Acronym	octdip
Name	octahedron-octahedron duoprism, dual of Delone cell of lattice D6*, vertex figure of traxh
Circumradius	1
Coordinates	(1/sqrt(2), 0, 0, 1/sqrt(2), 0, 0)   & all permutations in the first 3 as well as last 3 coordinates, all changes of sign
Volume	2/9 = 0.222222
Face vector	36, 144, 240, 204, 88, 16
Confer	general polytopal classes: Wythoffian polypeta   noble polytopes   lace simplices
External links

Incidence matrix according to Dynkin symbol

x3o4o x3o4o

. . . . . . | 36 |  4  4 |  4  16  4 | 1 16 16 1 |  4 16  4 | 4 4
------------+----+-------+-----------+-----------+----------+----
x . . . . . |  2 | 72  * |  2   4  0 | 1  8  4 0 |  4  8  1 | 4 2
. . . x . . |  2 |  * 72 |  0   4  2 | 0  4  8 1 |  1  8  4 | 2 4
------------+----+-------+-----------+-----------+----------+----
x3o . . . . |  3 |  3  0 | 48   *  * | 1  4  0 0 |  4  4  0 | 4 1
x . . x . . |  4 |  2  2 |  * 144  * | 0  2  2 0 |  1  4  1 | 2 2
. . . x3o . |  3 |  0  3 |  *   * 48 | 0  0  4 1 |  0  4  4 | 1 4
------------+----+-------+-----------+-----------+----------+----
x3o4o . . . ♦  6 | 12  0 |  8   0  0 | 6  *  * * |  4  0  0 | 4 0
x3o . x . . ♦  6 |  6  3 |  2   3  0 | * 96  * * |  1  2  0 | 2 1
x . . x3o . ♦  6 |  3  6 |  0   3  2 | *  * 96 * |  0  2  1 | 1 2
. . . x3o4o ♦  6 |  0 12 |  0   0  8 | *  *  * 6 |  0  0  4 | 0 4
------------+----+-------+-----------+-----------+----------+----
x3o4o x . . ♦ 12 | 24  6 | 16  12  0 | 2  8  0 0 | 12  *  * | 2 0
x3o . x3o . ♦  9 |  9  9 |  3   9  3 | 0  3  3 0 |  * 64  * | 1 1
x . . x3o4o ♦ 12 |  6 24 |  0  12 16 | 0  0  8 2 |  *  * 12 | 0 2
------------+----+-------+-----------+-----------+----------+----
x3o4o x3o . ♦ 18 | 36 18 | 24  36  6 | 3 24 12 0 |  3  8  0 | 8 *
x3o . x3o4o ♦ 18 | 18 36 |  6  36 24 | 0 12 24 3 |  0  8  3 | * 8

or
. . . . . .    | 36 |   8 |  8  16 |  2  32 |  8 16 |  8
---------------+----+-----+--------+--------+-------+---
x . . . . .  & |  2 | 144 |  2   4 |  1  12 |  5  8 |  6
---------------+----+-----+--------+--------+-------+---
x3o . . . .  & |  3 |   3 | 96   * |  1   4 |  4  4 |  5
x . . x . .    |  4 |   4 |  * 144 |  0   4 |  2  4 |  4
---------------+----+-----+--------+--------+-------+---
x3o4o . . .  & ♦  6 |  12 |  8   0 | 12   * |  4  0 |  4
x3o . x . .    ♦  6 |   9 |  2   3 |  * 192 |  1  2 |  3
---------------+----+-----+--------+--------+-------+---
x3o4o x . .  & ♦ 12 |  30 | 16  12 |  2   8 | 24  * |  2
x3o . x3o .    ♦  9 |  18 |  6   9 |  0   6 |  * 64 |  2
---------------+----+-----+--------+--------+-------+---
x3o4o x3o .  & ♦ 18 |  54 | 30  36 |  3  36 |  3  8 | 16

o3x3o x3o4o

. . . . . . | 36 |  4  4 |  2  2  16  4 | 1  8  8 16 1 |  4  8  8  4 | 4 2 2
------------+----+-------+--------------+--------------+-------------+------
. x . . . . |  2 | 72  * |  1  1   4  0 | 1  4  4  4 0 |  4  4  4  1 | 4 1 1
. . . x . . |  2 |  * 72 |  0  0   4  2 | 0  2  2  8 1 |  1  4  4  4 | 2 2 2
------------+----+-------+--------------+--------------+-------------+------
o3x . . . . |  3 |  3  0 | 24  *   *  * | 1  4  0  0 0 |  4  4  0  0 | 4 1 0
. x3o . . . |  3 |  3  0 |  * 24   *  * | 1  0  4  0 0 |  4  0  4  0 | 4 0 1
. x . x . . |  4 |  2  2 |  *  * 144  * | 0  1  1  2 0 |  1  2  2  1 | 2 1 1
. . . x3o . |  3 |  0  3 |  *  *   * 48 | 0  0  0  4 1 |  0  2  2  4 | 1 2 2
------------+----+-------+--------------+--------------+-------------+------
o3x3o . . . ♦  6 | 12  0 |  4  4   0  0 | 6  *  *  * * |  4  0  0  0 | 4 0 0
o3x . x . . ♦  6 |  6  3 |  2  0   3  0 | * 48  *  * * |  1  2  0  0 | 2 1 0
. x3o x . . ♦  6 |  6  3 |  0  2   3  0 | *  * 48  * * |  1  0  2  0 | 2 0 1
. x . x3o . ♦  6 |  3  6 |  0  0   3  2 | *  *  * 96 * |  0  1  1  1 | 1 1 1
. . . x3o4o ♦  6 |  0 12 |  0  0   0  8 | *  *  *  * 6 |  0  0  0  4 | 0 2 2
------------+----+-------+--------------+--------------+-------------+------
o3x3o x . . ♦ 12 | 24  6 |  8  8  12  0 | 2  4  4  0 0 | 12  *  *  * | 2 0 0
o3x . x3o . ♦  9 |  9  9 |  3  0   9  3 | 0  3  0  3 0 |  * 32  *  * | 1 1 0
. x3o x3o . ♦  9 |  9  9 |  0  3   9  3 | 0  0  3  3 0 |  *  * 32  * | 1 0 1
. x . x3o4o ♦ 12 |  6 24 |  0  0  12 16 | 0  0  0  8 2 |  *  *  * 12 | 0 1 1
------------+----+-------+--------------+--------------+-------------+------
o3x3o x3o . ♦ 18 | 36 18 | 12 12  36  6 | 3 12 12 12 0 |  3  4  4  0 | 8 * *
o3x . x3o4o ♦ 18 | 18 36 |  6  0  36 24 | 0 12  0 24 3 |  0  8  0  3 | * 4 *
. x3o x3o4o ♦ 18 | 18 36 |  0  6  36 24 | 0  0 12 24 3 |  0  0  8  3 | * * 4

o3x3o o3x3o

. . . . . . | 36 |  4  4 |  2  2  16  2  2 | 1  8  8  8  8 1 |  4  4  4  4  4  4 | 2 2 2 2
------------+----+-------+-----------------+-----------------+-------------------+--------
. x . . . . |  2 | 72  * |  1  1   4  0  0 | 1  4  4  2  2 0 |  4  2  2  2  2  1 | 2 2 1 1
. . . . x . |  2 |  * 72 |  0  0   4  1  1 | 0  2  2  4  4 1 |  1  2  2  2  2  4 | 1 1 2 2
------------+----+-------+-----------------+-----------------+-------------------+--------
o3x . . . . |  3 |  3  0 | 24  *   *  *  * | 1  4  0  0  0 0 |  4  2  2  0  0  0 | 2 2 1 0
. x3o . . . |  3 |  3  0 |  * 24   *  *  * | 1  0  4  0  0 0 |  4  0  0  2  2  0 | 2 2 0 1
. x . . x . |  4 |  2  2 |  *  * 144  *  * | 0  1  1  1  1 0 |  1  1  1  1  1  1 | 1 1 1 1
. . . o3x . |  3 |  0  3 |  *  *   * 24  * | 0  0  0  4  0 1 |  0  2  0  2  0  4 | 1 0 2 2
. . . . x3o |  3 |  0  3 |  *  *   *  * 24 | 0  0  0  0  4 1 |  0  0  2  0  2  4 | 0 1 2 2
------------+----+-------+-----------------+-----------------+-------------------+--------
o3x3o . . . ♦  6 | 12  0 |  4  4   0  0  0 | 6  *  *  *  * * |  4  0  0  0  0  0 | 2 2 0 0
o3x . . x . ♦  6 |  6  3 |  2  0   3  0  0 | * 48  *  *  * * |  1  1  1  0  0  0 | 1 1 1 0
. x3o . x . ♦  6 |  6  3 |  0  2   3  0  0 | *  * 48  *  * * |  1  0  0  1  1  0 | 1 1 0 1
. x . o3x . ♦  6 |  3  6 |  0  0   3  2  0 | *  *  * 48  * * |  0  1  0  1  0  1 | 1 0 1 1
. x . . x3o ♦  6 |  3  6 |  0  0   3  0  2 | *  *  *  * 48 * |  0  0  1  0  1  1 | 0 1 1 1
. . . o3x3o ♦  6 |  0 12 |  0  0   0  4  4 | *  *  *  *  * 6 |  0  0  0  0  0  4 | 0 0 2 2
------------+----+-------+-----------------+-----------------+-------------------+--------
o3x3o . x . ♦ 12 | 24  6 |  8  8  12  0  0 | 2  4  4  0  0 0 | 12  *  *  *  *  * | 1 1 0 0
o3x . o3x . ♦  9 |  9  9 |  3  0   9  3  0 | 0  3  0  3  0 0 |  * 16  *  *  *  * | 1 0 1 0
o3x . . x3o ♦  9 |  9  9 |  3  0   9  0  3 | 0  3  0  0  3 0 |  *  * 16  *  *  * | 0 1 1 0
. x3o o3x . ♦  9 |  9  9 |  0  3   9  3  0 | 0  0  3  3  0 0 |  *  *  * 16  *  * | 1 0 0 1
. x3o . x3o ♦  9 |  9  9 |  0  3   9  0  3 | 0  0  3  0  3 0 |  *  *  *  * 16  * | 0 1 0 1
. x . o3x3o ♦ 12 |  6 24 |  0  0  12  8  8 | 0  0  0  4  4 2 |  *  *  *  *  * 12 | 0 0 1 1
------------+----+-------+-----------------+-----------------+-------------------+--------
o3x3o o3x . ♦ 18 | 36 18 | 12 12  36  6  0 | 3 12 12 12  0 0 |  3  4  0  4  0  0 | 4 * * *
o3x3o . x3o ♦ 18 | 36 18 | 12 12  36  0  6 | 3 12 12  0 12 0 |  3  0  4  0  4  0 | * 4 * *
o3x . o3x3o ♦ 18 | 18 36 |  6  0  36 12 12 | 0 12  0 12 12 3 |  0  4  4  0  0  3 | * * 4 *
. x3o o3x3o ♦ 18 | 18 36 |  0  6  36 12 12 | 0  0 12 12 12 3 |  0  0  0  4  4  3 | * * * 4