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

ox3oo4xx3xx&#x   → height = 0
(tico || gyro prico)

o.3o.4o.3o.    | 192   * |   3  1   3   0   0   0 |   3  3   3   6   3   0   0   0   0   0 |  1  3   1   3   3   3   6  0  0  0  0 | 1  1  1  3  3 0
.o3.o4.o3.o    |   * 576 |   0  0   1   2   2   1 |   0  0   2   2   1   1   2   2   1   2 |  0  0   1   2   2   1   2  1  1  2  1 | 0  1  1  2  1 1
---------------+---------+------------------------+----------------------------------------+---------------------------------------+----------------
.. .. x. ..    |   2   0 | 288  *   *   *   *   * |   2  1   0   2   0   0   0   0   0   0 |  1  2   0   1   0   2   2  0  0  0  0 | 1  1  0  1  2 0
.. .. .. x.    |   2   0 |   * 96   *   *   *   * |   0  3   0   0   3   0   0   0   0   0 |  0  3   0   0   3   0   6  0  0  0  0 | 1  0  1  3  3 0
oo3oo4oo3oo&#x |   1   1 |   *  * 576   *   *   * |   0  0   2   2   1   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 |   *  *   * 576   *   * |   0  0   1   0   0   1   1   1   0   0 |  0  0   1   1   1   0   0  1  1  1  0 | 0  1  1  1  0 1
.. .. .x ..    |   0   2 |   *  *   *   * 576   * |   0  0   0   1   0   0   1   0   1   1 |  0  0   0   1   0   1   1  1  0  1  1 | 0  1  0  1  1 1
.. .. .. .x    |   0   2 |   *  *   *   *   * 288 |   0  0   0   0   1   0   0   2   0   2 |  0  0   0   0   2   0   2  0  1  2  1 | 0  0  1  2  1 1
---------------+---------+------------------------+----------------------------------------+---------------------------------------+----------------
.. o.4x. ..    |   4   0 |   4  0   0   0   0   0 | 144  *   *   *   *   *   *   *   *   * |  1  1   0   0   0   1   0  0  0  0  0 | 1  1  0  0  1 0
.. .. x.3x.    |   6   0 |   3  3   0   0   0   0 |   * 96   *   *   *   *   *   *   *   * |  0  2   0   0   0   0   2  0  0  0  0 | 1  0  0  1  2 0
ox .. .. ..&#x |   1   2 |   0  0   2   1   0   0 |   *  * 576   *   *   *   *   *   *   * |  0  0   1   1   1   0   0  0  0  0  0 | 0  1  1  1  0 0
.. .. xx ..&#x |   2   2 |   1  0   2   0   1   0 |   *  *   * 576   *   *   *   *   *   * |  0  0   0   1   0   1   1  0  0  0  0 | 0  1  0  1  1 0
.. .. .. xx&#x |   2   2 |   0  1   2   0   0   1 |   *  *   *   * 288   *   *   *   *   * |  0  0   0   0   2   0   2  0  0  0  0 | 0  0  1  2  1 0
.x3.o .. ..    |   0   3 |   0  0   0   3   0   0 |   *  *   *   *   * 192   *   *   *   * |  0  0   1   0   0   0   0  1  1  0  0 | 0  1  1  0  0 1
.x .. .x ..    |   0   4 |   0  0   0   2   2   0 |   *  *   *   *   *   * 288   *   *   * |  0  0   0   1   0   0   0  1  0  1  0 | 0  1  0  1  0 1
.x .. .. .x    |   0   4 |   0  0   0   2   0   2 |   *  *   *   *   *   *   * 288   *   * |  0  0   0   0   1   0   0  0  1  1  0 | 0  0  1  1  0 1
.. .o4.x ..    |   0   4 |   0  0   0   0   4   0 |   *  *   *   *   *   *   *   * 144   * |  0  0   0   0   0   1   0  1  0  0  1 | 0  1  0  0  1 1
.. .. .x3.x    |   0   6 |   0  0   0   0   3   3 |   *  *   *   *   *   *   *   *   * 192 |  0  0   0   0   0   0   1  0  0  1  1 | 0  0  0  1  1 1
---------------+---------+------------------------+----------------------------------------+---------------------------------------+----------------
o.3o.4x. ..    ♦   8   0 |  12  0   0   0   0   0 |   6  0   0   0   0   0   0   0   0   0 | 24  *   *   *   *   *   *  *  *  *  * | 1  1  0  0  0 0
.. o.4x.3x.    ♦  24   0 |  24 12   0   0   0   0 |   6  8   0   0   0   0   0   0   0   0 |  * 24   *   *   *   *   *  *  *  *  * | 1  0  0  0  1 0
ox3oo .. ..&#x ♦   1   3 |   0  0   3   3   0   0 |   0  0   3   0   0   1   0   0   0   0 |  *  * 192   *   *   *   *  *  *  *  * | 0  1  1  0  0 0
ox .. xx ..&#x ♦   2   4 |   1  0   4   2   2   0 |   0  0   2   2   0   0   1   0   0   0 |  *  *   * 288   *   *   *  *  *  *  * | 0  1  0  1  0 0
ox .. .. xx&#x ♦   2   4 |   0  1   4   2   0   2 |   0  0   2   0   2   0   0   1   0   0 |  *  *   *   * 288   *   *  *  *  *  * | 0  0  1  1  0 0
.. oo4xx ..&#x ♦   4   4 |   4  0   4   0   4   0 |   1  0   0   4   0   0   0   0   1   0 |  *  *   *   *   * 144   *  *  *  *  * | 0  1  0  0  1 0
.. .. xx3xx&#x ♦   6   6 |   3  3   6   0   3   3 |   0  1   0   3   3   0   0   0   0   1 |  *  *   *   *   *   * 192  *  *  *  * | 0  0  0  1  1 0
.x3.o4.x ..    ♦   0  24 |   0  0   0  24  24   0 |   0  0   0   0   0   8  12   0   6   0 |  *  *   *   *   *   *   * 24  *  *  * | 0  1  0  0  0 1
.x3.o .. .x    ♦   0   6 |   0  0   0   6   0   3 |   0  0   0   0   0   2   0   3   0   0 |  *  *   *   *   *   *   *  * 96  *  * | 0  0  1  0  0 1
.x .. .x3.x    ♦   0  12 |   0  0   0   6   6   6 |   0  0   0   0   0   0   3   3   0   2 |  *  *   *   *   *   *   *  *  * 96  * | 0  0  0  1  0 1
.. .o4.x3.x    ♦   0  24 |   0  0   0   0  24  12 |   0  0   0   0   0   0   0   0   6   8 |  *  *   *   *   *   *   *  *  *  * 24 | 0  0  0  0  1 1
---------------+---------+------------------------+----------------------------------------+---------------------------------------+----------------
o.3o.4x.3x.    ♦ 192   0 | 288 96   0   0   0   0 | 144 96   0   0   0   0   0   0   0   0 | 24 24   0   0   0   0   0  0  0  0  0 | 1  *  *  *  * *
ox3oo4xx ..&#x ♦   8  24 |  12  0  24  24  24   0 |   6  0  24  24   0   8  12   0   6   0 |  1  0   8  12   0   6   0  1  0  0  0 | * 24  *  *  * *
ox3oo .. xx&#x ♦   2   6 |   0  1   6   6   0   3 |   0  0   6   0   3   2   0   3   0   0 |  0  0   2   0   3   0   0  0  1  0  0 | *  * 96  *  * *
ox .. xx3xx&#x ♦   6  12 |   3  3  12   6   6   6 |   0  1   6   6   6   0   3   3   0   2 |  0  0   0   3   3   0   2  0  0  1  0 | *  *  * 96  * *
.. oo4xx3xx&#x ♦  24  24 |  24 12  24   0  24  12 |   6  8   0  24  12   0   0   0   6   8 |  0  1   0   0   0   6   8  0  0  0  1 | *  *  *  * 24 *
.x3.o4.x3.x    ♦   0 576 |   0  0   0 576 576 288 |   0  0   0   0   0 192 288 288 144 192 |  0  0   0   0   0   0   0 24 96 96 24 | *  *  *  *  * 1