Acronym hexarit Name (degenerate) hex atop rit Circumradius ∞   i.e. flat in euclidean space Confer general polytopal classes: fundamental lace prisms   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

```xo3oo3ox4oo&#x   → height = 0
(hex || rit)

o.3o.3o.4o.    | 8  * |  6 12  0 | 12 24  24  0  0 |  8 12 24  8  6  0 0 | 1  8  6 1 0
.o3.o3.o4.o    | * 32 |  0  3  6 |  0  3  12  6  3 |  0  1  6  6  6  2 3 | 0  2  3 3 1
---------------+------+----------+-----------------+---------------------+------------
x. .. .. ..    | 2  0 | 24  *  * |  4  4   0  0  0 |  4  4  4  0  0  0 0 | 1  4  1 0 0
oo3oo3oo4oo&#x | 1  1 |  * 96  * |  0  2   4  0  0 |  0  1  4  2  2  0 0 | 0  2  2 1 0
.. .. .x ..    | 0  2 |  *  * 96 |  0  0   2  2  1 |  0  0  1  2  2  1 2 | 0  1  1 2 1
---------------+------+----------+-----------------+---------------------+------------
x.3o. .. ..    | 3  0 |  3  0  0 | 32  *   *  *  * |  2  1  0  0  0  0 0 | 1  2  0 0 0
xo .. .. ..&#x | 2  1 |  1  2  0 |  * 96   *  *  * |  0  1  2  0  0  0 0 | 0  2  1 0 0
.. .. ox ..&#x | 1  2 |  0  2  1 |  *  * 192  *  * |  0  0  1  1  1  0 0 | 0  1  1 1 0
.. .o3.x ..    | 0  3 |  0  0  3 |  *  *   * 64  * |  0  0  0  1  0  1 1 | 0  1  0 1 1
.. .. .x4.o    | 0  4 |  0  0  4 |  *  *   *  * 24 |  0  0  0  0  2  0 2 | 0  0  1 2 1
---------------+------+----------+-----------------+---------------------+------------
x.3o.3o. ..    ♦ 4  0 |  6  0  0 |  4  0   0  0  0 | 16  *  *  *  *  * * | 1  1  0 0 0
xo3oo .. ..&#x ♦ 3  1 |  3  3  0 |  1  3   0  0  0 |  * 32  *  *  *  * * | 0  2  0 0 0
xo .. ox ..&#x ♦ 2  2 |  1  4  1 |  0  2   2  0  0 |  *  * 96  *  *  * * | 0  1  1 0 0
.. oo3ox ..&#x ♦ 1  3 |  0  3  3 |  0  0   3  1  0 |  *  *  * 64  *  * * | 0  1  0 1 0
.. .. ox4oo&#x ♦ 1  4 |  0  4  4 |  0  0   4  0  1 |  *  *  *  * 48  * * | 0  0  1 1 0
.o3.o3.x ..    ♦ 0  4 |  0  0  6 |  0  0   0  4  0 |  *  *  *  *  * 16 * | 0  1  0 0 1
.. .o3.x4.o    ♦ 0 12 |  0  0 24 |  0  0   0  8  6 |  *  *  *  *  *  * 8 | 0  0  0 1 1
---------------+------+----------+-----------------+---------------------+------------
x.3o.3o.4o.    ♦ 8  0 | 24  0  0 | 32  0   0  0  0 | 16  0  0  0  0  0 0 | 1  *  * * *
xo3oo3ox ..&#x ♦ 4  4 |  6 12  6 |  4 12  12  4  0 |  1  4  6  4  0  1 0 | * 16  * * *
xo .. ox4oo&#x ♦ 2  4 |  1  8  4 |  0  4   8  0  1 |  0  0  4  0  2  0 0 | *  * 24 * *
.. oo3ox4oo&#x ♦ 1 12 |  0 12 24 |  0  0  24  8  6 |  0  0  0  8  6  0 1 | *  *  * 8 *
.o3.o3.x4.o    ♦ 0 32 |  0  0 96 |  0  0   0 64 24 |  0  0  0  0  0 16 8 | *  *  * * 1
```

```ox3oo3ox *b3xo&#x   → height = 0
(hex || rit)

o.3o.3o. *b3o.    | 8  * |  6 12  0  0 | 12 12 12 24  0  0  0 | 4 4  4  6 12  4 12 12 0 0 0 | 1 1 4  6 4 0
.o3.o3.o *b3.o    | * 32 |  0  3  3  3 |  0  6  6  3  3  3  3 | 0 0  3  6  3  3  1  3 3 1 1 | 0 3 1  3 1 1
------------------+------+-------------+----------------------+-----------------------------+-------------
.. .. ..    x.    | 2  0 | 24  *  *  * |  4  0  0  4  0  0  0 | 2 2  0  0  2  0  4  2 0 0 0 | 1 0 2  1 0 0
oo3oo3oo *b3oo&#x | 1  1 |  * 96  *  * |  0  2  2  2  0  0  0 | 0 0  1  2  2  1  1  2 0 0 0 | 0 1 1  2 1 0
.x .. ..    ..    | 0  2 |  *  * 48  * |  0  2  0  0  2  1  0 | 0 0  2  2  1  0  0  0 2 1 0 | 0 2 1  1 0 1
.. .. .x    ..    | 0  2 |  *  *  * 48 |  0  0  2  0  0  1  2 | 0 0  0  2  0  2  0  1 2 0 1 | 0 2 0  1 1 1
------------------+------+-------------+----------------------+-----------------------------+-------------
.. o. .. *b3x.    | 3  0 |  3  0  0  0 | 32  *  *  *  *  *  * | 1 1  0  0  0  1  0  0 0 0 0 | 1 0 1  0 1 0
ox .. ..    ..&#x | 1  2 |  0  2  1  0 |  * 96  *  *  *  *  * | 0 0  1  1  1  0  0  0 0 0 0 | 0 1 1  1 0 0
.. .. ox    ..&#x | 1  2 |  0  2  0  1 |  *  * 96  *  *  *  * | 0 0  0  1  0  1  0  1 0 0 0 | 0 1 0  1 1 0
.. .. ..    xo&#x | 2  1 |  1  2  0  0 |  *  *  * 96  *  *  * | 0 0  0  0  1  0  1  1 0 0 0 | 0 0 1  1 1 0
.x3.o ..    ..    | 0  3 |  0  0  3  0 |  *  *  *  * 32  *  * | 0 0  1  0  0  0  0  0 1 1 0 | 0 1 1  0 0 1
.x .. .x    ..    | 0  4 |  0  0  2  2 |  *  *  *  *  * 24  * | 0 0  0  2  0  0  0  0 2 0 0 | 0 2 0  1 0 1
.. .o3.x    ..    | 0  3 |  0  0  0  3 |  *  *  *  *  *  * 32 | 0 0  0  0  0  1  0  0 1 0 1 | 0 1 0  0 1 1
------------------+------+-------------+----------------------+-----------------------------+-------------
o.3o. .. *b3x.    ♦ 4  0 |  6  0  0  0 |  4  0  0  0  0  0  0 | 8 *  *  *  *  *  *  * * * * | 1 0 1  0 0 0
.. o.3o. *b3x.    ♦ 4  0 |  6  0  0  0 |  4  0  0  0  0  0  0 | * 8  *  *  *  *  *  * * * * | 1 0 0  0 1 0
ox3oo ..    ..&#x ♦ 1  3 |  0  3  3  0 |  0  3  0  0  1  0  0 | * * 32  *  *  *  *  * * * * | 0 1 1  0 0 0
ox .. ox    ..&#x ♦ 1  4 |  0  4  2  2 |  0  2  2  0  0  1  0 | * *  * 48  *  *  *  * * * * | 0 1 0  1 0 0
ox .. ..    xo&#x ♦ 2  2 |  1  4  1  0 |  0  2  0  2  0  0  0 | * *  *  * 48  *  *  * * * * | 0 0 1  1 0 0
.. oo3ox    ..&#x ♦ 1  3 |  0  3  0  3 |  0  0  3  0  0  0  1 | * *  *  *  * 32  *  * * * * | 0 1 0  0 1 0
.. oo .. *b3xo&#x ♦ 3  1 |  3  3  0  0 |  1  0  0  3  0  0  0 | * *  *  *  *  * 32  * * * * | 0 0 1  0 1 0
.. .. ox    xo&#x ♦ 2  2 |  1  4  0  1 |  0  0  2  2  0  0  0 | * *  *  *  *  *  * 48 * * * | 0 0 0  1 1 0
.x3.o3.x    ..    ♦ 0 12 |  0  0 12 12 |  0  0  0  0  4  6  4 | * *  *  *  *  *  *  * 8 * * | 0 1 0  0 0 1
.x3.o .. *b3.o    ♦ 0  4 |  0  0  6  0 |  0  0  0  0  4  0  0 | * *  *  *  *  *  *  * * 8 * | 0 0 1  0 0 1
.. .o3.x *b3.o    ♦ 0  4 |  0  0  0  6 |  0  0  0  0  0  0  4 | * *  *  *  *  *  *  * * * 8 | 0 0 0  0 1 1
------------------+------+-------------+----------------------+-----------------------------+-------------
o.3o.3o. *b3x.    ♦ 8  0 | 24  0  0  0 | 32  0  0  0  0  0  0 | 8 8  0  0  0  0  0  0 0 0 0 | 1 * *  * * *
ox3oo3ox    ..&#x ♦ 1 12 |  0 12 12 12 |  0 12 12  0  4  6  4 | 0 0  4  6  0  4  0  0 1 0 0 | * 8 *  * * *
ox3oo .. *b3xo&#x ♦ 4  4 |  6 12  6  0 |  4 12  0 12  4  0  0 | 1 0  4  0  6  0  4  0 0 1 0 | * * 8  * * *
ox .. ox    xo&#x ♦ 2  4 |  1  8  2  2 |  0  4  4  4  0  1  0 | 0 0  0  2  2  0  0  2 0 0 0 | * * * 24 * *
.. oo3ox *b3xo&#x ♦ 4  4 |  6 12  0  6 |  4  0 12 12  0  0  4 | 0 1  0  0  0  4  4  6 0 0 1 | * * *  * 8 *
.x3.o3.x *b3.o    ♦ 0 32 |  0  0 48 48 |  0  0  0  0 32 24 32 | 0 0  0  0  0  0  0  0 8 8 8 | * * *  * * 1
```