Acronym prohp Name prismatorhombated-hexadecachoron prism,prismatotruncated-tesseract prism,runcitruncated-tesseract prism,central segment of carnit Circumradius sqrt[17+8 sqrt(2)]/2 = 2.660531 Coordinates ((1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations in all but last coord., all changes of sign Confer uniform relative: carnit   general polytopal classes: segmentotera Externallinks

Incidence matrix according to Dynkin symbol

```x x3o3x4x

. . . . . | 384 |   1   2   2   1 |   2   2  1   1   2   2   1  2 |  1  2  2  1  2  1  1  2  1 |  1  1  2 1 1
----------+-----+-----------------+-------------------------------+----------------------------+-------------
x . . . . |   2 | 192   *   *   * |   2   2  1   0   0   0   0  0 |  1  2  2  1  2  0  0  0  0 |  1  1  2 1 0
. x . . . |   2 |   * 384   *   * |   1   0  0   1   1   1   0  0 |  1  1  1  0  0  1  1  1  0 |  1  1  1 0 1
. . . x . |   2 |   *   * 384   * |   0   1  0   0   1   0   1  1 |  0  1  0  1  1  1  0  1  1 |  1  0  1 1 1
. . . . x |   2 |   *   *   * 192 |   0   0  1   0   0   2   0  2 |  0  0  2  0  2  0  1  2  1 |  0  1  2 1 1
----------+-----+-----------------+-------------------------------+----------------------------+-------------
x x . . . |   4 |   2   2   0   0 | 192   *  *   *   *   *   *  * |  1  1  1  0  0  0  0  0  0 |  1  1  1 0 0
x . . x . |   4 |   2   0   2   0 |   * 192  *   *   *   *   *  * |  0  1  0  1  1  0  0  0  0 |  1  0  1 1 0
x . . . x |   4 |   2   0   0   2 |   *   * 96   *   *   *   *  * |  0  0  2  0  2  0  0  0  0 |  2  0  1 1 0
. x3o . . |   3 |   0   3   0   0 |   *   *  * 128   *   *   *  * |  1  0  0  0  0  1  1  0  0 |  1  1  0 0 1
. x . x . |   4 |   0   2   2   0 |   *   *  *   * 192   *   *  * |  0  1  0  0  0  1  0  1  0 |  1  0  1 0 1
. x . . x |   4 |   0   2   0   2 |   *   *  *   *   * 192   *  * |  0  0  1  0  0  0  1  1  0 |  0  1  1 0 1
. . o3x . |   3 |   0   0   3   0 |   *   *  *   *   *   * 128  * |  0  0  0  1  0  1  0  0  1 |  1  0  0 1 1
. . . x4x |   8 |   0   0   4   4 |   *   *  *   *   *   *   * 96 |  0  0  0  0  1  0  0  1  1 |  0  0  1 1 1
----------+-----+-----------------+-------------------------------+----------------------------+-------------
x x3o . . ♦   6 |   3   6   0   0 |   3   0  0   2   0   0   0  0 | 64  *  *  *  *  *  *  *  * |  1  1  0 0 0
x x . x . ♦   8 |   4   4   4   0 |   2   2  0   0   2   0   0  0 |  * 96  *  *  *  *  *  *  * |  1  0  1 0 0
x x . . x ♦   8 |   4   4   0   4 |   2   0  2   0   0   2   0  0 |  *  * 96  *  *  *  *  *  * |  0  1  1 0 0
x . o3x . ♦   6 |   3   0   6   0 |   0   3  0   0   0   0   2  0 |  *  *  * 64  *  *  *  *  * |  1  0  0 1 0
x . . x4x ♦  16 |   8   0   8   8 |   0   4  4   0   0   0   0  2 |  *  *  *  * 48  *  *  *  * |  0  0  1 1 0
. x3o3x . ♦  12 |   0  12  12   0 |   0   0  0   4   6   0   4  0 |  *  *  *  *  * 32  *  *  * |  1  0  0 0 1
. x3o . x ♦   6 |   0   6   0   3 |   0   0  0   2   0   3   0  0 |  *  *  *  *  *  * 64  *  * |  0  1  0 0 1
. x . x4x ♦  16 |   0   8   8   8 |   0   0  0   0   4   4   0  2 |  *  *  *  *  *  *  * 48  * |  0  0  1 0 1
. . o3x4x ♦  24 |   0   0  24  12 |   0   0  0   0   0   0   8  6 |  *  *  *  *  *  *  *  * 16 |  0  0  0 1 1
----------+-----+-----------------+-------------------------------+----------------------------+-------------
x x3o3x . ♦  24 |  12  24  24   0 |  12  12  0   8  12   0   8  0 |  4  6  0  4  0  2  0  0  0 | 16  *  * * *
x x3o . x ♦  12 |   6  12   0   6 |   6   0  3   4   0   6   0  0 |  2  0  3  0  0  0  2  0  0 |  * 32  * * *
x x . x4x ♦  32 |  16  16  16  16 |   8   8  8   0   8   8   0  4 |  0  4  4  0  2  0  0  2  0 |  *  * 24 * *
x . o3x4x ♦  48 |  24   0  48  24 |   0  24 12   0   0   0  16 12 |  0  0  0  8  6  0  0  0  2 |  *  *  * 8 *
. x3o3x4x ♦ 192 |   0 192 192  96 |   0   0  0  64  96  96  64 48 |  0  0  0  0  0 16 32 24  8 |  *  *  * * 2
```

```xx3oo3xx4xx&#x   → height = 1
(proh || proh)

o.3o.3o.4o.    | 192   * |   2   2  1   1   0   0  0 |  1  2  2  1  2   2   2  0  0  0  0  0  0 |  1  1  2 1  1  2  2  1  2  0  0  0 0 | 1  1  1  2 1 0
.o3.o3.o4.o    |   * 192 |   0   0  0   1   2   2  1 |  0  0  0  0  0   2   2  1  1  2  2  1  2 |  0  0  0 0  1  2  2  1  2  1  1  2 1 | 0  1  1  2 1 1
---------------+---------+---------------------------+------------------------------------------+--------------------------------------+---------------
x. .. .. ..    |   2   0 | 192   *  *   *   *   *  * |  1  1  1  0  0   1   0  0  0  0  0  0  0 |  1  1  1 0  1  1  1  0  0  0  0  0 0 | 1  1  1  1 0 0
.. .. x. ..    |   2   0 |   * 192  *   *   *   *  * |  0  1  0  1  1   0   1  0  0  0  0  0  0 |  1  0  1 1  0  1  0  1  1  0  0  0 0 | 1  1  0  1 1 0
.. .. .. x.    |   2   0 |   *   * 96   *   *   *  * |  0  0  2  0  2   0   0  1  0  0  0  0  0 |  0  1  2 1  0  0  2  0  2  0  0  0 0 | 1  0  1  2 1 0
oo3oo3oo4oo&#x |   1   1 |   *   *  * 192   *   *  * |  0  0  0  0  0   2   2  1  0  0  0  0  0 |  0  0  0 0  1  2  2  1  2  0  0  0 0 | 0  1  1  2 1 0
.x .. .. ..    |   0   2 |   *   *  *   * 192   *  * |  0  0  0  0  0   1   0  0  1  1  1  0  0 |  0  0  0 0  1  1  1  0  0  1  1  1 0 | 0  1  1  1 0 1
.. .. .x ..    |   0   2 |   *   *  *   *   * 192  * |  0  0  0  0  0   0   1  0  0  1  0  1  1 |  0  0  0 0  0  1  0  1  1  1  0  1 1 | 0  1  0  1 1 1
.. .. .. .x    |   0   2 |   *   *  *   *   *   * 96 |  0  0  0  0  0   0   0  1  0  0  2  0  2 |  0  0  0 0  0  0  2  0  2  0  1  2 1 | 0  0  1  2 1 1
---------------+---------+---------------------------+------------------------------------------+--------------------------------------+---------------
x.3o. .. ..    |   3   0 |   3   0  0   0   0   0  0 | 64  *  *  *  *   *   *  *  *  *  *  *  * |  1  1  0 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 |  * 96  *  *  *   *   *  *  *  *  *  *  * |  1  0  1 0  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 |  *  * 96  *  *   *   *  *  *  *  *  *  * |  0  1  1 0  0  0  1  0  0  0  0  0 0 | 1  0  1  1 0 0
.. o.3x. ..    |   3   0 |   0   3  0   0   0   0  0 |  *  *  * 64  *   *   *  *  *  *  *  *  * |  1  0  0 1  0  0  0  1  0  0  0  0 0 | 1  1  0  0 1 0
.. .. x.4x.    |   8   0 |   0   4  4   0   0   0  0 |  *  *  *  * 48   *   *  *  *  *  *  *  * |  0  0  1 1  0  0  0  0  1  0  0  0 0 | 1  0  0  1 1 0
xx .. .. ..&#x |   2   2 |   1   0  0   2   1   0  0 |  *  *  *  *  * 192   *  *  *  *  *  *  * |  0  0  0 0  1  1  1  0  0  0  0  0 0 | 0  1  1  1 0 0
.. .. xx ..&#x |   2   2 |   0   1  0   2   0   1  0 |  *  *  *  *  *   * 192  *  *  *  *  *  * |  0  0  0 0  0  1  0  1  1  0  0  0 0 | 0  1  0  1 1 0
.. .. .. xx&#x |   2   2 |   0   0  1   2   0   0  1 |  *  *  *  *  *   *   * 96  *  *  *  *  * |  0  0  0 0  0  0  2  0  2  0  0  0 0 | 0  0  1  2 1 0
.x3.o .. ..    |   0   3 |   0   0  0   0   3   0  0 |  *  *  *  *  *   *   *  * 64  *  *  *  * |  0  0  0 0  1  0  0  0  0  1  1  0 0 | 0  1  1  0 0 1
.x .. .x ..    |   0   4 |   0   0  0   0   2   2  0 |  *  *  *  *  *   *   *  *  * 96  *  *  * |  0  0  0 0  0  1  0  0  0  1  0  1 0 | 0  1  0  1 0 1
.x .. .. .x    |   0   4 |   0   0  0   0   2   0  2 |  *  *  *  *  *   *   *  *  *  * 96  *  * |  0  0  0 0  0  0  1  0  0  0  1  1 0 | 0  0  1  1 0 1
.. .o3.x ..    |   0   3 |   0   0  0   0   0   3  0 |  *  *  *  *  *   *   *  *  *  *  * 64  * |  0  0  0 0  0  0  0  1  0  1  0  0 1 | 0  1  0  0 1 1
.. .. .x4.x    |   0   8 |   0   0  0   0   0   4  4 |  *  *  *  *  *   *   *  *  *  *  *  * 48 |  0  0  0 0  0  0  0  0  1  0  0  1 1 | 0  0  0  1 1 1
---------------+---------+---------------------------+------------------------------------------+--------------------------------------+---------------
x.3o.3x. ..    ♦  12   0 |  12  12  0   0   0   0  0 |  4  6  0  4  0   0   0  0  0  0  0  0  0 | 16  *  * *  *  *  *  *  *  *  *  * * | 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  0 |  * 32  * *  *  *  *  *  *  *  *  * * | 1  0  1  0 0 0
x. .. x.4x.    ♦  16   0 |   8   8  8   0   0   0  0 |  0  4  4  0  2   0   0  0  0  0  0  0  0 |  *  * 24 *  *  *  *  *  *  *  *  * * | 1  0  0  1 0 0
.. o.3x.4x.    ♦  24   0 |   0  24 12   0   0   0  0 |  0  0  0  8  6   0   0  0  0  0  0  0  0 |  *  *  * 8  *  *  *  *  *  *  *  * * | 1  0  0  0 1 0
xx3oo .. ..&#x ♦   3   3 |   3   0  0   3   3   0  0 |  1  0  0  0  0   3   0  0  1  0  0  0  0 |  *  *  * * 64  *  *  *  *  *  *  * * | 0  1  1  0 0 0
xx .. xx ..&#x ♦   4   4 |   2   2  0   4   2   2  0 |  0  1  0  0  0   2   2  0  0  1  0  0  0 |  *  *  * *  * 96  *  *  *  *  *  * * | 0  1  0  1 0 0
xx .. .. xx&#x ♦   4   4 |   2   0  2   4   2   0  2 |  0  0  1  0  0   2   0  2  0  0  1  0  0 |  *  *  * *  *  * 96  *  *  *  *  * * | 0  0  1  1 0 0
.. oo3xx ..&#x ♦   3   3 |   0   3  0   3   0   3  0 |  0  0  0  1  0   0   3  0  0  0  0  1  0 |  *  *  * *  *  *  * 64  *  *  *  * * | 0  1  0  0 1 0
.. .. xx4xx&#x ♦   8   8 |   0   4  4   8   0   4  4 |  0  0  0  0  1   0   4  4  0  0  0  0  1 |  *  *  * *  *  *  *  * 48  *  *  * * | 0  0  0  1 1 0
.x3.o3.x ..    ♦   0  12 |   0   0  0   0  12  12  0 |  0  0  0  0  0   0   0  0  4  6  0  4  0 |  *  *  * *  *  *  *  *  * 16  *  * * | 0  1  0  0 0 1
.x3.o .. .x    ♦   0   6 |   0   0  0   0   6   0  3 |  0  0  0  0  0   0   0  0  2  0  3  0  0 |  *  *  * *  *  *  *  *  *  * 32  * * | 0  0  1  0 0 1
.x .. .x4.x    ♦   0  16 |   0   0  0   0   8   8  8 |  0  0  0  0  0   0   0  0  0  4  4  0  2 |  *  *  * *  *  *  *  *  *  *  * 24 * | 0  0  0  1 0 1
.. .o3.x4.x    ♦   0  24 |   0   0  0   0   0  24 12 |  0  0  0  0  0   0   0  0  0  0  0  8  6 |  *  *  * *  *  *  *  *  *  *  *  * 8 | 0  0  0  0 1 1
---------------+---------+---------------------------+------------------------------------------+--------------------------------------+---------------
x.3o.3x.4x.    ♦ 192   0 | 192 192 96   0   0   0  0 | 64 96 96 64 48   0   0  0  0  0  0  0  0 | 16 32 24 8  0  0  0  0  0  0  0  0 0 | 1  *  *  * * *
xx3oo3xx ..&#x ♦  12  12 |  12  12  0  12  12  12  0 |  4  6  0  4  0  12  12  0  4  6  0  4  0 |  1  0  0 0  4  6  0  4  0  1  0  0 0 | * 16  *  * * *
xx3oo .. xx&#x ♦   6   6 |   6   0  3   6   6   0  3 |  2  0  3  0  0   6   0  3  2  0  3  0  0 |  0  1  0 0  2  0  3  0  0  0  1  0 0 | *  * 32  * * *
xx .. xx4xx&#x ♦  16  16 |   8   8  8  16   8   8  8 |  0  4  4  0  2   8   8  8  0  4  4  0  2 |  0  0  1 0  0  4  4  0  2  0  0  1 0 | *  *  * 24 * *
.. oo3xx4xx&#x ♦  24  24 |   0  24 12  24   0  24 12 |  0  0  0  8  6   0  24 12  0  0  0  8  6 |  0  0  0 1  0  0  0  8  6  0  0  0 1 | *  *  *  * 8 *
.x3.o3.x4.x    ♦   0 192 |   0   0  0   0 192 192 96 |  0  0  0  0  0   0   0  0 64 96 96 64 48 |  0  0  0 0  0  0  0  0  0 16 32 24 8 | *  *  *  * * 1

```