Acronym gippit Name great prismated triacontiditeron,omnitruncated hemipenteract Field of sections ` ©` Circumradius sqrt(15) = 3.872983 Vertex figure ` ©   ©` Coordinates (2 sqrt(2), 3/sqrt(2), sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign Confer general polytopal classes: lace simplices   partial Stott expansions Externallinks

Incidence matrix according to Dynkin symbol

```x3x3x3x4o

. . . . . | 1920 |   1   1   1    2 |   1   1   2   1   2   2   1 |  1   2   2   1   2   1  1 |  2  1  1  1
----------+------+------------------+-----------------------------+---------------------------+------------
x . . . . |    2 | 960   *   *    * |   1   1   2   0   0   0   0 |  1   2   2   1   0   0  0 |  2  1  1  0
. x . . . |    2 |   * 960   *    * |   1   0   0   1   2   0   0 |  1   2   0   0   2   1  0 |  2  1  0  1
. . x . . |    2 |   *   * 960    * |   0   1   0   1   0   2   0 |  1   0   2   0   2   0  1 |  2  0  1  1
. . . x . |    2 |   *   *   * 1920 |   0   0   1   0   1   1   1 |  0   1   1   1   1   1  1 |  1  1  1  1
----------+------+------------------+-----------------------------+---------------------------+------------
x3x . . . |    6 |   3   3   0    0 | 320   *   *   *   *   *   * |  1   2   0   0   0   0  0 |  2  1  0  0
x . x . . |    4 |   2   0   2    0 |   * 480   *   *   *   *   * |  1   0   2   0   0   0  0 |  2  0  1  0
x . . x . |    4 |   2   0   0    2 |   *   * 960   *   *   *   * |  0   1   1   1   0   0  0 |  1  1  1  0
. x3x . . |    6 |   0   3   3    0 |   *   *   * 320   *   *   * |  1   0   0   0   2   0  0 |  2  0  0  1
. x . x . |    4 |   0   2   0    2 |   *   *   *   * 960   *   * |  0   1   0   0   1   1  0 |  1  1  0  1
. . x3x . |    6 |   0   0   3    3 |   *   *   *   *   * 640   * |  0   0   1   0   1   0  1 |  1  0  1  1
. . . x4o |    4 |   0   0   0    4 |   *   *   *   *   *   * 480 |  0   0   0   1   0   1  1 |  0  1  1  1
----------+------+------------------+-----------------------------+---------------------------+------------
x3x3x . . ♦   24 |  12  12  12    0 |   4   6   0   4   0   0   0 | 80   *   *   *   *   *  * |  2  0  0  0
x3x . x . ♦   12 |   6   6   0    6 |   2   0   3   0   3   0   0 |  * 320   *   *   *   *  * |  1  1  0  0
x . x3x . ♦   12 |   6   0   6    6 |   0   3   3   0   0   2   0 |  *   * 320   *   *   *  * |  1  0  1  0
x . . x4o ♦    8 |   4   0   0    8 |   0   0   4   0   0   0   2 |  *   *   * 240   *   *  * |  0  1  1  0
. x3x3x . ♦   24 |   0  12  12   12 |   0   0   0   4   6   4   0 |  *   *   *   * 160   *  * |  1  0  0  1
. x . x4o ♦    8 |   0   4   0    8 |   0   0   0   0   4   0   2 |  *   *   *   *   * 240  * |  0  1  0  1
. . x3x4o ♦   24 |   0   0  12   24 |   0   0   0   0   0   8   6 |  *   *   *   *   *   * 80 |  0  0  1  1
----------+------+------------------+-----------------------------+---------------------------+------------
x3x3x3x . ♦  120 |  60  60  60   60 |  20  30  30  20  30  20   0 |  5  10  10   0   5   0  0 | 32  *  *  *
x3x . x4o ♦   24 |  12  12   0   24 |   4   0  12   0  12   0   6 |  0   4   0   3   0   3  0 |  * 80  *  *
x . x3x4o ♦   48 |  24   0  24   48 |   0  12  24   0   0  16  12 |  0   0   8   6   0   0  2 |  *  * 40  *
. x3x3x4o ♦  192 |   0  96  96  192 |   0   0   0  32  96  64  48 |  0   0   0   0  16  24  8 |  *  *  * 10

snubbed forms: s3s3s3s4o
```

```x3x3x3x4/3o

. . . .   . | 1920 |   1   1   1    2 |   1   1   2   1   2   2   1 |  1   2   2   1   2   1  1 |  2  1  1  1
------------+------+------------------+-----------------------------+---------------------------+------------
x . . .   . |    2 | 960   *   *    * |   1   1   2   0   0   0   0 |  1   2   2   1   0   0  0 |  2  1  1  0
. x . .   . |    2 |   * 960   *    * |   1   0   0   1   2   0   0 |  1   2   0   0   2   1  0 |  2  1  0  1
. . x .   . |    2 |   *   * 960    * |   0   1   0   1   0   2   0 |  1   0   2   0   2   0  1 |  2  0  1  1
. . . x   . |    2 |   *   *   * 1920 |   0   0   1   0   1   1   1 |  0   1   1   1   1   1  1 |  1  1  1  1
------------+------+------------------+-----------------------------+---------------------------+------------
x3x . .   . |    6 |   3   3   0    0 | 320   *   *   *   *   *   * |  1   2   0   0   0   0  0 |  2  1  0  0
x . x .   . |    4 |   2   0   2    0 |   * 480   *   *   *   *   * |  1   0   2   0   0   0  0 |  2  0  1  0
x . . x   . |    4 |   2   0   0    2 |   *   * 960   *   *   *   * |  0   1   1   1   0   0  0 |  1  1  1  0
. x3x .   . |    6 |   0   3   3    0 |   *   *   * 320   *   *   * |  1   0   0   0   2   0  0 |  2  0  0  1
. x . x   . |    4 |   0   2   0    2 |   *   *   *   * 960   *   * |  0   1   0   0   1   1  0 |  1  1  0  1
. . x3x   . |    6 |   0   0   3    3 |   *   *   *   *   * 640   * |  0   0   1   0   1   0  1 |  1  0  1  1
. . . x4/3o |    4 |   0   0   0    4 |   *   *   *   *   *   * 480 |  0   0   0   1   0   1  1 |  0  1  1  1
------------+------+------------------+-----------------------------+---------------------------+------------
x3x3x .   . ♦   24 |  12  12  12    0 |   4   6   0   4   0   0   0 | 80   *   *   *   *   *  * |  2  0  0  0
x3x . x   . ♦   12 |   6   6   0    6 |   2   0   3   0   3   0   0 |  * 320   *   *   *   *  * |  1  1  0  0
x . x3x   . ♦   12 |   6   0   6    6 |   0   3   3   0   0   2   0 |  *   * 320   *   *   *  * |  1  0  1  0
x . . x4/3o ♦    8 |   4   0   0    8 |   0   0   4   0   0   0   2 |  *   *   * 240   *   *  * |  0  1  1  0
. x3x3x   . ♦   24 |   0  12  12   12 |   0   0   0   4   6   4   0 |  *   *   *   * 160   *  * |  1  0  0  1
. x . x4/3o ♦    8 |   0   4   0    8 |   0   0   0   0   4   0   2 |  *   *   *   *   * 240  * |  0  1  0  1
. . x3x4/3o ♦   24 |   0   0  12   24 |   0   0   0   0   0   8   6 |  *   *   *   *   *   * 80 |  0  0  1  1
------------+------+------------------+-----------------------------+---------------------------+------------
x3x3x3x   . ♦  120 |  60  60  60   60 |  20  30  30  20  30  20   0 |  5  10  10   0   5   0  0 | 32  *  *  *
x3x . x4/3o ♦   24 |  12  12   0   24 |   4   0  12   0  12   0   6 |  0   4   0   3   0   3  0 |  * 80  *  *
x . x3x4/3o ♦   48 |  24   0  24   48 |   0  12  24   0   0  16  12 |  0   0   8   6   0   0  2 |  *  * 40  *
. x3x3x4/3o ♦  192 |   0  96  96  192 |   0   0   0  32  96  64  48 |  0   0   0   0  16  24  8 |  *  *  * 10
```

```x3x3x *b3x3x

. . .    . . | 1920 |   1   1   1   1   1 |   1   1   1   1   1   1   1   1   1   1 |  1  1   1   1   1   1  1   1  1   1 |  1  1  1  1  1
-------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
x . .    . . |    2 | 960   *   *   *   * |   1   1   1   1   0   0   0   0   0   0 |  1  1   1   1   1   1  0   0  0   0 |  1  1  1  1  0
. x .    . . |    2 |   * 960   *   *   * |   1   0   0   0   1   1   1   0   0   0 |  1  1   1   0   0   0  1   1  1   0 |  1  1  1  0  1
. . x    . . |    2 |   *   * 960   *   * |   0   1   0   0   1   0   0   1   1   0 |  1  0   0   1   1   0  1   1  0   1 |  1  1  0  1  1
. . .    x . |    2 |   *   *   * 960   * |   0   0   1   0   0   1   0   1   0   1 |  0  1   0   1   0   1  1   0  1   1 |  1  0  1  1  1
. . .    . x |    2 |   *   *   *   * 960 |   0   0   0   1   0   0   1   0   1   1 |  0  0   1   0   1   1  0   1  1   1 |  0  1  1  1  1
-------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
x3x .    . . |    6 |   3   3   0   0   0 | 320   *   *   *   *   *   *   *   *   * |  1  1   1   0   0   0  0   0  0   0 |  1  1  1  0  0
x . x    . . |    4 |   2   0   2   0   0 |   * 480   *   *   *   *   *   *   *   * |  1  0   0   1   1   0  0   0  0   0 |  1  1  0  1  0
x . .    x . |    4 |   2   0   0   2   0 |   *   * 480   *   *   *   *   *   *   * |  0  1   0   1   0   1  0   0  0   0 |  1  0  1  1  0
x . .    . x |    4 |   2   0   0   0   2 |   *   *   * 480   *   *   *   *   *   * |  0  0   1   0   1   1  0   0  0   0 |  0  1  1  1  0
. x3x    . . |    6 |   0   3   3   0   0 |   *   *   *   * 320   *   *   *   *   * |  1  0   0   0   0   0  1   1  0   0 |  1  1  0  0  1
. x . *b3x . |    6 |   0   3   0   3   0 |   *   *   *   *   * 320   *   *   *   * |  0  1   0   0   0   0  1   0  1   0 |  1  0  1  0  1
. x .    . x |    4 |   0   2   0   0   2 |   *   *   *   *   *   * 480   *   *   * |  0  0   1   0   0   0  0   1  1   0 |  0  1  1  0  1
. . x    x . |    4 |   0   0   2   2   0 |   *   *   *   *   *   *   * 480   *   * |  0  0   0   1   0   0  1   0  0   1 |  1  0  0  1  1
. . x    . x |    4 |   0   0   2   0   2 |   *   *   *   *   *   *   *   * 480   * |  0  0   0   0   1   0  0   1  0   1 |  0  1  0  1  1
. . .    x3x |    6 |   0   0   0   3   3 |   *   *   *   *   *   *   *   *   * 320 |  0  0   0   0   0   1  0   0  1   1 |  0  0  1  1  1
-------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
x3x3x    . . ♦   24 |  12  12  12   0   0 |   4   6   0   0   4   0   0   0   0   0 | 80  *   *   *   *   *  *   *  *   * |  1  1  0  0  0
x3x . *b3x . ♦   24 |  12  12   0  12   0 |   4   0   6   0   0   4   0   0   0   0 |  * 80   *   *   *   *  *   *  *   * |  1  0  1  0  0
x3x .    . x ♦   12 |   6   6   0   0   6 |   2   0   0   3   0   0   3   0   0   0 |  *  * 160   *   *   *  *   *  *   * |  0  1  1  0  0
x . x    x . ♦    8 |   4   0   4   4   0 |   0   2   2   0   0   0   0   2   0   0 |  *  *   * 240   *   *  *   *  *   * |  1  0  0  1  0
x . x    . x ♦    8 |   4   0   4   0   4 |   0   2   0   2   0   0   0   0   2   0 |  *  *   *   * 240   *  *   *  *   * |  0  1  0  1  0
x . .    x3x ♦   12 |   6   0   0   6   6 |   0   0   3   3   0   0   0   0   0   2 |  *  *   *   *   * 160  *   *  *   * |  0  0  1  1  0
. x3x *b3x . ♦   24 |   0  12  12  12   0 |   0   0   0   0   4   4   0   6   0   0 |  *  *   *   *   *   * 80   *  *   * |  1  0  0  0  1
. x3x    . x ♦   12 |   0   6   6   0   6 |   0   0   0   0   2   0   3   0   3   0 |  *  *   *   *   *   *  * 160  *   * |  0  1  0  0  1
. x . *b3x3x ♦   24 |   0  12   0  12  12 |   0   0   0   0   0   4   6   0   0   4 |  *  *   *   *   *   *  *   * 80   * |  0  0  1  0  1
. . x    x3x ♦   12 |   0   0   6   6   6 |   0   0   0   0   0   0   0   3   3   2 |  *  *   *   *   *   *  *   *  * 160 |  0  0  0  1  1
-------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
x3x3x *b3x . ♦  192 |  96  96  96  96   0 |  32  48  48   0  32  32   0  48   0   0 |  8  8   0  24   0   0  8   0  0   0 | 10  *  *  *  *
x3x3x    . x ♦   48 |  24  24  24   0  24 |   8  12   0  12   8   0  12   0  12   0 |  2  0   4   0   6   0  0   4  0   0 |  * 40  *  *  *
x3x . *b3x3x ♦  120 |  60  60   0  60  60 |  20   0  30  30   0  20  30   0   0  20 |  0  5  10   0   0  10  0   0  5   0 |  *  * 16  *  *
x . x    x3x ♦   24 |  12   0  12  12  12 |   0   6   6   6   0   0   0   6   6   4 |  0  0   0   3   3   2  0   0  0   2 |  *  *  * 80  *
. x3x *b3x3x ♦  120 |   0  60  60  60  60 |   0   0   0   0  20  20  30  30  30  20 |  0  0   0   0   0   0  5  10  5  10 |  *  *  *  * 16

snubbed forms: s3s3s *b3s3s
```

```x3x3x3x4s

demi( . . . . . ) | 1920 |   1   1   1   1   1 |   1   1   1   1   1   1   1   1   1   1 |  1   1   1  1   1   1  1   1   1  1 |  1  1  1  1  1
------------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
demi( x . . . . ) |    2 | 960   *   *   *   * |   1   1   1   0   0   0   0   1   0   0 |  1   1   1  0   1   0  0   1   1  0 |  1  1  1  0  1
demi( . x . . . ) |    2 |   * 960   *   *   * |   1   0   0   1   1   0   0   0   1   0 |  1   1   0  1   0   1  0   1   0  1 |  1  1  0  1  1
demi( . . x . . ) |    2 |   *   * 960   *   * |   0   1   0   1   0   1   0   0   0   1 |  1   0   1  1   0   0  1   0   1  1 |  1  0  1  1  1
demi( . . . x . ) |    2 |   *   *   * 960   * |   0   0   1   0   1   1   1   0   0   0 |  0   1   1  1   1   1  1   0   0  0 |  1  1  1  1  0
sefa( . . . x4s ) |    2 |   *   *   *   * 960 |   0   0   0   0   0   0   1   1   1   1 |  0   0   0  0   1   1  1   1   1  1 |  0  1  1  1  1
------------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
demi( x3x . . . ) |    6 |   3   3   0   0   0 | 320   *   *   *   *   *   *   *   *   * |  1   1   0  0   0   0  0   1   0  0 |  1  1  0  0  1
demi( x . x . . ) |    4 |   2   0   2   0   0 |   * 480   *   *   *   *   *   *   *   * |  1   0   1  0   0   0  0   0   1  0 |  1  0  1  0  1
demi( x . . x . ) |    4 |   2   0   0   2   0 |   *   * 480   *   *   *   *   *   *   * |  0   1   1  0   1   0  0   0   0  0 |  1  1  1  0  0
demi( . x3x . . ) |    6 |   0   3   3   0   0 |   *   *   * 320   *   *   *   *   *   * |  1   0   0  1   0   0  0   0   0  1 |  1  0  0  1  1
demi( . x . x . ) |    4 |   0   2   0   2   0 |   *   *   *   * 480   *   *   *   *   * |  0   1   0  1   0   1  0   0   0  0 |  1  1  0  1  0
demi( . . x3x . ) |    6 |   0   0   3   3   0 |   *   *   *   *   * 320   *   *   *   * |  0   0   1  1   0   0  1   0   0  0 |  1  0  1  1  0
. . . x4s   |    4 |   0   0   0   2   2 |   *   *   *   *   *   * 480   *   *   * |  0   0   0  0   1   1  1   0   0  0 |  0  1  1  1  0
sefa( x 2 . x4s ) |    4 |   2   0   0   0   2 |   *   *   *   *   *   *   * 480   *   * |  0   0   0  0   1   0  0   1   1  0 |  0  1  1  0  1
sefa( . x 2 x4s ) |    4 |   0   2   0   0   2 |   *   *   *   *   *   *   *   * 480   * |  0   0   0  0   0   1  0   1   0  1 |  0  1  0  1  1
sefa( . . x3x4s ) |    6 |   0   0   3   0   3 |   *   *   *   *   *   *   *   *   * 320 |  0   0   0  0   0   0  1   0   1  1 |  0  0  1  1  1
------------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
demi( x3x3x . . ) ♦   24 |  12  12  12   0   0 |   4   6   0   4   0   0   0   0   0   0 | 80   *   *  *   *   *  *   *   *  * |  1  0  0  0  1
demi( x3x . x . ) ♦   12 |   6   6   0   6   0 |   2   0   3   0   3   0   0   0   0   0 |  * 160   *  *   *   *  *   *   *  * |  1  1  0  0  0
demi( x . x3x . ) ♦   12 |   6   0   6   6   0 |   0   3   3   0   0   2   0   0   0   0 |  *   * 160  *   *   *  *   *   *  * |  1  0  1  0  0
demi( . x3x3x . ) ♦   24 |   0  12  12  12   0 |   0   0   0   4   6   4   0   0   0   0 |  *   *   * 80   *   *  *   *   *  * |  1  0  0  1  0
x 2 . x4s   ♦    8 |   4   0   0   4   4 |   0   0   2   0   0   0   2   2   0   0 |  *   *   *  * 240   *  *   *   *  * |  0  1  1  0  0
. x 2 x4s   ♦    8 |   0   4   0   4   4 |   0   0   0   0   2   0   2   0   2   0 |  *   *   *  *   * 240  *   *   *  * |  0  1  0  1  0
. . x3x4s   ♦   24 |   0   0  12  12  12 |   0   0   0   0   0   4   6   0   0   4 |  *   *   *  *   *   * 80   *   *  * |  0  0  1  1  0
sefa( x3x 2 x4s ) ♦   12 |   6   6   0   0   6 |   2   0   0   0   0   0   0   3   3   0 |  *   *   *  *   *   *  * 160   *  * |  0  1  0  0  1
sefa( x 2 x3x4s ) ♦   12 |   6   0   6   0   6 |   0   3   0   0   0   0   0   3   0   2 |  *   *   *  *   *   *  *   * 160  * |  0  0  1  0  1
sefa( . x3x3x4s ) ♦   24 |   0  12  12   0  12 |   0   0   0   4   0   0   0   0   6   4 |  *   *   *  *   *   *  *   *   * 80 |  0  0  0  1  1
------------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
demi( x3x3x3x . ) ♦  120 |  60  60  60  60   0 |  20  30  30  20  30  20   0   0   0   0 |  5  10  10  5   0   0  0   0   0  0 | 16  *  *  *  *
x3x 2 x4s   ♦   24 |  12  12   0  12  12 |   4   0   6   0   6   0   6   6   6   0 |  0   2   0  0   3   3  0   2   0  0 |  * 80  *  *  *
x 2 x3x4s   ♦   48 |  24   0  24  24  24 |   0  12  12   0   0   8  12  12   0   8 |  0   0   4  0   6   0  2   0   4  0 |  *  * 40  *  *
. x3x3x4s   ♦  192 |   0  96  96  96  96 |   0   0   0  32  48  32  48   0  48  32 |  0   0   0  8   0  24  8   0   0  8 |  *  *  * 10  *
sefa( x3x3x3x4s ) ♦  120 |  60  60  60   0  60 |  20  30   0  20   0   0   0  30  30  20 |  5   0   0  0   0   0  0  10  10  5 |  *  *  *  * 16

starting figure: x3x3x3x4x
```