Acronym rittit Name rectified tesseractic tetracomb,quartertesseractic tetracomb Confer general polytopal classes: partial Stott expansions Externallinks

This honeycomb also can be described as s4o3o3o4s', i.e. as sequential applications of alternated facetings, according to x4o3o3o4xs4o3o3o4x (= x3o3o *b3o4x) → x3o3o *b3o4s' (cf. below).

Incidence matrix according to Dynkin symbol

```o4x3o3o4o   (N → ∞)

. . . . . | 4N |  12 |  6  24 | 12  16 | 8 2
----------+----+-----+--------+--------+----
. x . . . |  2 | 24N |  1   4 |  4   4 | 4 1
----------+----+-----+--------+--------+----
o4x . . . |  4 |   4 | 6N   * |  4   0 | 4 0
. x3o . . |  3 |   3 |  * 32N |  1   2 | 2 1
----------+----+-----+--------+--------+----
o4x3o . . ♦ 12 |  24 |  6   8 | 4N   * | 2 0
. x3o3o . ♦  4 |   6 |  0   4 |  * 16N | 1 1
----------+----+-----+--------+--------+----
o4x3o3o . ♦ 32 |  96 | 24  64 |  8  16 | N *
. x3o3o4o ♦  8 |  24 |  0  32 |  0  16 | * N
```

```o3o3o *b3x4o   (N → ∞)

. . .    . . | 8N |  12 |  24   6 |   8   8 12 |  2 4 4
-------------+----+-----+---------+------------+-------
. . .    x . |  2 | 48N |   4   1 |   2   2  4 |  1 2 2
-------------+----+-----+---------+------------+-------
. o . *b3x . |  3 |   3 | 64N   * |   1   1  1 |  1 1 1
. . .    x4o |  4 |   4 |   * 12N |   0   0  4 |  0 2 2
-------------+----+-----+---------+------------+-------
o3o . *b3x . ♦  4 |   6 |   4   0 | 16N   *  * |  1 1 0
. o3o *b3x . ♦  4 |   6 |   4   0 |   * 16N  * |  1 0 1
. o . *b3x4o ♦ 12 |  24 |   8   6 |   *   * 8N |  0 1 1
-------------+----+-----+---------+------------+-------
o3o3o *b3x . ♦  8 |  24 |  32   0 |   8   8  0 | 2N * *
o3o . *b3x4o ♦ 32 |  96 |  64  24 |  16   0  8 |  * N *
. o3o *b3x4o ♦ 32 |  96 |  64  24 |   0  16  8 |  * * N
```

```x3o3x *b3o4o   (N → ∞)

. . .    . . | 8N |   6   6 |  12   6  12 | 12   8   8 |  8 1 1
-------------+----+---------+-------------+------------+-------
x . .    . . |  2 | 24N   * |   4   1   0 |  4   4   0 |  4 1 0
. . x    . . |  2 |   * 24N |   0   1   4 |  4   0   4 |  4 0 1
-------------+----+---------+-------------+------------+-------
x3o .    . . |  3 |   3   0 | 32N   *   * |  1   2   0 |  2 1 0
x . x    . . |  4 |   2   2 |   * 12N   * |  4   0   0 |  4 0 0
. o3x    . . |  3 |   0   3 |   *   * 32N |  1   0   2 |  2 0 1
-------------+----+---------+-------------+------------+-------
x3o3x    . . ♦ 12 |  12  12 |   4   6   4 | 8N   *   * |  2 0 0
x3o . *b3o . ♦  4 |   6   0 |   4   0   0 |  * 16N   * |  1 1 0
. o3x *b3o . ♦  4 |   0   6 |   0   0   4 |  *   * 16N |  1 0 1
-------------+----+---------+-------------+------------+-------
x3o3x *b3o . ♦ 32 |  48  48 |  32  24  32 |  8   8   8 | 2N * *
x3o . *b3o4o ♦  8 |  24   0 |  32   0   0 |  0  16   0 |  * N *
. o3x *b3o4o ♦  8 |   0  24 |   0   0  32 |  0   0  16 |  * * N
```

```x3o3x *b3o *b3o   (N → ∞)

. . .    .    . | 8N |   6   6 |  12   6  12 | 12  4  4  4  4 | 4 4 1 1
----------------+----+---------+-------------+----------------+--------
x . .    .    . |  2 | 24N   * |   4   1   0 |  4  2  2  0  0 | 2 2 1 0
. . x    .    . |  2 |   * 24N |   0   1   4 |  4  0  0  2  2 | 2 2 0 1
----------------+----+---------+-------------+----------------+--------
x3o .    .    . |  3 |   3   0 | 32N   *   * |  1  1  1  0  0 | 1 1 1 0
x . x    .    . |  4 |   2   2 |   * 12N   * |  4  0  0  0  0 | 2 2 0 0
. o3x    .    . |  3 |   0   3 |   *   * 32N |  1  0  0  1  1 | 1 1 0 1
----------------+----+---------+-------------+----------------+--------
x3o3x    .    . ♦ 12 |  12  12 |   4   6   4 | 8N  *  *  *  * | 1 1 0 0
x3o . *b3o    . ♦  4 |   6   0 |   4   0   0 |  * 8N  *  *  * | 1 0 1 0
x3o .    . *b3o ♦  4 |   6   0 |   4   0   0 |  *  * 8N  *  * | 0 1 1 0
. o3x *b3o    . ♦  4 |   0   6 |   0   0   4 |  *  *  * 8N  * | 1 0 0 1
. o3x    . *b3o ♦  4 |   0   6 |   0   0   4 |  *  *  *  * 8N | 0 1 0 1
----------------+----+---------+-------------+----------------+--------
x3o3x *b3o    . ♦ 32 |  48  48 |  32  24  32 |  8  8  0  8  0 | N * * *
x3o3x    . *b3o ♦ 32 |  48  48 |  32  24  32 |  8  0  8  0  8 | * N * *
x3o . *b3o *b3o ♦  8 |  24   0 |  32   0   0 |  0  8  8  0  0 | * * N *
. o3x *b3o *b3o ♦  8 |   0  24 |   0   0  32 |  0  0  0  8  8 | * * * N
```

```x3o3o *b3o4s   (N → ∞)

demi( . . .    . . ) | 8N |   6   6 |  12   6  12 |  4  4  4 12  4 | 1 4 1 4
---------------------+----+---------+-------------+----------------+--------
demi( x . .    . . ) |  2 | 24N   * |   4   1   0 |  2  2  0  4  0 | 1 2 0 2
o4s   |  2 |   * 24N |   0   1   4 |  0  0  2  4  2 | 0 2 1 2
---------------------+----+---------+-------------+----------------+--------
demi( x3o .    . . ) |  3 |   3   0 | 32N   *   * |  1  1  0  1  0 | 1 1 0 1
x . 2    o4s   |  4 |   2   2 |   * 12N   * |  0  0  0  4  0 | 0 2 0 2
sefa( . o . *b3o4s ) |  3 |   0   3 |   *   * 32N |  0  0  1  1  1 | 0 1 1 1
---------------------+----+---------+-------------+----------------+--------
demi( x3o3o    . . ) ♦  4 |   6   0 |   4   0   0 | 8N  *  *  *  * | 1 0 0 1
demi( x3o . *b3o . ) ♦  4 |   6   0 |   4   0   0 |  * 8N  *  *  * | 1 1 0 0
. o . *b3o4s   ♦  4 |   0   6 |   0   0   4 |  *  * 8N  *  * | 0 1 1 0
sefa( x3o . *b3o4s ) ♦ 12 |  12  12 |   4   6   4 |  *  *  * 8N  * | 0 1 0 1
sefa( . o3o *b3o4s ) ♦  4 |   0   6 |   0   0   4 |  *  *  *  * 8N | 0 0 1 1
---------------------+----+---------+-------------+----------------+--------
demi( x3o3o *b3o . ) ♦  8 |  24   0 |  32   0   0 |  8  8  0  0  0 | N * * *
x3o . *b3o4s   ♦ 32 |  48  48 |  32  24  32 |  0  8  8  8  0 | * N * *
. o3o *b3o4s   ♦  8 |   0  24 |   0   0  32 |  0  0  8  0  8 | * * N *
sefa( x3o3o *b3o4s ) ♦ 32 |  48  48 |  32  24  32 |  8  0  0  8  8 | * * * N

starting figure: x3o3o *b3o4x
```