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.

This set of 2 concentric vertex layers occurs also as second and fourth vertex layers of the vertex-first hext.

Incidence matrix according to Dynkin symbol

xo3ox4oo3oo&#x   → height = 0
(ico || rico)

o.3o.4o.3o.    | 24  * ♦  8   8   0 | 12  8  12  0   0 |  6 12   6  0  0 | 1  6  1 0
.o3.o4.o3.o    |  * 96 |  0   2   6 |  0  1   6  3   6 |  0  3   6  3  2 | 0  3  2 1
---------------+-------+------------+------------------+-----------------+----------
x. .. .. ..    |  2  0 | 96   *   * |  3  1   0  0   0 |  3  3   0  0  0 | 1  3  0 0
oo3oo4oo3oo&#x |  1  1 |  * 192   * |  0  1   3  0   0 |  0  3   3  0  0 | 0  3  1 0
.. .x .. ..    |  0  2 |  *   * 288 |  0  0   1  1   2 |  0  1   2  2  1 | 0  2  1 1
---------------+-------+------------+------------------+-----------------+----------
x.3o. .. ..    |  3  0 |  3   0   0 | 96  *   *  *   * |  2  1   0  0  0 | 1  2  0 0
xo .. .. ..&#x |  2  1 |  1   2   0 |  * 96   *  *   * |  0  3   0  0  0 | 0  3  0 0
.. ox .. ..&#x |  1  2 |  0   2   1 |  *  * 288  *   * |  0  1   2  0  0 | 0  2  1 0
.o3.x .. ..    |  0  3 |  0   0   3 |  *  *   * 96   * |  0  1   0  2  0 | 0  2  0 1
.. .x4.o ..    |  0  4 |  0   0   4 |  *  *   *  * 144 |  0  0   1  1  1 | 0  1  1 1
---------------+-------+------------+------------------+-----------------+----------
x.3o.4o. ..    ♦  6  0 | 12   0   0 |  8  0   0  0   0 | 24  *   *  *  * | 1  1  0 0
xo3ox .. ..&#x ♦  3  3 |  3   6   3 |  1  3   3  1   0 |  * 96   *  *  * | 0  2  0 0
.. ox4oo ..&#x ♦  1  4 |  0   4   4 |  0  0   4  0   1 |  *  * 144  *  * | 0  1  1 0
.o3.x4.o ..    ♦  0 12 |  0   0  24 |  0  0   0  8   6 |  *  *   * 24  * | 0  1  0 1
.. .x4.o3.o    ♦  0  8 |  0   0  12 |  0  0   0  0   6 |  *  *   *  * 24 | 0  0  1 1
---------------+-------+------------+------------------+-----------------+----------
x.3o.4o.3o.    ♦ 24  0 | 96   0   0 | 96  0   0  0   0 | 24  0   0  0  0 | 1  *  * *
xo3ox4oo ..&#x ♦  6 12 | 12  24  24 |  8 12  24  8   6 |  1  8   6  1  0 | * 24  * *
.. ox4oo3oo&#x ♦  1  8 |  0   8  12 |  0  0  12  0   6 |  0  0   6  0  1 | *  * 24 *
.o3.x4.o3.o    ♦  0 96 |  0   0 288 |  0  0   0 96 144 |  0  0   0 24 24 | *  *  * 1

ox3xo3ox4oo&#x   → height = 0
(ico || rico)

o.3o.3o.4o.    | 24  * ♦  8   8  0   0 |  4  8  4  8   8  0  0  0  0 |  4 2  4  4  8  2  0  0 0 | 1  4  1 2 0
.o3.o3.o4.o    |  * 96 |  0   2  2   4 |  0  0  2  1   4  1  4  2  2 |  0 0  1  4  2  2  2  2 1 | 0  2  2 1 1
---------------+-------+---------------+-----------------------------+--------------------------+------------
.. x. .. ..    |  2  0 | 96   *  *   * |  1  2  0  1   0  0  0  0  0 |  2 1  1  0  2  0  0  0 0 | 1  2  0 1 0
oo3oo3oo4oo&#x |  1  1 |  * 192  *   * |  0  0  1  1   2  0  0  0  0 |  0 0  1  2  2  1  0  0 0 | 1  2  1 1 0
.x .. .. ..    |  0  2 |  *   * 96   * |  0  0  1  0   0  1  2  0  0 |  0 0  1  2  0  0  2  1 0 | 0  2  1 0 1
.. .. .x ..    |  0  2 |  *   *  * 192 |  0  0  0  0   1  0  1  1  1 |  0 0  0  1  1  1  1  1 1 | 0  1  1 1 1
---------------+-------+---------------+-----------------------------+--------------------------+------------
o.3x. .. ..    |  3  0 |  3   0  0   0 | 32  *  *  *   *  *  *  *  * |  2 0  1  0  0  0  0  0 0 | 1  2  0 0 0
.. x.3o. ..    |  3  0 |  3   0  0   0 |  * 64  *  *   *  *  *  *  * |  1 1  0  0  1  0  0  0 0 | 1  1  0 1 0
ox .. .. ..&#x |  1  2 |  0   2  1   0 |  *  * 96  *   *  *  *  *  * |  0 0  1  2  0  0  0  0 0 | 0  2  1 0 0
.. xo .. ..&#x |  2  1 |  1   2  0   0 |  *  *  * 96   *  *  *  *  * |  0 0  1  0  2  0  0  0 0 | 0  2  0 1 0
.. .. ox ..&#x |  1  2 |  0   2  0   1 |  *  *  *  * 192  *  *  *  * |  0 0  0  1  1  1  0  0 0 | 0  1  1 1 0
.x3.o .. ..    |  0  3 |  0   0  3   0 |  *  *  *  *   * 32  *  *  * |  0 0  1  0  0  0  2  0 0 | 0  2  0 0 1
.x .. .x ..    |  0  4 |  0   0  2   2 |  *  *  *  *   *  * 96  *  * |  0 0  0  1  0  0  1  1 0 | 0  1  1 0 1
.. .o3.x ..    |  0  3 |  0   0  0   3 |  *  *  *  *   *  *  * 64  * |  0 0  0  0  1  0  1  0 1 | 0  1  0 1 1
.. .. .x4.o    |  0  4 |  0   0  0   4 |  *  *  *  *   *  *  *  * 48 |  0 0  0  0  0  1  0  1 1 | 0  0  1 1 1
---------------+-------+---------------+-----------------------------+--------------------------+------------
o.3x.3o. ..    ♦  6  0 | 12   0  0   0 |  4  4  0  0   0  0  0  0  0 | 16 *  *  *  *  *  *  * * | 1  1  0 0 0
.. x.3o.4o.    ♦  6  0 | 12   0  0   0 |  0  8  0  0   0  0  0  0  0 |  * 8  *  *  *  *  *  * * | 1  0  0 1 0
ox3xo .. ..&#x ♦  3  3 |  3   6  3   0 |  1  0  3  3   0  1  0  0  0 |  * * 32  *  *  *  *  * * | 0  2  0 0 0
ox .. ox ..&#x ♦  1  4 |  0   4  2   2 |  0  0  2  0   2  0  1  0  0 |  * *  * 96  *  *  *  * * | 0  1  1 0 0
.. xo3ox ..&#x ♦  3  3 |  3   6  0   3 |  0  1  0  3   3  0  0  1  0 |  * *  *  * 64  *  *  * * | 0  1  0 1 0
.. .. ox4oo&#x ♦  1  4 |  0   4  0   4 |  0  0  0  0   4  0  0  0  1 |  * *  *  *  * 48  *  * * | 0  0  1 1 0
.x3.o3.x ..    ♦  0 12 |  0   0 12  12 |  0  0  0  0   0  4  6  4  0 |  * *  *  *  *  * 16  * * | 0  1  0 0 1
.x .. .x4.o    ♦  0  8 |  0   0  4   8 |  0  0  0  0   0  0  4  0  2 |  * *  *  *  *  *  * 24 * | 0  0  1 0 1
.. .o3.x4.o    ♦  0 12 |  0   0  0  24 |  0  0  0  0   0  0  0  8  6 |  * *  *  *  *  *  *  * 8 | 0  0  0 1 1
---------------+-------+---------------+-----------------------------+--------------------------+------------
o.3x.3o.4o.    ♦ 24  0 | 96 192  0   0 | 32 64  0  0   0  0  0  0  0 | 16 8  0  0  0  0  0  0 0 | 1  *  * * *
ox3xo3ox ..&#x ♦  6 12 | 12  24 12  12 |  4  4 12 12  12  4  6  4  0 |  1 0  4  6  4  0  1  0 0 | * 16  * * *
ox .. ox4oo&#x ♦  1  8 |  0   8  4   8 |  0  0  4  0   8  0  4  0  2 |  0 0  0  4  0  2  0  1 0 | *  * 24 * *
.. xo3ox4oo&#x ♦  6 12 | 12  24  0  24 |  0  8  0 12  24  0  0  8  6 |  0 1  0  0  8  6  0  0 1 | *  *  * 8 *
.x3.o3.x4.o    ♦  0 96 |  0   0 96 192 |  0  0  0  0   0 32 96 64 48 |  0 0  0  0  0  0 16 24 8 | *  *  * * 1

ox3xo3ox *b3ox&#x   → height = 0
(ico || rico)

o.3o.3o. *b3o.    | 24  * ♦  8   8  0  0  0 |  4  4  4  4  8  4  4  0  0  0  0  0  0 | 2 2 2  4  2  2  4  4  2 0 0  0 0 | 1 2 2  1 2 0
.o3.o3.o *b3.o    |  * 96 |  0   2  2  2  2 |  0  0  0  2  1  2  2  1  2  2  1  1  2 | 0 0 0  1  2  2  1  1  2 1 1  2 1 | 0 1 1  2 1 1
------------------+-------+-----------------+----------------------------------------+----------------------------------+-------------
.. x. ..    ..    |  2  0 | 96   *  *  *  * |  1  1  1  0  1  0  0  0  0  0  0  0  0 | 1 1 1  1  0  0  1  1  0 0 0  0 0 | 1 1 1  0 1 0
oo3oo3oo *b3oo&#x |  1  1 |  * 192  *  *  * |  0  0  0  1  1  1  1  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 |  *   * 96  *  * |  0  0  0  1  0  0  0  1  1  1  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 |  *   *  * 96  * |  0  0  0  0  0  1  0  0  1  0  1  0  1 | 0 0 0  0  1  0  1  0  1 1 0  1 1 | 0 1 0  1 1 1
.. .. ..    .x    |  0  2 |  *   *  *  * 96 |  0  0  0  0  0  0  1  0  0  1  0  1  1 | 0 0 0  0  0  0  0  1  1 0 1  1 1 | 0 0 1  1 1 1
------------------+-------+-----------------+----------------------------------------+----------------------------------+-------------
o.3x. ..    ..    |  3  0 |  3   0  0  0  0 | 32  *  *  *  *  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0  0  0 0 0  0 0 | 1 1 1  0 0 0
.. x.3o.    ..    |  3  0 |  3   0  0  0  0 |  * 32  *  *  *  *  *  *  *  *  *  *  * | 1 0 1  0  0  0  1  0  0 0 0  0 0 | 1 1 0  0 1 0
.. x. .. *b3o.    |  3  0 |  3   0  0  0  0 |  *  * 32  *  *  *  *  *  *  *  *  *  * | 0 1 1  0  0  0  0  1  0 0 0  0 0 | 1 0 1  0 1 0
ox .. ..    ..&#x |  1  2 |  0   2  1  0  0 |  *  *  * 96  *  *  *  *  *  *  *  *  * | 0 0 0  1  1  1  0  0  0 0 0  0 0 | 0 1 1  1 0 0
.. xo ..    ..&#x |  2  1 |  1   2  0  0  0 |  *  *  *  * 96  *  *  *  *  *  *  *  * | 0 0 0  1  0  0  1  1  0 0 0  0 0 | 0 1 1  0 1 0
.. .. ox    ..&#x |  1  2 |  0   2  0  1  0 |  *  *  *  *  * 96  *  *  *  *  *  *  * | 0 0 0  0  1  0  1  0  1 0 0  0 0 | 0 1 0  1 1 0
.. .. ..    ox&#x |  1  2 |  0   2  0  0  1 |  *  *  *  *  *  * 96  *  *  *  *  *  * | 0 0 0  0  0  1  0  1  1 0 0  0 0 | 0 0 1  1 1 0
.x3.o ..    ..    |  0  3 |  0   0  3  0  0 |  *  *  *  *  *  *  * 32  *  *  *  *  * | 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  2  2  0 |  *  *  *  *  *  *  *  * 48  *  *  *  * | 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  2  0  2 |  *  *  *  *  *  *  *  *  * 48  *  *  * | 0 0 0  0  0  1  0  0  0 0 1  1 0 | 0 0 1  1 0 1
.. .o3.x    ..    |  0  3 |  0   0  0  3  0 |  *  *  *  *  *  *  *  *  *  * 32  *  * | 0 0 0  0  0  0  1  0  0 1 0  0 1 | 0 1 0  0 1 1
.. .o .. *b3.x    |  0  3 |  0   0  0  0  3 |  *  *  *  *  *  *  *  *  *  *  * 32  * | 0 0 0  0  0  0  0  1  0 0 1  0 1 | 0 0 1  0 1 1
.. .. .x    .x    |  0  4 |  0   0  0  2  2 |  *  *  *  *  *  *  *  *  *  *  *  * 48 | 0 0 0  0  0  0  0  0  1 0 0  1 1 | 0 0 0  1 1 1
------------------+-------+-----------------+----------------------------------------+----------------------------------+-------------
o.3x.3o.    ..    ♦  6  0 | 12   0  0  0  0 |  4  4  0  0  0  0  0  0  0  0  0  0  0 | 8 * *  *  *  *  *  *  * * *  * * | 1 1 0  0 0 0
o.3x. .. *b3o.    ♦  6  0 | 12   0  0  0  0 |  4  0  4  0  0  0  0  0  0  0  0  0  0 | * 8 *  *  *  *  *  *  * * *  * * | 1 0 1  0 0 0
.. x.3o. *b3o.    ♦  6  0 | 12   0  0  0  0 |  0  4  4  0  0  0  0  0  0  0  0  0  0 | * * 8  *  *  *  *  *  * * *  * * | 1 0 0  0 1 0
ox3xo ..    ..&#x ♦  3  3 |  3   6  3  0  0 |  1  0  0  3  3  0  0  1  0  0  0  0  0 | * * * 32  *  *  *  *  * * *  * * | 0 1 1  0 0 0
ox .. ox    ..&#x ♦  1  4 |  0   4  2  2  0 |  0  0  0  2  0  2  0  0  1  0  0  0  0 | * * *  * 48  *  *  *  * * *  * * | 0 1 0  1 0 0
ox .. ..    ox&#x ♦  1  4 |  0   4  2  0  2 |  0  0  0  2  0  0  2  0  0  1  0  0  0 | * * *  *  * 48  *  *  * * *  * * | 0 0 1  1 0 0
.. xo3ox    ..&#x ♦  3  3 |  3   6  0  3  0 |  0  1  0  0  3  3  0  0  0  0  1  0  0 | * * *  *  *  * 32  *  * * *  * * | 0 1 0  0 1 0
.. xo .. *b3ox&#x ♦  3  3 |  3   6  0  0  3 |  0  0  1  0  3  0  3  0  0  0  0  1  0 | * * *  *  *  *  * 32  * * *  * * | 0 0 1  0 1 0
.. .. ox    ox&#x ♦  1  4 |  0   4  0  2  2 |  0  0  0  0  0  2  2  0  0  0  0  0  1 | * * *  *  *  *  *  * 48 * *  * * | 0 0 0  1 1 0
.x3.o3.x    ..    ♦  0 12 |  0   0 12 12  0 |  0  0  0  0  0  0  0  4  6  0  4  0  0 | * * *  *  *  *  *  *  * 8 *  * * | 0 1 0  0 0 1
.x3.o .. *b3.x    ♦  0 12 |  0   0 12  0 12 |  0  0  0  0  0  0  0  4  0  6  0  4  0 | * * *  *  *  *  *  *  * * 8  * * | 0 0 1  0 0 1
.x .. .x    .x    ♦  0  8 |  0   0  4  4  4 |  0  0  0  0  0  0  0  0  2  2  0  0  2 | * * *  *  *  *  *  *  * * * 24 * | 0 0 0  1 0 1
.. .o3.x *b3.x    ♦  0 12 |  0   0  0 12 12 |  0  0  0  0  0  0  0  0  0  0  4  4  6 | * * *  *  *  *  *  *  * * *  * 8 | 0 0 0  0 1 1
------------------+-------+-----------------+----------------------------------------+----------------------------------+-------------
o.3x.3o. *b3o.    ♦ 24  0 | 96   0  0  0  0 | 32 32 32  0  0  0  0  0  0  0  0  0  0 | 8 8 8  0  0  0  0  0  0 0 0  0 0 | 1 * *  * * *
ox3xo3ox    ..&#x ♦  6 12 | 12  24 12 12  0 |  4  4  0 12 12 12  0  4  6  0  4  0  0 | 1 0 0  4  6  0  4  0  0 1 0  0 0 | * 8 *  * * *
ox3xo .. *b3ox&#x ♦  6 12 | 12  24 12  0 12 |  4  0  4 12 12  0 12  4  0  6  0  4  0 | 0 1 0  4  0  6  0  4  0 0 1  0 0 | * * 8  * * *
ox .. ox    ox&#x ♦  1  8 |  0   8  4  4  4 |  0  0  0  4  0  4  4  0  2  2  0  0  2 | 0 0 0  0  2  2  0  0  2 0 0  1 0 | * * * 24 * *
.. xo3ox *b3ox&#x ♦  6 12 | 12  24  0 12 12 |  0  4  4  0 12 12 12  0  0  0  4  4  6 | 0 0 1  0  0  0  4  4  6 0 0  0 1 | * * *  * 8 *
.x3.o3.x *b3.x    ♦  0 96 |  0   0 96 96 96 |  0  0  0  0  0  0  0 32 48 48 32 32 48 | 0 0 0  0  0  0  0  0  0 8 8 24 8 | * * *  * * 1