Acronym bisch Name bisnub cubic honeycomb ` ©` Confer general polytopal classes: isogonal Externallinks

Although all cells individually have uniform realisations, the honeycomb as a total can not be made uniform: The mere alternated faceting (here starting at batch) e.g. would use edges of 2 different sizes: |s4o| = x(4) = sqrt(2) = 1.414214 and |sefa(s3s)| = x(6) = sqrt(3) = 1.732051 (refering to elements of o4s3s4o here).

Incidence matrix according to Dynkin symbol

```o4s3s4o   (N → ∞)

demi( . . . . ) | 6N |  1  1   8 |  4   6   6 | 2 2  4
----------------+----+-----------+------------+-------
o4s . .   |  2 | 3N  *   * |  0   4   0 | 2 0  2
. . s4o   |  2 |  * 3N   * |  0   0   4 | 0 2  2
sefa( . s3s . ) |  2 |  *  * 24N |  1   1   1 | 1 1  1
----------------+----+-----------+------------+-------
. s3s .   |  3 |  0  0   3 | 8N   *   * | 1 1  0
sefa( o4s3s . ) |  3 |  1  0   2 |  * 12N   * | 1 0  1
sefa( . s3s4o ) |  3 |  0  1   2 |  *   * 12N | 0 1  1
----------------+----+-----------+------------+-------
o4s3s .   ♦ 12 |  6  0  24 |  8  12   0 | N *  *
. s3s4o   ♦ 12 |  0  6  24 |  8   0  12 | * N  *
sefa( o4s3s4o ) ♦  4 |  1  1   4 |  0   2   2 | * * 6N
```
```or
demi( . . . . )   | 3N |  2   8 |  4  12 | 4  4
------------------+----+--------+--------+-----
o4s . .   & |  2 | 3N   * |  0   4 | 2  2
sefa( . s3s . )   |  2 |  * 12N |  1   2 | 2  1
------------------+----+--------+--------+-----
. s3s .     |  3 |  0   3 | 4N   * | 2  0
sefa( o4s3s . ) & |  3 |  1   2 |  * 12N | 1  1
------------------+----+--------+--------+-----
o4s3s .   & ♦ 12 |  6  24 |  8  12 | N  *
sefa( o4s3s4o )   ♦  4 |  2   4 |  0   4 | * 3N

starting figure: o4x3x4o
```

```s3s3s *b4o   (N → ∞)

demi( . . .    . ) | 12N |  1  1   4   4 |  2  2   6   3   3 |  2 1 1   4
-------------------+-----+---------------+-------------------+-----------
s 2 s    .   |   2 | 6N  *   *   * |  0  0   4   0   0 |  2 0 0   2
. s . *b4o   |   2 |  * 6N   *   * |  0  0   0   2   2 |  0 1 1   2
sefa( s3s .    . ) |   2 |  *  * 24N   * |  1  0   1   1   0 |  1 1 0   1
sefa( . s3s    . ) |   2 |  *  *   * 24N |  0  1   1   0   1 |  1 0 1   1
-------------------+-----+---------------+-------------------+-----------
s3s .    .   |   3 |  0  0   3   0 | 8N  *   *   *   * |  1 1 0   0
. s3s    .   |   3 |  0  0   0   3 |  * 8N   *   *   * |  1 0 1   0
sefa( s3s3s    . ) |   3 |  1  0   1   1 |  *  * 24N   *   * |  1 0 0   1
sefa( s3s . *b4o ) |   3 |  0  1   2   0 |  *  *   * 12N   * |  0 1 0   1
sefa( . s3s *b4o ) |   3 |  0  1   0   2 |  *  *   *   * 12N |  0 0 1   1
-------------------+-----+---------------+-------------------+-----------
s3s3s    .   ♦  12 |  6  0  12  12 |  4  4  12   0   0 | 2N * *   *
s3s . *b4o   ♦  12 |  0  6  24   0 |  8  0   0  12   0 |  * N *   *
. s3s *b4o   ♦  12 |  0  6   0  24 |  0  8   0   0  12 |  * * N   *
sefa( s3s3s *b4o ) ♦   4 |  1  1   2   2 |  0  0   2   1   1 |  * * * 12N

starting figure: x3x3x *b4o
```

```s3s3s3s3*a   (N → ∞)

demi( . . . .    ) | 12N |  1  1   2   2   2   2 |  1  1  1  1   3   3   3   3 | 1 1 1 1   4
-------------------+-----+-----------------------+-----------------------------+------------
s 2 s .      |   2 | 6N  *   *   *   *   * |  0  0  0  0   2   0   2   0 | 1 0 1 0   2
. s 2 s      |   2 |  * 6N   *   *   *   * |  0  0  0  0   0   2   0   2 | 0 1 0 1   2
sefa( s3s . .    ) |   2 |  *  * 12N   *   *   * |  1  0  0  0   1   1   0   0 | 1 1 0 0   1
sefa( s . . s3*a ) |   2 |  *  *   * 12N   *   * |  0  1  0  0   0   1   1   0 | 0 1 1 0   1
sefa( . s3s .    ) |   2 |  *  *   *   * 12N   * |  0  0  1  0   1   0   0   1 | 1 0 0 1   1
sefa( . . s3s    ) |   2 |  *  *   *   *   * 12N |  0  0  0  1   0   0   1   1 | 0 0 1 1   1
-------------------+-----+-----------------------+-----------------------------+------------
s3s . .      |   3 |  0  0   3   0   0   0 | 4N  *  *  *   *   *   *   * | 1 1 0 0   0
s . . s3*a   |   3 |  0  0   0   3   0   0 |  * 4N  *  *   *   *   *   * | 0 1 1 0   0
. s3s .      |   3 |  0  0   0   0   3   0 |  *  * 4N  *   *   *   *   * | 1 0 0 1   0
. . s3s      |   3 |  0  0   0   0   0   3 |  *  *  * 4N   *   *   *   * | 0 0 1 1   0
sefa( s3s3s .    ) |   3 |  1  0   1   0   1   0 |  *  *  *  * 12N   *   *   * | 1 0 0 0   1
sefa( s3s . s3*a ) |   3 |  0  1   1   1   0   0 |  *  *  *  *   * 12N   *   * | 0 1 0 0   1
sefa( s . s3s3*a ) |   3 |  1  0   0   1   0   1 |  *  *  *  *   *   * 12N   * | 0 0 1 0   1
sefa( . s3s3s    ) |   3 |  0  1   0   0   1   1 |  *  *  *  *   *   *   * 12N | 0 0 0 1   1
-------------------+-----+-----------------------+-----------------------------+------------
s3s3s .      ♦  12 |  6  0  12   0  12   0 |  4  0  4  0  12   0   0   0 | N * * *   *
s3s . s3*a   ♦  12 |  0  6  12  12   0   0 |  4  4  0  0   0  12   0   0 | * N * *   *
s . s3s3*a   ♦  12 |  6  0   0  12   0  12 |  0  4  0  4   0   0  12   0 | * * N *   *
. s3s3s      ♦  12 |  0  6   0   0  12  12 |  0  0  4  4   0   0   0  12 | * * * N   *
sefa( s3s3s3s3*a ) ♦   4 |  1  1   1   1   1   1 |  0  0  0  0   1   1   1   1 | * * * * 12N

starting figure: x3x3x3x3*a
```