Acronym scant Name small cellated penteractitriacontiditeron,stericated penteract,stericated pentacross Circumradius sqrt[7+2 sqrt(2)]/2 = 1.567516 Vertex figure ` ©` Coordinates ((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign General of army (is itself convex) Colonel of regiment (is itself locally convex – other uniform polyteral members: sinnont   & others) Confer uniform relative: sidpithip Externallinks

Incidence matrix according to Dynkin symbol

```x3o3o3o4x

. . . . . | 160 |   4   4 |   6  12   6 |   4  12  12  4 |  1  4  6  4  1
----------+-----+---------+-------------+----------------+---------------
x . . . . |   2 | 320   * |   3   3   0 |   3   6   3  0 |  1  3  3  1  0
. . . . x |   2 |   * 320 |   0   3   3 |   0   3   6  3 |  0  1  3  3  1
----------+-----+---------+-------------+----------------+---------------
x3o . . . |   3 |   3   0 | 320   *   * |   2   2   0  0 |  1  2  1  0  0
x . . . x |   4 |   2   2 |   * 480   * |   0   2   2  0 |  0  1  2  1  0
. . . o4x |   4 |   0   4 |   *   * 240 |   0   0   2  2 |  0  0  1  2  1
----------+-----+---------+-------------+----------------+---------------
x3o3o . . ♦   4 |   6   0 |   4   0   0 | 160   *   *  * |  1  1  0  0  0
x3o . . x ♦   6 |   6   3 |   2   3   0 |   * 320   *  * |  0  1  1  0  0
x . . o4x ♦   8 |   4   8 |   0   4   2 |   *   * 240  * |  0  0  1  1  0
. . o3o4x ♦   8 |   0  12 |   0   0   6 |   *   *   * 80 |  0  0  0   1 1
----------+-----+---------+-------------+----------------+---------------
x3o3o3o . ♦   5 |  10   0 |  10   0   0 |   5   0   0  0 | 32  *  *  *  *
x3o3o . x ♦   8 |  12   4 |   8   6   0 |   2   4   0  0 |  * 80  *  *  *
x3o . o4x ♦  12 |  12  12 |   4  12   3 |   0   4   3  0 |  *  * 80  *  *
x . o3o4x ♦  16 |   8  24 |   0  12  12 |   0   0   6  2 |  *  *  * 40  *
. o3o3o4x ♦  16 |   0  32 |   0   0  24 |   0   0   0  8 |  *  *  *  * 10
```

```oxxo3oooo3oooo4xxxx&#xt   → outer heights = 1/sqrt(2) = 0.707107
central height = 1
(tes || pseudo sidpith || pseudo sidpith || tes)

o...3o...3o...4o...     & | 32   * |  4   4   0   0  0 |  6   6  12   0   0  0  0  0 |  4   4  12 12  0  0  0  0  0  0  0 | 1  1  4  6  4  0  0  0 0
.o..3.o..3.o..4.o..     & |  * 128 |  0   1   3   3  1 |  0   3   3   3   6  3  3  3 |  0   3   6  3  1  3  3  1  3  6  3 | 0  1  3  3  1  1  3  3 1
--------------------------+--------+-------------------+-----------------------------+------------------------------------+-------------------------
.... .... .... x...     & |  2   0 | 64   *   *   *  * |  3   0   3   0   0  0  0  0 |  3   0   3  6  0  0  0  0  0  0  0 | 1  0  1  3  3  0  0  0 0
oo..3oo..3oo..4oo..&#x  & |  1   1 |  * 128   *   *  * |  0   3   3   0   0  0  0  0 |  0   3   6  3  0  0  0  0  0  0  0 | 0  1  3  3  1  0  0  0 0
.x.. .... .... ....     & |  0   2 |  *   * 192   *  * |  0   1   0   2   2  0  1  0 |  0   2   2  0  1  2  1  0  2  2  0 | 0  1  2  1  0  1  2  1 0
.... .... .... .x..     & |  0   2 |  *   *   * 192  * |  0   0   1   0   2  2  0  1 |  0   0   2  2  0  1  2  1  0  2  0 | 0  0  1  2  1  0  1  2 1
.oo.3.oo.3.oo.4.oo.&#x    |  0   2 |  *   *   *   * 64 |  0   0   0   0   0  0  3  3 |  0   0   0  0  0  0  0  0  3  6  3 | 0  0  0  0  0  1  3  3 1
--------------------------+--------+-------------------+-----------------------------+------------------------------------+-------------------------
.... .... o...4x...     & |  4   0 |  4   0   0   0  0 | 48   *   *   *   *  *  *  * |  2   0   0  2  0  0  0  0  0  0  0 | 1  0  0  1  2  0  0  0 0
ox.. .... .... ....&#x  & |  1   2 |  0   2   1   0  0 |  * 192   *   *   *  *  *  * |  0   2   2  0  0  0  0  0  0  0  0 | 0  1  2  1  0  0  0  0 0
.... .... .... xx..&#x  & |  2   2 |  1   2   0   1  0 |  *   * 192   *   *  *  *  * |  0   0   2  2  0  0  0  0  0  0  0 | 0  0  1  2  1  0  0  0 0
.x..3.o.. .... ....     & |  0   3 |  0   0   3   0  0 |  *   *   * 128   *  *  *  * |  0   1   0  0  1  1  0  0  1  0  0 | 0  1  1  0  0  1  1  0 0
.x.. .... .... .x..     & |  0   4 |  0   0   2   2  0 |  *   *   *   * 192  *  *  * |  0   0   1  0  0  1  1  0  0  1  0 | 0  0  1  1  0  0  1  1 0
.... .... .o..4.x..     & |  0   4 |  0   0   0   4  0 |  *   *   *   *   * 96  *  * |  0   0   0  1  0  0  1  1  0  0  1 | 0  0  0  1  1  0  0  1 1
.xx. .... .... ....       |  0   4 |  0   0   2   0  2 |  *   *   *   *   *  * 96  * |  0   0   0  0  0  0  0  0  2  2  0 | 0  0  0  0  0  1  2  1 0
.... .... .... .xx.       |  0   4 |  0   0   0   2  2 |  *   *   *   *   *  *  * 96 |  0   0   0  0  0  0  0  0  0  2  2 | 0  0  0  0  0  0  1  2 1
--------------------------+--------+-------------------+-----------------------------+------------------------------------+-------------------------
.... o...3o...4x...     & ♦  8   0 | 12   0   0   0  0 |  6   0   0   0   0  0  0  0 | 16   *   *  *  *  *  *  *  *  *  * | 1  0  0  0  1  0  0  0 0
ox..3oo.. .... ....&#x  & ♦  1   3 |  0   3   3   0  0 |  0   3   0   1   0  0  0  0 |  * 128   *  *  *  *  *  *  *  *  * | 0  1  1  0  0  0  0  0 0
ox.. .... .... xx..&#x  & ♦  2   4 |  1   4   2   2  0 |  0   2   2   0   1  0  0  0 |  *   * 192  *  *  *  *  *  *  *  * | 0  0  1  1  0  0  0  0 0
.... .... oo..4xx..&#x  & ♦  4   4 |  4   4   0   4  0 |  1   0   4   0   0  1  0  0 |  *   *   * 96  *  *  *  *  *  *  * | 0  0  0  1  1  0  0  0 0
.x..3.o..3.o.. ....     & ♦  0   4 |  0   0   6   0  0 |  0   0   0   4   0  0  0  0 |  *   *   *  * 32  *  *  *  *  *  * | 0  1  0  0  0  1  0  0 0
.x..3.o.. .... .x..     & ♦  0   6 |  0   0   6   3  0 |  0   0   0   2   3  0  0  0 |  *   *   *  *  * 64  *  *  *  *  * | 0  0  1  0  0  0  1  0 0
.x.. .... .o..4.x..     & ♦  0   8 |  0   0   4   8  0 |  0   0   0   0   4  2  0  0 |  *   *   *  *  *  * 48  *  *  *  * | 0  0  0  1  0  0  0  1 0
.... .o..3.o..4.x..     & ♦  0   8 |  0   0   0  12  0 |  0   0   0   0   0  6  0  0 |  *   *   *  *  *  *  * 16  *  *  * | 0  0  0  0  1  0  0  0 1
.xx.3.oo. .... ....&#x    ♦  0   6 |  0   0   6   0  3 |  0   0   0   2   0  0  3  0 |  *   *   *  *  *  *  *  * 64  *  * | 0  0  0  0  0  1  1  0 0
.xx. .... .... .xx.&#x    ♦  0   8 |  0   0   4   4  4 |  0   0   0   0   2  0  2  2 |  *   *   *  *  *  *  *  *  * 96  * | 0  0  0  0  0  0  1  1 0
.... .... .oo.4.xx.&#x    ♦  0   8 |  0   0   0   8  4 |  0   0   0   0   0  2  0  4 |  *   *   *  *  *  *  *  *  *  * 48 | 0  0  0  0  0  0  0  1 1
--------------------------+--------+-------------------+-----------------------------+------------------------------------+-------------------------
o...3o...3o...4x...     & ♦ 16   0 | 32   0   0   0  0 | 24   0   0   0   0  0  0  0 |  8   0   0  0  0  0  0  0  0  0  0 | 2  *  *  *  *  *  *  * *
ox..3oo..3oo.. ....&#x  & ♦  1   4 |  0   4   6   0  0 |  0   6   0   4   0  0  0  0 |  0   4   0  0  1  0  0  0  0  0  0 | * 32  *  *  *  *  *  * *
ox..3oo.. .... xx..&#x  & ♦  2   6 |  1   6   6   3  0 |  0   6   3   2   3  0  0  0 |  0   2   3  0  0  1  0  0  0  0  0 | *  * 64  *  *  *  *  * *
ox.. .... oo..4xx..&#x  & ♦  4   8 |  4   8   4   8  0 |  1   4   8   0   4  2  0  0 |  0   0   4  2  0  0  1  0  0  0  0 | *  *  * 48  *  *  *  * *
.... oo..3oo..4xx..&#x  & ♦  8   8 | 12   8   0  12  0 |  6   0  12   0   0  6  0  0 |  1   0   0  6  0  0  0  1  0  0  0 | *  *  *  * 16  *  *  * *
.xx.3.oo.3.oo. ....&#x    ♦  0   8 |  0   0  12   0  4 |  0   0   0   8   0  0  6  0 |  0   0   0  0  2  0  0  0  4  0  0 | *  *  *  *  * 16  *  * *
.xx.3.oo. .... .xx.&#x    ♦  0  12 |  0   0  12   6  6 |  0   0   0   4   6  0  6  3 |  0   0   0  0  0  2  0  0  2  3  0 | *  *  *  *  *  * 32  * *
.xx. .... .oo.4.xx.&#x    ♦  0  16 |  0   0   8  16  8 |  0   0   0   0   8  4  4  8 |  0   0   0  0  0  0  2  0  0  4  2 | *  *  *  *  *  *  * 24 *
.... .oo.3.oo.4.xx.&#x    ♦  0  16 |  0   0   0  24  8 |  0   0   0   0   0 12  0 12 |  0   0   0  0  0  0  0  2  0  0  6 | *  *  *  *  *  *  *  * 8
```

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