Acronym thexatah Name (degenerate) thex atop tah 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

```xo3xx3ox4oo&#x   → height = 0
(thex || tah)

o.3o.3o.4o.    | 48  * |  1  4   4  0  0 |  4  4  4  4   4  0  0  0 |  4 1  4  4  4  1  0 0 | 1  4  1 1 0
.o3.o3.o4.o    |  * 96 |  0  0   2  2  2 |  0  0  1  2   4  1  4  1 |  0 0  1  2  4  2  2 2 | 0  2  1 2 1
---------------+-------+-----------------+--------------------------+-----------------------+------------
x. .. .. ..    |  2  0 | 24  *   *  *  * |  4  0  4  0   0  0  0  0 |  4 0  4  4  0  0  0 0 | 1  4  1 0 0
.. x. .. ..    |  2  0 |  * 96   *  *  * |  1  2  0  1   0  0  0  0 |  2 1  1  0  2  0  0 0 | 1  2  0 1 0
oo3oo3oo4oo&#x |  1  1 |  *  * 192  *  * |  0  0  1  1   2  0  0  0 |  0 0  1  2  2  1  0 0 | 0  2  1 1 0
.. .x .. ..    |  0  2 |  *  *   * 96  * |  0  0  0  1   0  1  2  0 |  0 0  1  0  2  0  2 1 | 0  2  0 1 1
.. .. .x ..    |  0  2 |  *  *   *  * 96 |  0  0  0  0   2  0  2  1 |  0 0  0  1  2  2  1 2 | 0  1  1 2 1
---------------+-------+-----------------+--------------------------+-----------------------+------------
x.3x. .. ..    |  6  0 |  3  3   0  0  0 | 32  *  *  *   *  *  *  * |  2 0  1  0  0  0  0 0 | 1  2  0 0 0
.. x.3o. ..    |  3  0 |  0  3   0  0  0 |  * 64  *  *   *  *  *  * |  1 1  0  0  1  0  0 0 | 1  1  0 1 0
xo .. .. ..&#x |  2  1 |  1  0   2  0  0 |  *  * 96  *   *  *  *  * |  0 0  1  2  0  0  0 0 | 0  2  1 0 0
.. xx .. ..&#x |  2  2 |  0  1   2  1  0 |  *  *  * 96   *  *  *  * |  0 0  1  0  2  0  0 0 | 0  2  0 1 0
.. .. ox ..&#x |  1  2 |  0  0   2  0  1 |  *  *  *  * 192  *  *  * |  0 0  0  1  1  1  0 0 | 0  1  1 1 0
.o3.x .. ..    |  0  3 |  0  0   0  3  0 |  *  *  *  *   * 32  *  * |  0 0  1  0  0  0  2 0 | 0  2  0 0 1
.. .x3.x ..    |  0  6 |  0  0   0  3  3 |  *  *  *  *   *  * 64  * |  0 0  0  0  1  0  1 1 | 0  1  0 1 1
.. .. .x4.o    |  0  4 |  0  0   0  0  4 |  *  *  *  *   *  *  * 24 |  0 0  0  0  0  2  0 2 | 0  0  1 2 1
---------------+-------+-----------------+--------------------------+-----------------------+------------
x.3x.3o. ..    ♦ 12  0 |  6 12   0  0  0 |  4  4  0  0   0  0  0  0 | 16 *  *  *  *  *  * * | 1  1  0 0 0
.. x.3o.4o.    ♦  6  0 |  0 12   0  0  0 |  0  8  0  0   0  0  0  0 |  * 8  *  *  *  *  * * | 1  0  0 1 0
xo3xx .. ..&#x ♦  6  3 |  3  3   6  3  0 |  1  0  3  3   0  1  0  0 |  * * 32  *  *  *  * * | 0  2  0 0 0
xo .. ox ..&#x ♦  2  2 |  1  0   4  0  1 |  0  0  2  0   2  0  0  0 |  * *  * 96  *  *  * * | 0  1  1 0 0
.. xx3ox ..&#x ♦  3  6 |  0  3   6  3  3 |  0  1  0  3   3  0  1  0 |  * *  *  * 64  *  * * | 0  1  0 1 0
.. .. ox4oo&#x ♦  1  4 |  0  0   4  0  4 |  0  0  0  0   4  0  0  1 |  * *  *  *  * 48  * * | 0  0  1 1 0
.o3.x3.x ..    ♦  0 12 |  0  0   0 12  6 |  0  0  0  0   0  4  4  0 |  * *  *  *  *  * 16 * | 0  1  0 0 1
.. .x3.x4.o    ♦  0 24 |  0  0   0 12 24 |  0  0  0  0   0  0  8  6 |  * *  *  *  *  *  * 8 | 0  0  0 1 1
---------------+-------+-----------------+--------------------------+-----------------------+------------
x.3x.3o.4o.    ♦ 48  0 | 24 96   0  0  0 | 32 64  0  0   0  0  0  0 | 16 8  0  0  0  0  0 0 | 1  *  * * *
xo3xx3ox ..&#x ♦ 12 12 |  6 12  24 12  6 |  4  4 12 12  12  4  4  0 |  1 0  4  6  4  0  1 0 | * 16  * * *
xo .. ox4oo&#x ♦  2  4 |  1  0   8  0  4 |  0  0  4  0   8  0  0  1 |  0 0  0  4  0  2  0 0 | *  * 24 * *
.. xx3ox4oo&#x ♦  6 24 |  0 12  24 12 24 |  0  8  0 12  24  0  8  6 |  0 1  0  0  8  6  0 1 | *  *  * 8 *
.o3.x3.x4.o    ♦  0 96 |  0  0   0 96 96 |  0  0  0  0   0 32 64 24 |  0 0  0  0  0  0 16 8 | *  *  * * 1
```

```ox3xx3ox *b3xo&#x   → height = 0
(thex || tah)

o.3o.3o. *b3o.    | 48  * |  4  1   4  0  0  0 |  2  2  4  2  4  2  4  0  0  0  0 | 1 2 2  2  1  2  2  4  2 0 0 0 | 1 1 2  1 2 0
.o3.o3.o *b3.o    |  * 96 |  0  0   2  1  2  1 |  0  0  0  2  2  2  1  2  1  2  1 | 0 0 0  2  2  1  2  1  1 2 1 1 | 0 2 1  1 2 1
------------------+-------+--------------------+----------------------------------+-------------------------------+-------------
.. x. ..    ..    |  2  0 | 96  *   *  *  *  * |  1  1  1  0  1  0  0  0  0  0  0 | 1 1 1  1  0  0  1  1  0 0 0 0 | 1 1 1  0 1 0
.. .. ..    x.    |  2  0 |  * 24   *  *  *  * |  0  0  4  0  0  0  4  0  0  0  0 | 0 2 2  0  0  2  0  4  2 0 0 0 | 1 0 2  1 2 0
oo3oo3oo *b3oo&#x |  1  1 |  *  * 192  *  *  * |  0  0  0  1  1  1  1  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 |  *  *   * 48  *  * |  0  0  0  2  0  0  0  2  1  0  0 | 0 0 0  2  2  1  0  0  0 2 1 1 | 0 2 1  1 0 1
.. .x ..    ..    |  0  2 |  *  *   *  * 96  * |  0  0  0  0  1  0  0  1  0  1  1 | 0 0 0  1  0  0  1  1  0 1 1 1 | 0 1 1  0 1 1
.. .. .x    ..    |  0  2 |  *  *   *  *  * 48 |  0  0  0  0  0  2  0  0  1  2  0 | 0 0 0  0  2  0  2  0  1 2 0 0 | 0 2 0  1 1 1
------------------+-------+--------------------+----------------------------------+-------------------------------+-------------
o.3x. ..    ..    |  3  0 |  3  0   0  0  0  0 | 32  *  *  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0  0  0 0 0 0 | 1 1 1  0 0 0
.. x.3o.    ..    |  3  0 |  3  0   0  0  0  0 |  * 32  *  *  *  *  *  *  *  *  * | 1 0 1  0  0  0  1  0  0 0 0 0 | 1 1 0  0 1 0
.. x. .. *b3x.    |  6  0 |  3  3   0  0  0  0 |  *  * 32  *  *  *  *  *  *  *  * | 0 1 1  0  0  0  0  1  0 0 0 0 | 1 0 1  0 1 0
ox .. ..    ..&#x |  1  2 |  0  0   2  1  0  0 |  *  *  * 96  *  *  *  *  *  *  * | 0 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 |  *  *  *  * 96  *  *  *  *  *  * | 0 0 0  1  0  0  1  1  0 0 0 0 | 0 1 1  0 1 0
.. .. ox    ..&#x |  1  2 |  0  0   2  0  0  1 |  *  *  *  *  * 96  *  *  *  *  * | 0 0 0  0  1  0  1  0  1 0 0 0 | 0 1 0  1 1 0
.. .. ..    xo&#x |  2  1 |  0  1   2  0  0  0 |  *  *  *  *  *  * 96  *  *  *  * | 0 0 0  0  0  1  0  1  1 0 0 0 | 0 0 1  1 1 0
.x3.x ..    ..    |  0  6 |  0  0   0  3  3  0 |  *  *  *  *  *  *  * 32  *  *  * | 0 0 0  1  0  0  0  0  0 1 1 0 | 0 1 1  0 0 1
.x .. .x    ..    |  0  4 |  0  0   0  2  0  2 |  *  *  *  *  *  *  *  * 24  *  * | 0 0 0  0  2  0  0  0  0 2 0 0 | 0 2 0  1 0 1
.. .x3.x    ..    |  0  6 |  0  0   0  0  3  3 |  *  *  *  *  *  *  *  *  * 32  * | 0 0 0  0  0  0  1  0  0 1 0 1 | 0 1 0  0 1 1
.. .x .. *b3.o    |  0  3 |  0  0   0  0  3  0 |  *  *  *  *  *  *  *  *  *  * 32 | 0 0 0  0  0  0  0  1  0 0 1 1 | 0 0 1  0 1 1
------------------+-------+--------------------+----------------------------------+-------------------------------+-------------
o.3x.3o.    ..    ♦  6  0 | 12  0   0  0  0  0 |  4  4  0  0  0  0  0  0  0  0  0 | 8 * *  *  *  *  *  *  * * * * | 1 1 0  0 0 0
o.3x. .. *b3x.    ♦ 12  0 | 12  6   0  0  0  0 |  4  0  4  0  0  0  0  0  0  0  0 | * 8 *  *  *  *  *  *  * * * * | 1 0 1  0 0 0
.. x.3o. *b3x.    ♦ 12  0 | 12  6   0  0  0  0 |  0  4  4  0  0  0  0  0  0  0  0 | * * 8  *  *  *  *  *  * * * * | 1 0 0  0 1 0
ox3xx ..    ..&#x ♦  3  6 |  3  0   6  3  3  0 |  1  0  0  3  3  0  0  1  0  0  0 | * * * 32  *  *  *  *  * * * * | 0 1 1  0 0 0
ox .. ox    ..&#x ♦  1  4 |  0  0   4  2  0  2 |  0  0  0  2  0  2  0  0  1  0  0 | * * *  * 48  *  *  *  * * * * | 0 1 0  1 0 0
ox .. ..    xo&#x ♦  2  2 |  0  1   4  1  0  0 |  0  0  0  2  0  0  2  0  0  0  0 | * * *  *  * 48  *  *  * * * * | 0 0 1  1 0 0
.. xx3ox    ..&#x ♦  3  6 |  3  0   6  0  3  3 |  0  1  0  0  3  3  0  0  0  1  0 | * * *  *  *  * 32  *  * * * * | 0 1 0  0 1 0
.. xx .. *b3xo&#x ♦  6  3 |  3  3   6  0  3  0 |  0  0  1  0  3  0  3  0  0  0  1 | * * *  *  *  *  * 32  * * * * | 0 0 1  0 1 0
.. .. ox    xo&#x ♦  2  2 |  0  1   4  0  0  1 |  0  0  0  0  0  2  2  0  0  0  0 | * * *  *  *  *  *  * 48 * * * | 0 0 0  1 1 0
.x3.x3.x    ..    ♦  0 24 |  0  0   0 12 12 12 |  0  0  0  0  0  0  0  4  6  4  0 | * * *  *  *  *  *  *  * 8 * * | 0 1 0  0 0 1
.x3.x .. *b3.o    ♦  0 12 |  0  0   0  6 12  0 |  0  0  0  0  0  0  0  4  0  0  4 | * * *  *  *  *  *  *  * * 8 * | 0 0 1  0 0 1
.. .x3.x *b3.o    ♦  0 12 |  0  0   0  6 12  0 |  0  0  0  0  0  0  0  0  0  4  4 | * * *  *  *  *  *  *  * * * 8 | 0 0 0  0 1 1
------------------+-------+--------------------+----------------------------------+-------------------------------+-------------
o.3x.3o. *b3x.    ♦ 48  0 | 96 24   0  0  0  0 | 32 32 32  0  0  0  0  0  0  0  0 | 8 8 8  0  0  0  0  0  0 0 0 0 | 1 * *  * * *
ox3xx3ox    ..&#x ♦  6 24 | 12  0  24 12 12 12 |  4  4  0 12 12 12  0  4  6  4  0 | 1 0 0  4  6  0  4  0  0 1 0 0 | * 8 *  * * *
ox3xx .. *b3xo&#x ♦ 12 12 | 12  6  24  6 12  0 |  4  0  4 12 12  0 12  4  0  0  4 | 0 1 0  4  0  6  0  4  0 0 1 0 | * * 8  * * *
ox .. ox    xo&#x ♦  2  4 |  0  1   8  2  0  2 |  0  0  0  4  0  4  4  0  1  0  0 | 0 0 0  0  2  2  0  0  2 0 0 0 | * * * 24 * *
.. xx3ox *b3xo&#x ♦ 12 12 | 12  6  24  0 12  6 |  0  4  4  0 12 12 12  0  0  4  4 | 0 0 1  0  0  0  4  4  6 0 0 1 | * * *  * 8 *
.x3.x3.x *b3.o    ♦  0 96 |  0  0   0 48 96 48 |  0  0  0  0  0  0  0 32 24 32 32 | 0 0 0  0  0  0  0  0  0 8 8 8 | * * *  * * 1
```