0 4 12 | 0 0 0 0 0 0 0 6 8 | 0 0 0 0 0 0 0 0 0 0 4 2 | * * * * * * * * * 3 | 0 0 0 0 1 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x.3o. x.3o.3o. ♦ 12 0 | 12 18 0 0 0 | 4 18 12 0 0 0 0 0 0 | 6 12 3 0 0 0 0 0 0 0 0 0 | 4 3 0 0 0 0 0 0 0 0 | 1 * * * * *
xx3oo xo3oo ..&#x ♦ 9 3 | 9 9 9 3 0 | 3 9 3 9 9 0 1 0 0 | 3 3 0 3 9 0 3 0 0 0 0 0 | 1 0 3 0 3 0 0 0 0 0 | * 4 * * * *
xx3oo xo .. ox&#x ♦ 6 6 | 6 3 12 6 3 | 2 3 0 12 6 6 2 3 0 | 1 0 0 4 6 6 0 3 0 1 0 0 | 0 0 2 2 0 3 0 0 0 0 | * * 6 * * *
xx3oo .. oo3ox&#x ♦ 3 9 | 3 0 9 9 9 | 1 0 0 9 0 9 3 9 3 | 0 0 0 3 0 9 0 0 3 3 3 0 | 0 0 0 3 0 0 3 0 1 0 | * * * 4 * *
xx .. xo3oo3ox&#x ♦ 8 8 | 4 12 24 4 12 | 0 6 8 12 24 24 0 6 8 | 0 4 2 0 12 12 8 12 8 0 4 2 | 0 1 0 0 4 6 4 2 0 1 | * * * * 3 *
.x3.o .o3.o3.x ♦ 0 12 | 0 0 0 12 18 | 0 0 0 0 0 0 4 18 12 | 0 0 0 0 0 0 0 0 0 6 12 3 | 0 0 0 0 0 0 0 0 4 3 | * * * * * 1
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