Acronym gibrant Name great birhombated penteractitriacontiditeron,bicantitruncated penteract Field of sections ` ©` Circumradius sqrt(23/2) = 3.391165 Vertex figure ` ©   ©` Coordinates (3/sqrt(2), 3/sqrt(2), sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign Confer general polytopal classes: partial Stott expansions Externallinks

Incidence matrix according to Dynkin symbol

```o3x3x3x4o

. . . . . | 960 |   2   1   2 |   1   2   4   2   1 |  1   2   4   2  1 |  2  1  2
----------+-----+-------------+---------------------+-------------------+---------
. x . . . |   2 | 960   *   * |   1   1   2   0   0 |  1   2   2   1  0 |  2  1  1
. . x . . |   2 |   * 480   * |   0   2   0   2   0 |  1   0   4   0  1 |  2  0  2
. . . x . |   2 |   *   * 960 |   0   0   2   1   1 |  0   1   2   2  1 |  1  1  2
----------+-----+-------------+---------------------+-------------------+---------
o3x . . . |   3 |   3   0   0 | 320   *   *   *   * |  1   2   0   0  0 |  2  1  0
. x3x . . |   6 |   3   3   0 |   * 320   *   *   * |  1   0   2   0  0 |  2  0  1
. x . x . |   4 |   2   0   2 |   *   * 960   *   * |  0   1   1   1  0 |  1  1  1
. . x3x . |   6 |   0   3   3 |   *   *   * 320   * |  0   0   2   0  1 |  1  0  2
. . . x4o |   4 |   0   0   4 |   *   *   *   * 240 |  0   0   0   2  1 |  0  1  2
----------+-----+-------------+---------------------+-------------------+---------
o3x3x . . ♦  12 |  12   6   0 |   4   4   0   0   0 | 80   *   *   *  * |  2  0  0
o3x . x . ♦   6 |   6   0   3 |   2   0   3   0   0 |  * 320   *   *  * |  1  1  0
. x3x3x . ♦  24 |  12  12  12 |   0   4   6   4   0 |  *   * 160   *  * |  1  0  1
. x . x4o ♦   8 |   4   0   8 |   0   0   4   0   2 |  *   *   * 240  * |  0  1  1
. . x3x4o ♦  24 |   0  12  24 |   0   0   0   8   6 |  *   *   *   * 40 |  0  0  2
----------+-----+-------------+---------------------+-------------------+---------
o3x3x3x . ♦  60 |  60  30  30 |  20  20  30  10   0 |  5  10   5   0  0 | 32  *  *
o3x . x4o ♦  12 |  12   0  12 |   4   0  12   0   3 |  0   4   0   3  0 |  * 80  *
. x3x3x4o ♦ 192 |  96  96 192 |   0  32  96  64  48 |  0   0  16  24  8 |  *  * 10
```

```o3x3x3x4/3o

. . . .   . | 960 |   2   1   2 |   1   2   4   2   1 |  1   2   4   2  1 |  2  1  2
------------+-----+-------------+---------------------+-------------------+---------
. x . .   . |   2 | 960   *   * |   1   1   2   0   0 |  1   2   2   1  0 |  2  1  1
. . x .   . |   2 |   * 480   * |   0   2   0   2   0 |  1   0   4   0  1 |  2  0  2
. . . x   . |   2 |   *   * 960 |   0   0   2   1   1 |  0   1   2   2  1 |  1  1  2
------------+-----+-------------+---------------------+-------------------+---------
o3x . .   . |   3 |   3   0   0 | 320   *   *   *   * |  1   2   0   0  0 |  2  1  0
. x3x .   . |   6 |   3   3   0 |   * 320   *   *   * |  1   0   2   0  0 |  2  0  1
. x . x   . |   4 |   2   0   2 |   *   * 960   *   * |  0   1   1   1  0 |  1  1  1
. . x3x   . |   6 |   0   3   3 |   *   *   * 320   * |  0   0   2   0  1 |  1  0  2
. . . x4/3o |   4 |   0   0   4 |   *   *   *   * 240 |  0   0   0   2  1 |  0  1  2
------------+-----+-------------+---------------------+-------------------+---------
o3x3x .   . ♦  12 |  12   6   0 |   4   4   0   0   0 | 80   *   *   *  * |  2  0  0
o3x . x   . ♦   6 |   6   0   3 |   2   0   3   0   0 |  * 320   *   *  * |  1  1  0
. x3x3x   . ♦  24 |  12  12  12 |   0   4   6   4   0 |  *   * 160   *  * |  1  0  1
. x . x4/3o ♦   8 |   4   0   8 |   0   0   4   0   2 |  *   *   * 240  * |  0  1  1
. . x3x4/3o ♦  24 |   0  12  24 |   0   0   0   8   6 |  *   *   *   * 40 |  0  0  2
------------+-----+-------------+---------------------+-------------------+---------
o3x3x3x   . ♦  60 |  60  30  30 |  20  20  30  10   0 |  5  10   5   0  0 | 32  *  *
o3x . x4/3o ♦  12 |  12   0  12 |   4   0  12   0   3 |  0   4   0   3  0 |  * 80  *
. x3x3x4/3o ♦ 192 |  96  96 192 |   0  32  96  64  48 |  0   0  16  24  8 |  *  * 10
```

```x3x3x *b3x3o

. . .    . . | 960 |   1   1   1   2 |   1   1   2   1   2   2   1 |  1  2   2   1  2  1   1 |  2  1  1  1
-------------+-----+-----------------+-----------------------------+-------------------------+------------
x . .    . . |   2 | 480   *   *   * |   1   1   2   0   0   0   0 |  1  2   2   1  0  0   0 |  2  1  1  0
. x .    . . |   2 |   * 480   *   * |   1   0   0   1   2   0   0 |  1  2   0   0  2  1   0 |  2  1  0  1
. . x    . . |   2 |   *   * 480   * |   0   1   0   1   0   2   0 |  1  0   2   0  2  0   1 |  2  0  1  1
. . .    x . |   2 |   *   *   * 960 |   0   0   1   0   1   1   1 |  0  1   1   1  1  1   1 |  1  1  1  1
-------------+-----+-----------------+-----------------------------+-------------------------+------------
x3x .    . . |   6 |   3   3   0   0 | 160   *   *   *   *   *   * |  1  2   0   0  0  0   0 |  2  1  0  0
x . x    . . |   4 |   2   0   2   0 |   * 240   *   *   *   *   * |  1  0   2   0  0  0   0 |  2  0  1  0
x . .    x . |   4 |   2   0   0   2 |   *   * 480   *   *   *   * |  0  1   1   1  0  0   0 |  1  1  1  0
. x3x    . . |   6 |   0   3   3   0 |   *   *   * 160   *   *   * |  1  0   0   0  2  0   0 |  2  0  0  1
. x . *b3x . |   6 |   0   3   0   3 |   *   *   *   * 320   *   * |  0  1   0   0  1  1   0 |  1  1  0  1
. . x    x . |   4 |   0   0   2   2 |   *   *   *   *   * 480   * |  0  0   1   0  1  0   1 |  1  0  1  1
. . .    x3o |   3 |   0   0   0   3 |   *   *   *   *   *   * 320 |  0  0   0   1  0  1   1 |  0  1  1  1
-------------+-----+-----------------+-----------------------------+-------------------------+------------
x3x3x    . . ♦  24 |  12  12  12   0 |   4   6   0   4   0   0   0 | 40  *   *   *  *  *   * |  2  0  0  0
x3x . *b3x . ♦  24 |  12  12   0  12 |   4   0   6   0   4   0   0 |  * 80   *   *  *  *   * |  1  1  0  0
x . x    x . ♦   8 |   4   0   4   4 |   0   2   2   0   0   2   0 |  *  * 240   *  *  *   * |  1  0  1  0
x . .    x3o ♦   6 |   3   0   0   6 |   0   0   3   0   0   0   2 |  *  *   * 160  *  *   * |  0  1  1  0
. x3x *b3x . ♦  24 |   0  12  12  12 |   0   0   0   4   4   6   0 |  *  *   *   * 80  *   * |  1  0  0  1
. x . *b3x3o ♦  12 |   0   6   0  12 |   0   0   0   0   4   0   4 |  *  *   *   *  * 80   * |  0  1  0  1
. . x    x3o ♦   6 |   0   0   3   6 |   0   0   0   0   0   3   2 |  *  *   *   *  *  * 160 |  0  0  1  1
-------------+-----+-----------------+-----------------------------+-------------------------+------------
x3x3x *b3x . ♦ 192 |  96  96  96  96 |  32  48  48  32  32  48   0 |  8  8  24   0  8  0   0 | 10  *  *  *
x3x . *b3x3o ♦  60 |  30  30   0  60 |  10   0  30   0  20   0  20 |  0  5   0  10  0  5   0 |  * 16  *  *
x . x    x3o ♦  12 |   6   0   6  12 |   0   3   6   0   0   6   4 |  0  0   3   2  0  0   2 |  *  * 80  *
. x3x *b3x3o ♦  60 |   0  30  30  60 |   0   0   0  10  20  30  20 |  0  0   0   0  5  5  10 |  *  *  * 16
```

```o3x3x3x4s

demi( . . . . . ) | 960 |   2   1   1   1 |   1   2   2   1   1   2   1 |  1   1  2   2  1   1  2 |  1  1  2  1
------------------+-----+-----------------+-----------------------------+-------------------------+------------
demi( . x . . . ) |   2 | 960   *   *   * |   1   1   1   0   0   1   0 |  1   1  1   1  0   1  1 |  1  1  1  1
demi( . . x . . ) |   2 |   * 480   *   * |   0   2   0   1   0   0   1 |  1   0  2   0  1   0  2 |  1  0  2  1
demi( . . . x . ) |   2 |   *   * 480   * |   0   0   2   1   1   0   0 |  0   1  2   2  1   0  0 |  1  1  2  0
sefa( . . . x4s ) |   2 |   *   *   * 480 |   0   0   0   0   1   2   1 |  0   0  0   2  1   1  2 |  0  1  2  1
------------------+-----+-----------------+-----------------------------+-------------------------+------------
demi( o3x . . . ) |   3 |   3   0   0   0 | 320   *   *   *   *   *   * |  1   1  0   0  0   1  0 |  1  1  0  1
demi( . x3x . . ) |   6 |   3   3   0   0 |   * 320   *   *   *   *   * |  1   0  1   0  0   0  1 |  1  0  1  1
demi( . x . x . ) |   4 |   2   0   2   0 |   *   * 480   *   *   *   * |  0   1  1   1  0   0  0 |  1  1  1  0
demi( . . x3x . ) |   6 |   0   3   3   0 |   *   *   * 160   *   *   * |  0   0  2   0  1   0  0 |  1  0  2  0
. . . x4s   |   4 |   0   0   2   2 |   *   *   *   * 240   *   * |  0   0  0   2  1   0  0 |  0  1  2  0
sefa( . x 2 x4s ) |   4 |   2   0   0   2 |   *   *   *   *   * 480   * |  0   0  0   1  0   1  1 |  0  1  1  1
sefa( . . x3x4s ) |   6 |   0   3   0   3 |   *   *   *   *   *   * 160 |  0   0  0   0  1   0  2 |  0  0  2  1
------------------+-----+-----------------+-----------------------------+-------------------------+------------
demi( o3x3x . . ) ♦  12 |  12   6   0   0 |   4   4   0   0   0   0   0 | 80   *  *   *  *   *  * |  1  0  0  1
demi( o3x . x . ) ♦   6 |   6   0   3   0 |   2   0   3   0   0   0   0 |  * 160  *   *  *   *  * |  1  1  0  0
demi( . x3x3x . ) ♦  24 |  12  12  12   0 |   0   4   6   4   0   0   0 |  *   * 80   *  *   *  * |  1  0  1  0
. x 2 x4s   ♦   8 |   4   0   4   4 |   0   0   2   0   2   2   0 |  *   *  * 240  *   *  * |  0  1  1  0
. . x3x4s   ♦  24 |   0  12  12  12 |   0   0   0   4   6   0   4 |  *   *  *   * 40   *  * |  0  0  2  0
sefa( o3x 2 x4s ) ♦   6 |   6   0   0   3 |   2   0   0   0   0   3   0 |  *   *  *   *  * 160  * |  0  1  0  1
sefa( . x3x3x4s ) ♦  24 |  12  12   0  12 |   0   4   0   0   0   6   4 |  *   *  *   *  *   * 80 |  0  0  1  1
------------------+-----+-----------------+-----------------------------+-------------------------+------------
demi( o3x3x3x . ) ♦  60 |  60  30  30   0 |  20  20  30  10   0   0   0 |  5  10  5   0  0   0  0 | 16  *  *  *
o3x 2 x4s   ♦  12 |  12   0   6   6 |   4   0   6   0   3   6   0 |  0   2  0   3  0   2  0 |  * 80  *  *
. x3x3x4s   ♦ 192 |  96  96  96  96 |   0  32  48  32  48  48  32 |  0   0  8  24  8   0  8 |  *  * 10  *
sefa( o3x3x3x4s ) ♦  60 |  60  30   0  30 |  20  20   0   0   0  30  10 |  5   0  0   0  0  10  5 |  *  *  * 16

starting figure: o3x3x3x4x
```