Acronym ritathex Name (degenerate) rit atop thex Circumradius ∞   i.e. flat in euclidean space Confer general polytopal classes: lace simplices   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

```ox3ox3xo4oo&#x   → height = 0
(rit || thex)

o.3o.3o.4o.    | 32  * |  6   6  0  0 |  6  3  3  3  12  0  0 |  2 3  1  6  6  6  0 0 | 1  2  3 3 0
.o3.o3.o4.o    |  * 48 |  0   4  1  4 |  0  0  4  4   4  4  4 |  0 0  4  4  4  1  4 1 | 0  4  1 1 1
---------------+-------+--------------+-----------------------+-----------------------+------------
.. .. x. ..    |  2  0 | 96   *  *  * |  2  1  0  0   2  0  0 |  1 2  0  1  2  2  0 0 | 1  1  1 2 0
oo3oo3oo4oo&#x |  1  1 |  * 192  *  * |  0  0  1  1   2  0  0 |  0 0  1  2  2  1  0 0 | 0  2  1 1 0
.x .. .. ..    |  0  2 |  *   * 24  * |  0  0  4  0   0  4  0 |  0 0  4  4  0  0  4 0 | 0  4  1 0 1
.. .x .. ..    |  0  2 |  *   *  * 96 |  0  0  0  1   0  1  2 |  0 0  1  0  2  0  2 1 | 0  2  0 1 1
---------------+-------+--------------+-----------------------+-----------------------+------------
.. o.3x. ..    |  3  0 |  3   0  0  0 | 64  *  *  *   *  *  * |  1 1  0  0  1  0  0 0 | 1  1  0 1 0
.. .. x.4o.    |  4  0 |  4   0  0  0 |  * 24  *  *   *  *  * |  0 2  0  0  0  2  0 0 | 1  0  1 2 0
ox .. .. ..&#x |  1  2 |  0   2  1  0 |  *  * 96  *   *  *  * |  0 0  1  2  0  0  0 0 | 0  2  1 0 0
.. ox .. ..&#x |  1  2 |  0   2  0  1 |  *  *  * 96   *  *  * |  0 0  1  0  2  0  0 0 | 0  2  0 1 0
.. .. xo ..&#x |  2  1 |  1   2  0  0 |  *  *  *  * 192  *  * |  0 0  0  1  1  1  0 0 | 0  1  1 1 0
.x3.x .. ..    |  0  6 |  0   0  3  3 |  *  *  *  *   * 32  * |  0 0  1  0  0  0  2 0 | 0  2  0 0 1
.. .x3.o ..    |  0  3 |  0   0  0  3 |  *  *  *  *   *  * 64 |  0 0  0  0  1  0  1 1 | 0  1  0 1 1
---------------+-------+--------------+-----------------------+-----------------------+------------
o.3o.3x. ..    ♦  4  0 |  6   0  0  0 |  4  0  0  0   0  0  0 | 16 *  *  *  *  *  * * | 1  1  0 0 0
.. o.3x.4o.    ♦ 12  0 | 24   0  0  0 |  8  6  0  0   0  0  0 |  * 8  *  *  *  *  * * | 1  0  0 1 0
ox3ox .. ..&#x ♦  1  6 |  0   6  3  3 |  0  0  3  3   0  1  0 |  * * 32  *  *  *  * * | 0  2  0 0 0
ox .. xo ..&#x ♦  2  2 |  1   4  1  0 |  0  0  2  0   2  0  0 |  * *  * 96  *  *  * * | 0  1  1 0 0
.. ox3xo ..&#x ♦  3  3 |  3   6  0  3 |  1  0  0  3   3  0  1 |  * *  *  * 64  *  * * | 0  1  0 1 0
.. .. xo4oo&#x ♦  4  1 |  4   4  0  0 |  0  1  0  0   4  0  0 |  * *  *  *  * 48  * * | 0  0  1 1 0
.x3.x3.o ..    ♦  0 12 |  0   0  6 12 |  0  0  0  0   0  4  4 |  * *  *  *  *  * 16 * | 0  1  0 0 1
.. .x3.o4.o    ♦  0  6 |  0   0  0 12 |  0  0  0  0   0  0  8 |  * *  *  *  *  *  * 8 | 0  0  0 1 1
---------------+-------+--------------+-----------------------+-----------------------+------------
o.3o.3x.4o.    ♦ 32  0 | 96   0  0  0 | 64 24  0  0   0  0  0 | 16 8  0  0  0  0  0 0 | 1  *  * * *
ox3ox3xo ..&#x ♦  4 12 |  6  24  6 12 |  4  0 12 12  12  4  4 |  1 0  4  6  4  0  1 0 | * 16  * * *
ox .. xo4oo&#x ♦  4  2 |  4   8  1  0 |  0  1  4  0   8  0  0 |  0 0  0  4  0  2  0 0 | *  * 24 * *
.. ox3xo4oo&#x ♦ 12  6 | 24  24  0 12 |  8  6  0 12  24  0  8 |  0 1  0  0  8  6  0 1 | *  *  * 8 *
.x3.x3.o4.o    ♦  0 48 |  0   0 24 96 |  0  0  0  0   0 32 64 |  0 0  0  0  0  0 16 8 | *  *  * * 1
```

```xo3ox3xo *b3ox&#x   → height = 0
(rit || thex)

o.3o.3o. *b3o.    | 32  * |  3  3   6  0  0 |  3  3  3  6  3  6  3  0  0  0 | 3 1 1  3  6  3  3  1  2 0 0 0 | 1 3 1  3 1 0
.o3.o3.o *b3.o    |  * 48 |  0  0   4  4  1 |  0  0  0  2  4  2  4  2  2  4 | 0 0 0  2  1  2  2  4  2 1 2 2 | 0 1 2  1 2 1
------------------+-------+-----------------+-------------------------------+-------------------------------+-------------
x. .. ..    ..    |  2  0 | 48  *   *  *  * |  2  1  0  2  0  0  0  0  0  0 | 2 1 0  2  2  1  0  0  0 0 0 0 | 1 2 1  1 0 0
.. .. x.    ..    |  2  0 |  * 48   *  *  * |  0  1  2  0  0  2  0  0  0  0 | 2 0 1  0  2  0  2  0  1 0 0 0 | 1 2 0  1 1 0
oo3oo3oo *b3oo&#x |  1  1 |  *  * 192  *  * |  0  0  0  1  1  1  1  0  0  0 | 0 0 0  1  1  1  1  1  1 0 0 0 | 0 1 1  1 1 0
.. .x ..    ..    |  0  2 |  *  *   * 96  * |  0  0  0  0  1  0  0  1  1  1 | 0 0 0  1  0  0  1  1  0 1 1 1 | 0 1 1  0 1 1
.. .. ..    .x    |  0  2 |  *  *   *  * 24 |  0  0  0  0  0  0  4  0  0  4 | 0 0 0  0  0  2  0  4  0 0 2 2 | 0 0 2  1 2 1
------------------+-------+-----------------+-------------------------------+-------------------------------+-------------
x.3o. ..    ..    |  3  0 |  3  0   0  0  0 | 32  *  *  *  *  *  *  *  *  * | 1 1 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 |  * 24  *  *  *  *  *  *  *  * | 2 0 0  0  2  0  0  0  0 0 0 0 | 1 2 0  1 0 0
.. o.3x.    ..    |  3  0 |  0  3   0  0  0 |  *  * 32  *  *  *  *  *  *  * | 1 0 1  0  0  0  1  0  0 0 0 0 | 1 1 0  0 1 0
xo .. ..    ..&#x |  2  1 |  1  0   2  0  0 |  *  *  * 96  *  *  *  *  *  * | 0 0 0  1  1  1  0  0  0 0 0 0 | 0 1 1  1 0 0
.. ox ..    ..&#x |  1  2 |  0  0   2  1  0 |  *  *  *  * 96  *  *  *  *  * | 0 0 0  1  0  0  1  1  0 0 0 0 | 0 1 1  0 1 0
.. .. xo    ..&#x |  2  1 |  0  1   2  0  0 |  *  *  *  *  * 96  *  *  *  * | 0 0 0  0  1  0  1  0  1 0 0 0 | 0 1 0  1 1 0
.. .. ..    ox&#x |  1  2 |  0  0   2  0  1 |  *  *  *  *  *  * 96  *  *  * | 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  3  0 |  *  *  *  *  *  *  * 32  *  * | 0 0 0  1  0  0  0  0  0 1 1 0 | 0 1 1  0 0 1
.. .x3.o    ..    |  0  3 |  0  0   0  3  0 |  *  *  *  *  *  *  *  * 32  * | 0 0 0  0  0  0  1  0  0 1 0 1 | 0 1 0  0 1 1
.. .x .. *b3.x    |  0  6 |  0  0   0  3  3 |  *  *  *  *  *  *  *  *  * 32 | 0 0 0  0  0  0  0  1  0 0 1 1 | 0 0 1  0 1 1
------------------+-------+-----------------+-------------------------------+-------------------------------+-------------
x.3o.3x.    ..    ♦ 12  0 | 12 12   0  0  0 |  4  6  4  0  0  0  0  0  0  0 | 8 * *  *  *  *  *  *  * * * * | 1 1 0  0 0 0
x.3o. .. *b3o.    ♦  4  0 |  6  0   0  0  0 |  4  0  0  0  0  0  0  0  0  0 | * 8 *  *  *  *  *  *  * * * * | 1 0 1  0 0 0
.. o.3x. *b3o.    ♦  4  0 |  0  6   0  0  0 |  0  0  4  0  0  0  0  0  0  0 | * * 8  *  *  *  *  *  * * * * | 1 0 0  0 1 0
xo3ox ..    ..&#x ♦  3  3 |  3  0   6  3  0 |  1  0  0  3  3  0  0  1  0  0 | * * * 32  *  *  *  *  * * * * | 0 1 1  0 0 0
xo .. xo    ..&#x ♦  4  1 |  2  2   4  0  0 |  0  1  0  2  0  2  0  0  0  0 | * * *  * 48  *  *  *  * * * * | 0 1 0  1 0 0
xo .. ..    ox&#x ♦  2  2 |  1  0   4  0  1 |  0  0  0  2  0  0  2  0  0  0 | * * *  *  * 48  *  *  * * * * | 0 0 1  1 0 0
.. ox3xo    ..&#x ♦  3  3 |  0  3   6  3  0 |  0  0  1  0  3  3  0  0  1  0 | * * *  *  *  * 32  *  * * * * | 0 1 0  0 1 0
.. ox .. *b3ox&#x ♦  1  6 |  0  0   6  3  3 |  0  0  0  0  3  0  3  0  0  1 | * * *  *  *  *  * 32  * * * * | 0 0 1  0 1 0
.. .. xo    ox&#x ♦  2  2 |  0  1   4  0  1 |  0  0  0  0  0  2  2  0  0  0 | * * *  *  *  *  *  * 48 * * * | 0 0 0  1 1 0
.o3.x3.o    ..    ♦  0  6 |  0  0   0 12  0 |  0  0  0  0  0  0  0  4  4  0 | * * *  *  *  *  *  *  * 8 * * | 0 1 0  0 0 1
.o3.x .. *b3.x    ♦  0 12 |  0  0   0 12  6 |  0  0  0  0  0  0  0  4  0  4 | * * *  *  *  *  *  *  * * 8 * | 0 0 1  0 0 1
.. .x3.o *b3.x    ♦  0 12 |  0  0   0 12  6 |  0  0  0  0  0  0  0  0  4  4 | * * *  *  *  *  *  *  * * * 8 | 0 0 0  0 1 1
------------------+-------+-----------------+-------------------------------+-------------------------------+-------------
x.3o.3x. *b3o.    ♦ 32  0 | 48 48   0  0  0 | 32 24 32  0  0  0  0  0  0  0 | 8 8 8  0  0  0  0  0  0 0 0 0 | 1 * *  * * *
xo3ox3xo    ..&#x ♦ 12  6 | 12 12  24 12  0 |  4  6  4 12 12 12  0  4  4  0 | 1 0 0  4  6  0  4  0  0 1 0 0 | * 8 *  * * *
xo3ox .. *b3ox&#x ♦  4 12 |  6  0  24 12  6 |  4  0  0 12 12  0 12  4  0  4 | 0 1 0  4  0  6  0  4  0 0 1 0 | * * 8  * * *
xo .. xo    ox&#x ♦  4  2 |  2  2   8  0  1 |  0  1  0  4  0  4  4  0  0  0 | 0 0 0  0  2  2  0  0  2 0 0 0 | * * * 24 * *
.. ox3xo *b3ox&#x ♦  4 12 |  0  6  24 12  6 |  0  0  4  0 12 12 12  0  4  4 | 0 0 1  0  0  0  4  4  6 0 0 1 | * * *  * 8 *
.o3.x3.o *b3.x    ♦  0 48 |  0  0   0 96 24 |  0  0  0  0  0  0  0 32 32 32 | 0 0 0  0  0  0  0  0  0 8 8 8 | * * *  * * 1
```