- more general:
- n,oct-dip (n,m-ap)-dip
- related segmentotera:
- hisquippy
- general polytopal classes:
- Wythoffian polytera segmentotera lace simplices
links
| Acronym | hoct |
| Name | hexagon octahedron duoprism |
| Circumradius | sqrt(3/2) = 1.224745 |
| Volume | sqrt(3/2) = 1.224745 |
| Face vector | 36, 108, 126, 66, 14 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x6o x3o4o . . . . . | 36 | 2 4 | 1 8 4 | 4 8 1 | 4 2 ----------+----+-------+---------+---------+---- x . . . . | 2 | 36 * | 1 4 0 | 4 4 0 | 4 1 . . x . . | 2 | * 72 | 0 2 2 | 1 4 1 | 2 2 ----------+----+-------+---------+---------+---- x6o . . . | 6 | 6 0 | 6 * * | 4 0 0 | 4 0 x . x . . | 4 | 2 2 | * 72 * | 1 2 0 | 2 1 . . x3o . | 3 | 0 3 | * * 48 | 0 2 1 | 1 2 ----------+----+-------+---------+---------+---- x6o x . . ♦ 12 | 12 6 | 2 6 0 | 12 * * | 2 0 x . x3o . ♦ 6 | 3 6 | 0 3 2 | * 48 * | 1 1 . . x3o4o ♦ 6 | 0 12 | 0 0 8 | * * 6 | 0 2 ----------+----+-------+---------+---------+---- x6o x3o . ♦ 18 | 18 18 | 3 18 6 | 3 6 0 | 8 * x . x3o4o ♦ 12 | 6 24 | 0 12 16 | 0 8 2 | * 6
x3x x3o4o . . . . . | 36 | 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1 ----------+----+----------+------------+------------+------ x . . . . | 2 | 18 * * | 1 4 0 0 | 4 4 0 0 | 4 1 0 . x . . . | 2 | * 18 * | 1 0 4 0 | 4 0 4 0 | 4 0 1 . . x . . | 2 | * * 72 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------+----+----------+------------+------------+------ x3x . . . | 6 | 3 3 0 | 6 * * * | 4 0 0 0 | 4 0 0 x . x . . | 4 | 2 0 2 | * 36 * * | 1 2 0 0 | 2 1 0 . x x . . | 4 | 0 2 2 | * * 36 * | 1 0 2 0 | 2 0 1 . . x3o . | 3 | 0 0 3 | * * * 48 | 0 1 1 1 | 1 1 1 ----------+----+----------+------------+------------+------ x3x x . . ♦ 12 | 6 6 6 | 2 3 3 0 | 12 * * * | 2 0 0 x . x3o . ♦ 6 | 3 0 6 | 0 3 0 2 | * 24 * * | 1 1 0 . x x3o . ♦ 6 | 0 3 6 | 0 0 3 2 | * * 24 * | 1 0 1 . . x3o4o ♦ 6 | 0 0 12 | 0 0 0 8 | * * * 6 | 0 1 1 ----------+----+----------+------------+------------+------ x3x x3o . ♦ 18 | 9 9 18 | 3 9 9 6 | 3 3 3 0 | 8 * * x . x3o4o ♦ 12 | 6 0 24 | 0 12 0 16 | 0 8 0 2 | * 3 * . x x3o4o ♦ 12 | 0 6 24 | 0 0 12 16 | 0 0 8 2 | * * 3
x6o o3x3o . . . . . | 36 | 2 4 | 1 8 2 2 | 4 4 4 1 | 2 2 2 ----------+----+-------+------------+------------+------ x . . . . | 2 | 36 * | 1 4 0 0 | 4 2 2 0 | 2 2 1 . . . x . | 2 | * 72 | 0 2 1 1 | 1 2 2 1 | 1 1 2 ----------+----+-------+------------+------------+------ x6o . . . | 6 | 6 0 | 6 * * * | 4 0 0 0 | 2 2 0 x . . x . | 4 | 2 2 | * 72 * * | 1 1 1 0 | 1 1 1 . . o3x . | 3 | 0 3 | * * 24 * | 0 2 0 1 | 1 0 2 . . . x3o | 3 | 0 3 | * * * 24 | 0 0 2 1 | 0 1 2 ----------+----+-------+------------+------------+------ x6o . x . ♦ 12 | 12 6 | 2 6 0 0 | 12 * * * | 1 1 0 x . o3x . ♦ 6 | 3 6 | 0 3 2 0 | * 24 * * | 1 0 1 x . . x3o ♦ 6 | 3 6 | 0 3 0 2 | * * 24 * | 0 1 1 . . o3x3o ♦ 6 | 0 12 | 0 0 4 4 | * * * 6 | 0 0 2 ----------+----+-------+------------+------------+------ x6o o3x . ♦ 18 | 18 18 | 3 18 6 0 | 3 6 0 0 | 4 * * x6o . x3o ♦ 18 | 18 18 | 3 18 0 6 | 3 0 6 0 | * 4 * x . o3x3o ♦ 12 | 6 24 | 0 12 8 8 | 0 4 4 2 | * * 6
x3x o3x3o . . . . . | 36 | 1 1 4 | 1 4 4 2 2 | 4 2 2 2 2 1 | 2 2 1 1 ----------+----+----------+---------------+------------------+-------- x . . . . | 2 | 18 * * | 1 4 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0 . x . . . | 2 | * 18 * | 1 0 4 0 0 | 4 0 0 2 2 0 | 2 2 0 1 . . . x . | 2 | * * 72 | 0 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 ----------+----+----------+---------------+------------------+-------- x3x . . . | 6 | 3 3 0 | 6 * * * * | 4 0 0 0 0 0 | 2 2 0 0 x . . x . | 4 | 2 0 2 | * 36 * * * | 1 1 1 0 0 0 | 1 1 1 0 . x . x . | 4 | 0 2 2 | * * 36 * * | 1 0 0 1 1 0 | 1 1 0 1 . . o3x . | 3 | 0 0 3 | * * * 24 * | 0 1 0 1 0 1 | 1 0 1 1 . . . x3o | 3 | 0 0 3 | * * * * 24 | 0 0 1 0 1 1 | 0 1 1 1 ----------+----+----------+---------------+------------------+-------- x3x . x . ♦ 12 | 6 6 6 | 2 3 3 0 0 | 12 * * * * * | 1 1 0 0 x . o3x . ♦ 6 | 3 0 6 | 0 3 0 2 0 | * 12 * * * * | 1 0 1 0 x . . x3o ♦ 6 | 3 0 6 | 0 3 0 0 2 | * * 12 * * * | 0 1 1 0 . x o3x . ♦ 6 | 0 3 6 | 0 0 3 2 0 | * * * 12 * * | 1 0 0 1 . x . x3o ♦ 6 | 0 3 6 | 0 0 3 0 2 | * * * * 12 * | 0 1 0 1 . . o3x3o ♦ 6 | 0 0 12 | 0 0 0 4 4 | * * * * * 6 | 0 0 1 1 ----------+----+----------+---------------+------------------+-------- x3x o3x . ♦ 18 | 9 9 18 | 3 9 9 6 0 | 3 3 0 3 0 0 | 4 * * * x3x . x3o ♦ 18 | 9 9 18 | 3 9 9 0 6 | 3 0 3 0 3 0 | * 4 * * x . o3x3o ♦ 12 | 6 0 24 | 0 12 0 8 8 | 0 4 4 0 0 2 | * * 3 * . x o3x3o ♦ 12 | 0 6 24 | 0 0 12 8 8 | 0 0 0 4 4 2 | * * * 3
xo3ox xx6oo&#x → height = sqrt(2/3) = 0.816497
(thiddip || {3}-gyro thiddip)
o.3o. o.6o. | 18 * | 2 2 2 0 0 | 1 4 1 2 1 4 0 0 0 | 2 2 1 4 2 2 0 0 | 1 2 2 1 0
.o3.o .o6.o | * 18 | 0 0 2 2 2 | 0 0 0 1 2 4 1 4 1 | 0 0 1 2 4 2 2 2 | 0 2 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x. .. .. .. | 2 0 | 18 * * * * | 1 2 0 1 0 0 0 0 0 | 2 1 1 2 0 0 0 0 | 1 2 1 0 0
.. .. x. .. | 2 0 | * 18 * * * | 0 2 1 0 0 2 0 0 0 | 1 2 0 2 1 2 0 0 | 1 1 2 1 0
oo3oo oo6oo&#x | 1 1 | * * 36 * * | 0 0 0 1 1 2 0 0 0 | 0 0 1 2 2 1 0 0 | 0 2 1 1 0
.. .x .. .. | 0 2 | * * * 18 * | 0 0 0 0 1 0 1 2 0 | 0 0 1 0 2 0 2 1 | 0 2 0 1 1
.. .. .x .. | 0 2 | * * * * 18 | 0 0 0 0 0 2 0 2 1 | 0 0 0 1 2 2 1 2 | 0 1 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. .. .. | 3 0 | 3 0 0 0 0 | 6 * * * * * * * * | 2 0 1 0 0 0 0 0 | 1 2 0 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 | * 18 * * * * * * * | 1 1 0 1 0 0 0 0 | 1 1 1 0 0
.. .. x.6o. | 6 0 | 0 6 0 0 0 | * * 3 * * * * * * | 0 2 0 0 0 2 0 0 | 1 0 2 1 0
xo .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * * 18 * * * * * | 0 0 1 2 0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x | 1 2 | 0 0 2 1 0 | * * * * 18 * * * * | 0 0 1 0 2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * * 36 * * * | 0 0 0 1 1 1 0 0 | 0 1 1 1 0
.o3.x .. .. | 0 3 | 0 0 0 3 0 | * * * * * * 6 * * | 0 0 1 0 0 0 2 0 | 0 2 0 0 1
.. .x .x .. | 0 4 | 0 0 0 2 2 | * * * * * * * 18 * | 0 0 0 0 1 0 1 1 | 0 1 0 1 1
.. .. .x6.o | 0 6 | 0 0 0 0 6 | * * * * * * * * 3 | 0 0 0 0 0 2 0 2 | 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 * * * * * * * | 1 1 0 0 0
x. .. x.6o. ♦ 12 0 | 6 12 0 0 0 | 0 6 2 0 0 0 0 0 0 | * 3 * * * * * * | 1 0 1 0 0
xo3ox .. ..&#x ♦ 3 3 | 3 0 6 3 0 | 1 0 0 3 3 0 1 0 0 | * * 6 * * * * * | 0 2 0 0 0
xo .. xx ..&#x ♦ 4 2 | 2 2 4 0 1 | 0 1 0 2 0 2 0 0 0 | * * * 18 * * * * | 0 1 1 0 0
.. ox xx ..&#x ♦ 2 4 | 0 1 4 2 2 | 0 0 0 0 2 2 0 1 0 | * * * * 18 * * * | 0 1 0 1 0
.. .. xx6oo&#x ♦ 6 6 | 0 6 6 0 6 | 0 0 1 0 0 6 0 0 1 | * * * * * 6 * * | 0 0 1 1 0
.o3.x .x .. ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 2 3 0 | * * * * * * 6 * | 0 1 0 0 1
.. .x .x6.o ♦ 0 12 | 0 0 0 6 12 | 0 0 0 0 0 0 0 6 2 | * * * * * * * 3 | 0 0 0 1 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.6o. ♦ 18 0 | 18 18 0 0 0 | 6 18 3 0 0 0 0 0 0 | 6 3 0 0 0 0 0 0 | 1 * * * *
xo3ox xx ..&#x ♦ 6 6 | 6 3 12 6 3 | 2 3 0 6 6 6 2 3 0 | 1 0 2 3 3 0 1 0 | * 6 * * *
xo .. xx6oo&#x ♦ 12 6 | 6 12 12 0 6 | 0 6 2 6 0 12 0 0 1 | 0 1 0 6 0 2 0 0 | * * 3 * *
.. ox xx6oo&#x ♦ 6 12 | 0 6 12 6 12 | 0 0 1 0 6 12 0 6 2 | 0 0 0 0 6 2 0 1 | * * * 3 *
.o3.x .x6.o ♦ 0 18 | 0 0 0 18 18 | 0 0 0 0 0 0 6 18 3 | 0 0 0 0 0 0 6 3 | * * * * 1
xo3ox xx3xx&#x → height = sqrt(2/3) = 0.816497
(thiddip || {3}-gyro thiddip)
o.3o. o.3o. | 18 * | 2 1 1 2 0 0 0 | 1 2 2 1 2 1 2 2 0 0 0 0 | 1 1 2 1 2 2 1 1 2 0 0 0 | 1 1 1 2 1 0
.o3.o .o3.o | * 18 | 0 0 0 2 2 1 1 | 0 0 0 0 1 2 2 2 1 2 2 1 | 0 0 0 1 1 1 2 2 2 1 1 2 | 0 1 1 1 2 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x. .. .. .. | 2 0 | 18 * * * * * * | 1 1 1 0 1 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 0 0
.. .. x. .. | 2 0 | * 9 * * * * * | 0 2 0 1 0 0 2 0 0 0 0 0 | 1 0 2 0 2 0 1 0 2 0 0 0 | 1 1 0 2 1 0
.. .. .. x. | 2 0 | * * 9 * * * * | 0 0 2 1 0 0 0 2 0 0 0 0 | 0 1 2 0 0 2 0 1 2 0 0 0 | 1 0 1 2 1 0
oo3oo oo3oo&#x | 1 1 | * * * 36 * * * | 0 0 0 0 1 1 1 1 0 0 0 0 | 0 0 0 1 1 1 1 1 1 0 0 0 | 0 1 1 1 1 0
.. .x .. .. | 0 2 | * * * * 18 * * | 0 0 0 0 0 1 0 0 1 1 1 0 | 0 0 0 1 0 0 1 1 0 1 1 1 | 0 1 1 0 1 1
.. .. .x .. | 0 2 | * * * * * 9 * | 0 0 0 0 0 0 2 0 0 2 0 1 | 0 0 0 0 1 0 2 0 2 1 0 2 | 0 1 0 1 2 1
.. .. .. .x | 0 2 | * * * * * * 9 | 0 0 0 0 0 0 0 2 0 0 2 1 | 0 0 0 0 0 1 0 2 2 0 1 2 | 0 0 1 1 2 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x.3o. .. .. | 3 0 | 3 0 0 0 0 0 0 | 6 * * * * * * * * * * * | 1 1 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 | * 9 * * * * * * * * * * | 1 0 1 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 | * * 9 * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
.. .. x.3x. | 6 0 | 0 3 3 0 0 0 0 | * * * 3 * * * * * * * * | 0 0 2 0 0 0 0 0 2 0 0 0 | 1 0 0 2 1 0
xo .. .. ..&#x | 2 1 | 1 0 0 2 0 0 0 | * * * * 18 * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
.. ox .. ..&#x | 1 2 | 0 0 0 2 1 0 0 | * * * * * 18 * * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 | 0 1 1 0 1 0
.. .. xx ..&#x | 2 2 | 0 1 0 2 0 1 0 | * * * * * * 18 * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 | 0 1 0 1 1 0
.. .. .. xx&#x | 2 2 | 0 0 1 2 0 0 1 | * * * * * * * 18 * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 | 0 0 1 1 1 0
.o3.x .. .. | 0 3 | 0 0 0 0 3 0 0 | * * * * * * * * 6 * * * | 0 0 0 1 0 0 0 0 0 1 1 0 | 0 1 1 0 0 1
.. .x .x .. | 0 4 | 0 0 0 0 2 2 0 | * * * * * * * * * 9 * * | 0 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 0 1 1
.. .x .. .x | 0 4 | 0 0 0 0 2 0 2 | * * * * * * * * * * 9 * | 0 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 0 1 1
.. .. .x3.x | 0 6 | 0 0 0 0 0 3 3 | * * * * * * * * * * * 3 | 0 0 0 0 0 0 0 0 2 0 0 2 | 0 0 0 1 2 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x.3o. x. .. ♦ 6 0 | 6 3 0 0 0 0 0 | 2 3 0 0 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * | 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 | * 3 * * * * * * * * * * | 1 0 1 0 0 0
x. .. x.3x. ♦ 12 0 | 6 6 6 0 0 0 0 | 0 3 3 2 0 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * | 1 0 0 1 0 0
xo3ox .. ..&#x ♦ 3 3 | 3 0 0 6 3 0 0 | 1 0 0 0 3 3 0 0 1 0 0 0 | * * * 6 * * * * * * * * | 0 1 1 0 0 0
xo .. xx ..&#x ♦ 4 2 | 2 2 0 4 0 1 0 | 0 1 0 0 2 0 2 0 0 0 0 0 | * * * * 9 * * * * * * * | 0 1 0 1 0 0
xo .. .. xx&#x ♦ 4 2 | 2 0 2 4 0 0 1 | 0 0 1 0 2 0 0 2 0 0 0 0 | * * * * * 9 * * * * * * | 0 0 1 1 0 0
.. ox xx ..&#x ♦ 2 4 | 0 1 0 4 2 2 0 | 0 0 0 0 0 2 2 0 0 1 0 0 | * * * * * * 9 * * * * * | 0 1 0 0 1 0
.. ox .. xx&#x ♦ 2 4 | 0 0 1 4 2 0 2 | 0 0 0 0 0 2 0 2 0 0 1 0 | * * * * * * * 9 * * * * | 0 0 1 0 1 0
.. .. xx3xx&#x ♦ 6 6 | 0 3 3 6 0 3 3 | 0 0 0 1 0 0 3 3 0 0 0 1 | * * * * * * * * 6 * * * | 0 0 0 1 1 0
.o3.x .x .. ♦ 0 6 | 0 0 0 0 6 3 0 | 0 0 0 0 0 0 0 0 2 3 0 0 | * * * * * * * * * 3 * * | 0 1 0 0 0 1
.o3.x .. .x ♦ 0 6 | 0 0 0 0 6 0 3 | 0 0 0 0 0 0 0 0 2 0 3 0 | * * * * * * * * * * 3 * | 0 0 1 0 0 1
.. .x .x3.x ♦ 0 12 | 0 0 0 0 6 6 6 | 0 0 0 0 0 0 0 0 0 3 3 2 | * * * * * * * * * * * 3 | 0 0 0 0 1 1
---------------+-------+------------------+-----------------------------+-------------------------+------------
x.3o. x.3x. ♦ 18 0 | 18 9 9 0 0 0 0 | 6 9 9 3 0 0 0 0 0 0 0 0 | 3 3 3 0 0 0 0 0 0 0 0 0 | 1 * * * * *
xo3ox xx ..&#x ♦ 6 6 | 6 3 0 12 6 3 0 | 2 3 0 0 6 6 6 0 2 3 0 0 | 1 0 0 2 3 0 3 0 0 1 0 0 | * 3 * * * *
xo3ox .. xx&#x ♦ 6 6 | 6 0 3 12 6 0 3 | 2 0 3 0 6 6 0 6 2 0 3 0 | 0 1 0 2 0 3 0 3 0 0 1 0 | * * 3 * * *
xo .. xx3xx&#x ♦ 12 6 | 6 6 6 12 0 3 3 | 0 3 3 2 6 0 6 6 0 0 0 1 | 0 0 1 0 3 3 0 0 2 0 0 0 | * * * 3 * *
.. ox xx3xx&#x ♦ 6 12 | 0 3 3 12 6 6 6 | 0 0 0 1 0 6 6 6 0 3 3 2 | 0 0 0 0 0 0 3 3 2 0 0 1 | * * * * 3 *
.o3.x .x3.x ♦ 0 18 | 0 0 0 0 18 9 9 | 0 0 0 0 0 0 0 0 6 9 9 3 | 0 0 0 0 0 0 0 0 0 3 3 3 | * * * * * 1
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