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

xo3ox4xx3xx&#x   → height = 0
(prico || gyro grico)

o.3o.4o.3o.    | 576   * |   2   2   1    2   0   0   0 |   1   2   2   1   2   2   1   2   2   0   0   0  0 |  1  1  2  1   1   2   2   1   1   2  0  0  0 | 1  1  1  2  1 0
.o3.o4.o3.o    |   * 576 |   0   0   0    2   2   1   1 |   0   0   0   0   0   1   2   2   2   1   2   2  1 |  0  0  0  0   1   1   1   2   2   2  1  1  2 | 0  1  1  1  2 1
---------------+---------+------------------------------+----------------------------------------------------+----------------------------------------------+----------------
x. .. .. ..    |   2   0 | 576   *   *    *   *   *   * |   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 |   * 576   *    *   *   *   * |   0   1   0   1   1   0   0   1   0   0   0   0  0 |  1  0  1  1   0   1   0   1   0   1  0  0  0 | 1  1  0  1  1 0
.. .. .. x.    |   2   0 |   *   * 288    *   *   *   * |   0   0   2   0   2   0   0   0   2   0   0   0  0 |  0  1  2  1   0   0   2   0   1   2  0  0  0 | 1  0  1  2  1 0
oo3oo4oo3oo&#x |   1   1 |   *   *   * 1152   *   *   * |   0   0   0   0   0   1   1   1   1   0   0   0  0 |  0  0  0  0   1   1   1   1   1   1  0  0  0 | 0  1  1  1  1 0
.. .x .. ..    |   0   2 |   *   *   *    * 576   *   * |   0   0   0   0   0   0   1   0   0   1   1   1  0 |  0  0  0  0   1   0   0   1   1   0  1  1  1 | 0  1  1  0  1 1
.. .. .x ..    |   0   2 |   *   *   *    *   * 288   * |   0   0   0   0   0   0   0   2   0   0   2   0  1 |  0  0  0  0   0   1   0   2   0   2  1  0  2 | 0  1  0  1  2 1
.. .. .. .x    |   0   2 |   *   *   *    *   *   * 288 |   0   0   0   0   0   0   0   0   1   0   0   2  1 |  0  0  0  0   0   0   1   0   2   2  0  1  2 | 0  0  1  1  2 1
---------------+---------+------------------------------+----------------------------------------------------+----------------------------------------------+----------------
x.3o. .. ..    |   3   0 |   3   0   0    0   0   0   0 | 192   *   *   *   *   *   *   *   *   *   *   *  * |  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 |   * 288   *   *   *   *   *   *   *   *   *   *  * |  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 |   *   * 288   *   *   *   *   *   *   *   *   *  * |  0  1  1  0   0   0   1   0   0   0  0  0  0 | 1  0  1  1  0 0
.. o.4x. ..    |   4   0 |   0   4   0    0   0   0   0 |   *   *   * 144   *   *   *   *   *   *   *   *  * |  1  0  0  1   0   0   0   1   0   0  0  0  0 | 1  1  0  0  1 0
.. .. x.3x.    |   6   0 |   0   3   3    0   0   0   0 |   *   *   *   * 192   *   *   *   *   *   *   *  * |  0  0  1  1   0   0   0   0   0   1  0  0  0 | 1  0  0  1  1 0
xo .. .. ..&#x |   2   1 |   1   0   0    2   0   0   0 |   *   *   *   *   * 576   *   *   *   *   *   *  * |  0  0  0  0   1   1   1   0   0   0  0  0  0 | 0  1  1  1  0 0
.. ox .. ..&#x |   1   2 |   0   0   0    2   1   0   0 |   *   *   *   *   *   * 576   *   *   *   *   *  * |  0  0  0  0   1   0   0   1   1   0  0  0  0 | 0  1  1  0  1 0
.. .. xx ..&#x |   2   2 |   0   1   0    2   0   1   0 |   *   *   *   *   *   *   * 576   *   *   *   *  * |  0  0  0  0   0   1   0   1   0   1  0  0  0 | 0  1  0  1  1 0
.. .. .. xx&#x |   2   2 |   0   0   1    2   0   0   1 |   *   *   *   *   *   *   *   * 576   *   *   *  * |  0  0  0  0   0   0   1   0   1   1  0  0  0 | 0  0  1  1  1 0
.o3.x .. ..    |   0   3 |   0   0   0    0   3   0   0 |   *   *   *   *   *   *   *   *   * 192   *   *  * |  0  0  0  0   1   0   0   0   0   0  1  1  0 | 0  1  1  0  0 1
.. .x4.x ..    |   0   8 |   0   0   0    0   4   4   0 |   *   *   *   *   *   *   *   *   *   * 144   *  * |  0  0  0  0   0   0   0   1   0   0  1  0  1 | 0  1  0  0  1 1
.. .x .. .x    |   0   4 |   0   0   0    0   2   0   2 |   *   *   *   *   *   *   *   *   *   *   * 288  * |  0  0  0  0   0   0   0   0   1   0  0  1  1 | 0  0  1  0  1 1
.. .. .x3.x    |   0   6 |   0   0   0    0   0   3   3 |   *   *   *   *   *   *   *   *   *   *   *   * 96 |  0  0  0  0   0   0   0   0   0   2  0  0  2 | 0  0  0  1  2 1
---------------+---------+------------------------------+----------------------------------------------------+----------------------------------------------+----------------
x.3o.4x. ..    ♦  24   0 |  24  24   0    0   0   0   0 |   8  12   0   6   0   0   0   0   0   0   0   0  0 | 24  *  *  *   *   *   *   *   *   *  *  *  * | 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 |  * 96  *  *   *   *   *   *   *   *  *  *  * | 1  0  1  0  0 0
x. .. x.3x.    ♦  12   0 |   6   6   6    0   0   0   0 |   0   3   3   0   2   0   0   0   0   0   0   0  0 |  *  * 96  *   *   *   *   *   *   *  *  *  * | 1  0  0  1  0 0
.. o.4x.3x.    ♦  24   0 |   0  24  12    0   0   0   0 |   0   0   0   6   8   0   0   0   0   0   0   0  0 |  *  *  * 24   *   *   *   *   *   *  *  *  * | 1  0  0  0  1 0
xo3ox .. ..&#x ♦   3   3 |   3   0   0    6   3   0   0 |   1   0   0   0   0   3   3   0   0   1   0   0  0 |  *  *  *  * 192   *   *   *   *   *  *  *  * | 0  1  1  0  0 0
xo .. xx ..&#x ♦   4   2 |   2   2   0    4   0   1   0 |   0   1   0   0   0   2   0   2   0   0   0   0  0 |  *  *  *  *   * 288   *   *   *   *  *  *  * | 0  1  0  1  0 0
xo .. .. xx&#x ♦   4   2 |   2   0   2    4   0   0   1 |   0   0   1   0   0   2   0   0   2   0   0   0  0 |  *  *  *  *   *   * 288   *   *   *  *  *  * | 0  0  1  1  0 0
.. ox4xx ..&#x ♦   4   8 |   0   4   0    8   4   4   0 |   0   0   0   1   0   0   4   4   0   0   1   0  0 |  *  *  *  *   *   *   * 144   *   *  *  *  * | 0  1  0  0  1 0
.. ox .. xx&#x ♦   2   4 |   0   0   1    4   2   0   2 |   0   0   0   0   0   0   2   0   2   0   0   1  0 |  *  *  *  *   *   *   *   * 288   *  *  *  * | 0  0  1  0  1 0
.. .. xx3xx&#x ♦   6   6 |   0   3   3    6   0   3   3 |   0   0   0   0   1   0   0   3   3   0   0   0  1 |  *  *  *  *   *   *   *   *   * 192  *  *  * | 0  0  0  1  1 0
.o3.x4.x ..    ♦   0  24 |   0   0   0    0  24  12   0 |   0   0   0   0   0   0   0   0   0   8   6   0  0 |  *  *  *  *   *   *   *   *   *   * 24  *  * | 0  1  0  0  0 1
.o3.x .. .x    ♦   0   6 |   0   0   0    0   6   0   3 |   0   0   0   0   0   0   0   0   0   2   0   3  0 |  *  *  *  *   *   *   *   *   *   *  * 96  * | 0  0  1  0  0 1
.. .x4.x3.x    ♦   0  48 |   0   0   0    0  24  24  24 |   0   0   0   0   0   0   0   0   0   0   6  12  8 |  *  *  *  *   *   *   *   *   *   *  *  * 24 | 0  0  0  0  1 1
---------------+---------+------------------------------+----------------------------------------------------+----------------------------------------------+----------------
x.3o.4x.3x.    ♦ 576   0 | 576 576 288    0   0   0   0 | 192 288 288 144 192   0   0   0   0   0   0   0  0 | 24 96 96 24   0   0   0   0   0   0  0  0  0 | 1  *  *  *  * *
xo3ox4xx ..&#x ♦  24  24 |  24  24   0   48  24  12   0 |   8  12   0   6   0  24  24  24   0   8   6   0  0 |  1  0  0  0   8  12   0   6   0   0  1  0  0 | * 24  *  *  * *
xo3ox .. xx&#x ♦   6   6 |   6   0   3   12   6   0   3 |   2   0   3   0   0   6   6   0   6   2   0   3  0 |  0  1  0  0   2   0   3   0   3   0  0  1  0 | *  * 96  *  * *
xo .. xx3xx&#x ♦  12   6 |   6   6   6   12   0   3   3 |   0   3   3   0   2   6   0   6   6   0   0   0  1 |  0  0  1  0   0   3   3   0   0   2  0  0  0 | *  *  * 96  * *
.. ox4xx3xx&#x ♦  24  48 |   0  24  12   48  24  24  24 |   0   0   0   6   8   0  24  24  24   0   6  12  8 |  0  0  0  1   0   0   0   6  12   8  0  0  1 | *  *  *  * 24 *
.o3.x4.x3.x    ♦   0 576 |   0   0   0    0 576 288 288 |   0   0   0   0   0   0   0   0   0 192 144 288 96 |  0  0  0  0   0   0   0   0   0   0 24 96 24 | *  *  *  *  * 1