Acronym ..., proh || gidpith
Name (degenerate) proh atop gidpith
Circumradius ∞   i.e. flat in euclidean space
Confer
general polytopal classes:
decomposition  

It either can be thought of as a degenerate 5D segmentotope with zero height, or as a 4D euclidean decomposition of the larger base into smaller bits.


Incidence matrix according to Dynkin symbol

xx3ox3xx4xx&#x   → height = 0
(proh || gidpith)

o.3o.3o.4o.    | 192   * |   2   2  1   2   0   0   0   0 |  1  2  2  1  2   2   1   2   2  0  0  0  0  0  0 |  1  1  2 1  1  2  2  1  2  2  0  0  0 0 | 1  1  1  2 1 0
.o3.o3.o4.o    |   * 384 |   0   0  0   1   1   1   1   1 |  0  0  0  0  0   1   1   1   1  1  1  1  1  1  1 |  0  0  0 0  1  1  1  1  1  1  1  1  1 1 | 0  1  1  1 1 1
---------------+---------+--------------------------------+--------------------------------------------------+-----------------------------------------+---------------
x. .. .. ..    |   2   0 | 192   *  *   *   *   *   *   * |  1  1  1  0  0   1   0   0   0  0  0  0  0  0  0 |  1  1  1 0  1  1  1  0  0  0  0  0  0 0 | 1  1  1  1 0 0
.. .. x. ..    |   2   0 |   * 192  *   *   *   *   *   * |  0  1  0  1  1   0   0   1   0  0  0  0  0  0  0 |  1  0  1 1  0  1  0  1  0  1  0  0  0 0 | 1  1  0  1 1 0
.. .. .. x.    |   2   0 |   *   * 96   *   *   *   *   * |  0  0  2  0  2   0   0   0   2  0  0  0  0  0  0 |  0  1  2 1  0  0  2  0  1  2  0  0  0 0 | 1  0  1  2 1 0
oo3oo3oo4oo&#x |   1   1 |   *   *  * 384   *   *   *   * |  0  0  0  0  0   1   1   1   1  0  0  0  0  0  0 |  0  0  0 0  1  1  1  1  1  1  0  0  0 0 | 0  1  1  1 1 0
.x .. .. ..    |   0   2 |   *   *  *   * 192   *   *   * |  0  0  0  0  0   1   0   0   0  1  1  1  0  0  0 |  0  0  0 0  1  1  1  0  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  0  1  1  0 |  0  0  0 0  1  0  0  1  1  0  1  1  0 1 | 0  1  1  0 1 1
.. .. .x ..    |   0   2 |   *   *  *   *   *   * 192   * |  0  0  0  0  0   0   0   1   0  0  1  0  1  0  1 |  0  0  0 0  0  1  0  1  0  1  1  0  1 1 | 0  1  0  1 1 1
.. .. .. .x    |   0   2 |   *   *  *   *   *   *   * 192 |  0  0  0  0  0   0   0   0   1  0  0  1  0  1  1 |  0  0  0 0  0  0  1  0  1  1  0  1  1 1 | 0  0  1  1 1 1
---------------+---------+--------------------------------+--------------------------------------------------+-----------------------------------------+---------------
x.3o. .. ..    |   3   0 |   3   0  0   0   0   0   0   0 | 64  *  *  *  *   *   *   *   *  *  *  *  *  *  * |  1  1  0 0  1  0  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   0 |  * 96  *  *  *   *   *   *   *  *  *  *  *  *  * |  1  0  1 0  0  1  0  0  0  0  0  0  0 0 | 1  1  0  1 0 0
x. .. .. x.    |   4   0 |   2   0  2   0   0   0   0   0 |  *  * 96  *  *   *   *   *   *  *  *  *  *  *  * |  0  1  1 0  0  0  1  0  0  0  0  0  0 0 | 1  0  1  1 0 0
.. o.3x. ..    |   3   0 |   0   3  0   0   0   0   0   0 |  *  *  * 64  *   *   *   *   *  *  *  *  *  *  * |  1  0  0 1  0  0  0  1  0  0  0  0  0 0 | 1  1  0  0 1 0
.. .. x.4x.    |   8   0 |   0   4  4   0   0   0   0   0 |  *  *  *  * 48   *   *   *   *  *  *  *  *  *  * |  0  0  1 1  0  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   0 |  *  *  *  *  * 192   *   *   *  *  *  *  *  *  * |  0  0  0 0  1  1  1  0  0  0  0  0  0 0 | 0  1  1  1 0 0
.. ox .. ..&#x |   1   2 |   0   0  0   2   0   1   0   0 |  *  *  *  *  *   * 192   *   *  *  *  *  *  *  * |  0  0  0 0  1  0  0  1  1  0  0  0  0 0 | 0  1  1  0 1 0
.. .. xx ..&#x |   2   2 |   0   1  0   2   0   0   1   0 |  *  *  *  *  *   *   * 192   *  *  *  *  *  *  * |  0  0  0 0  0  1  0  1  0  1  0  0  0 0 | 0  1  0  1 1 0
.. .. .. xx&#x |   2   2 |   0   0  1   2   0   0   0   1 |  *  *  *  *  *   *   *   * 192  *  *  *  *  *  * |  0  0  0 0  0  0  1  0  1  1  0  0  0 0 | 0  0  1  1 1 0
.x3.x .. ..    |   0   6 |   0   0  0   0   3   3   0   0 |  *  *  *  *  *   *   *   *   * 64  *  *  *  *  * |  0  0  0 0  1  0  0  0  0  0  1  1  0 0 | 0  1  1  0 0 1
.x .. .x ..    |   0   4 |   0   0  0   0   2   0   2   0 |  *  *  *  *  *   *   *   *   *  * 96  *  *  *  * |  0  0  0 0  0  1  0  0  0  0  1  0  1 0 | 0  1  0  1 0 1
.x .. .. .x    |   0   4 |   0   0  0   0   2   0   0   2 |  *  *  *  *  *   *   *   *   *  *  * 96  *  *  * |  0  0  0 0  0  0  1  0  0  0  0  1  1 0 | 0  0  1  1 0 1
.. .x3.x ..    |   0   6 |   0   0  0   0   0   3   3   0 |  *  *  *  *  *   *   *   *   *  *  *  * 64  *  * |  0  0  0 0  0  0  0  1  0  0  1  0  0 1 | 0  1  0  0 1 1
.. .x .. .x    |   0   4 |   0   0  0   0   0   2   0   2 |  *  *  *  *  *   *   *   *   *  *  *  *  * 96  * |  0  0  0 0  0  0  0  0  1  0  0  1  0 1 | 0  0  1  0 1 1
.. .. .x4.x    |   0   8 |   0   0  0   0   0   0   4   4 |  *  *  *  *  *   *   *   *   *  *  *  *  *  * 48 |  0  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   0 |  4  6  0  4  0   0   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   0 |  2  0  3  0  0   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 |  0  4  4  0  2   0   0   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  0  8  6   0   0   0   0  0  0  0  0  0  0 |  *  *  * 8  *  *  *  *  *  *  *  *  * * | 1  0  0  0 1 0
xx3ox .. ..&#x    3   6 |   3   0  0   6   3   3   0   0 |  1  0  0  0  0   3   3   0   0  1  0  0  0  0  0 |  *  *  * * 64  *  *  *  *  *  *  *  * * | 0  1  1  0 0 0
xx .. xx ..&#x    4   4 |   2   2  0   4   2   0   2   0 |  0  1  0  0  0   2   0   2   0  0  1  0  0  0  0 |  *  *  * *  * 96  *  *  *  *  *  *  * * | 0  1  0  1 0 0
xx .. .. xx&#x    4   4 |   2   0  2   4   2   0   0   2 |  0  0  1  0  0   2   0   0   2  0  0  1  0  0  0 |  *  *  * *  *  * 96  *  *  *  *  *  * * | 0  0  1  1 0 0
.. ox3xx ..&#x    3   6 |   0   3  0   6   0   3   3   0 |  0  0  0  1  0   0   3   3   0  0  0  0  1  0  0 |  *  *  * *  *  *  * 64  *  *  *  *  * * | 0  1  0  0 1 0
.. ox .. xx&#x    2   4 |   0   0  1   4   0   2   0   2 |  0  0  0  0  0   0   2   0   2  0  0  0  0  1  0 |  *  *  * *  *  *  *  * 96  *  *  *  * * | 0  0  1  0 1 0
.. .. xx4xx&#x    8   8 |   0   4  4   8   0   0   4   4 |  0  0  0  0  1   0   0   4   4  0  0  0  0  0  1 |  *  *  * *  *  *  *  *  * 48  *  *  * * | 0  0  0  1 1 0
.x3.x3.x ..       0  24 |   0   0  0   0  12  12  12   0 |  0  0  0  0  0   0   0   0   0  4  6  0  4  0  0 |  *  *  * *  *  *  *  *  *  * 16  *  * * | 0  1  0  0 0 1
.x3.x .. .x       0  12 |   0   0  0   0   6   6   0   6 |  0  0  0  0  0   0   0   0   0  2  0  3  0  3  0 |  *  *  * *  *  *  *  *  *  *  * 32  * * | 0  0  1  0 0 1
.x .. .x4.x       0  16 |   0   0  0   0   8   0   8   8 |  0  0  0  0  0   0   0   0   0  0  4  4  0  0  2 |  *  *  * *  *  *  *  *  *  *  *  * 24 * | 0  0  0  1 0 1
.. .x3.x4.x       0  48 |   0   0  0   0   0  24  24  24 |  0  0  0  0  0   0   0   0   0  0  0  0  8 12  6 |  *  *  * *  *  *  *  *  *  *  *  *  * 8 | 0  0  0  0 1 1
---------------+---------+--------------------------------+--------------------------------------------------+-----------------------------------------+---------------
x.3o.3x.4x.     192   0 | 192 192 96   0   0   0   0   0 | 64 96 96 64 48   0   0   0   0  0  0  0  0  0  0 | 16 32 24 8  0  0  0  0  0  0  0  0  0 0 | 1  *  *  * * *
xx3ox3xx ..&#x   12  24 |  12  12  0  24  12  12  12   0 |  4  6  0  4  0  12  12  12   0  4  6  0  4  0  0 |  1  0  0 0  4  6  0  4  0  0  1  0  0 0 | * 16  *  * * *
xx3ox .. xx&#x    6  12 |   6   0  3  12   6   6   0   6 |  2  0  3  0  0   6   6   0   6  2  0  3  0  3  0 |  0  1  0 0  2  0  3  0  3  0  0  1  0 0 | *  * 32  * * *
xx .. xx4xx&#x   16  16 |   8   8  8  16   8   0   8   8 |  0  4  4  0  2   8   0   8   8  0  4  4  0  0  2 |  0  0  1 0  0  4  4  0  0  2  0  0  1 0 | *  *  * 24 * *
.. ox3xx4xx&#x   24  48 |   0  24 12  48   0  24  24  24 |  0  0  0  8  6   0  24  24  24  0  0  0  8 12  6 |  0  0  0 1  0  0  0  8 12  6  0  0  0 1 | *  *  *  * 8 *
.x3.x3.x4.x       0 384 |   0   0  0   0 192 192 192 192 |  0  0  0  0  0   0   0   0   0 64 96 96 64 96 48 |  0  0  0 0  0  0  0  0  0  0 16 32 24 8 | *  *  *  * * 1

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