Acronym ahexah Name hyperbolic alternated hexagonal-tiling honeycomb Circumradius sqrt(-2/3) = 0.816497 i Vertex figure ` ©`

This non-compact hyperbolic tesselation uses the euclidean tiling trat in the sense of an infinite horohedron as one type of cells.

Incidence matrix according to Dynkin symbol

```o3o3x3o3*b   (N,M → ∞)

. . . .    | NM ♦  12 |  12   6 |  4  4
-----------+----+-----+---------+------
. . x .    |  2 | 6NM |   2   1 |  1  2
-----------+----+-----+---------+------
. o3x .    |  3 |   3 | 4NM   * |  1  1
. . x3o    |  3 |   3 |   * 2NM |  0  2
-----------+----+-----+---------+------
o3o3x .    ♦  4 |   6 |   4   0 | NM  *
. o3x3o3*b ♦  M |  3M |   M   M |  * 4N
```

```o3o3o6s   (N,M → ∞)

demi( . . . . ) | NM ♦  12 |   6  12 |  4  4
----------------+----+-----+---------+------
sefa( . . o6s ) |  2 | 6NM |   1   2 |  2  1
----------------+----+-----+---------+------
. . o6s   |  3 |   3 | 2NM   * |  2  0
sefa( . o3o6s ) |  3 |   3 |   * 4NM |  1  1
----------------+----+-----+---------+------
. o3o6s   ♦  M |  3M |   M   M | 4N  *
sefa( o3o3o6s ) ♦  4 |   6 |   0   4 |  * NM

starting figure: o3o3o6x
```

```s3s6o3o   (N,M,K → ∞)

demi( . . . . ) | NMK ♦    6    6 |   3   3    9   3 |  3  1   4
----------------+-----+-----------+------------------+----------
sefa( s3s . . ) |   2 | 3NMK    * |   1   0    2   0 |  2  0   1
sefa( . s6o . ) |   2 |    * 3NMK |   0   1    1   1 |  1  1   1
----------------+-----+-----------+------------------+----------
s3s . .   |   3 |    3    0 | NMK   *    *   * |  2  0   0
. s6o .   |   3 |    0    3 |   * NMK    *   * |  1  1   0
sefa( s3s6o . ) |   3 |    2    1 |   *   * 3NMK   * |  1  0   1
sefa( . s6o3o ) |   3 |    0    3 |   *   *    * NMK |  0  1   1
----------------+-----+-----------+------------------+----------
s3s6o .   ♦  3M |   6M   3M |  2M   M   3M   0 | NK  *   *
. s6o3o   ♦   K |    0   3K |   0   K    0   K |  * NM   *
sefa( s3s6o3o ) ♦   4 |    3    3 |   0   0    3   1 |  *  * NMK

starting figure: x3x6o3o
```

```o6s3s6o   (N,M,K → ∞)

demi( . . . . ) | 3NMK ♦    2     8    2 |   1    4   1    6    6 |   2   2    4
----------------+------+-----------------+------------------------+-------------
sefa( o6s . . ) |    2 | 3NMK     *    * |   1    0   0    2    0 |   2   0    1
sefa( . s3s . ) |    2 |    * 12NMK    * |   0    1   0    1    1 |   1   1    1
sefa( . . s6o ) |    2 |    *     * 3NMK |   0    0   1    0    2 |   0   2    1
----------------+------+-----------------+------------------------+-------------
o6s . .   |    3 |    3     0    0 | NMK    *   *    *    * |   2   0    0
. s3s .   |    3 |    0     3    0 |   * 4NMK   *    *    * |   1   1    0
. . s6o   |    3 |    0     0    3 |   *    * NMK    *    * |   0   2    0
sefa( o6s3s . ) |    3 |    1     2    0 |   *    *   * 6NMK    * |   1   0    1
sefa( . s3s6o ) |    3 |    0     2    1 |   *    *   *    * 6NMK |   0   1    1
----------------+------+-----------------+------------------------+-------------
o6s3s .   ♦   3M |   3M    6M    0 |   M   2M   0   3M    0 | 2NK   *    *
. s3s6o   ♦   3K |    0    6K   3K |   0   2K   K    0   3K |   * 2NM    *
sefa( o6s3s6o ) ♦    4 |    1     4    1 |   0    0   0    2    2 |   *   * 3NMK

starting figure: o6x3x6o
```

```o6s3s3s3*b   (N,M,K,L → ∞)

demi( . . . .    ) | 3NMKL ♦     2     4     4     2 |    1     2     2    1     3     3     6 |   1   1    2     4
-------------------+-------+-------------------------+-----------------------------------------+-------------------
sefa( o6s . .    ) |     2 | 3NMKL     *     *     * |    1     0     0    0     1     1     0 |   1   1    0     1
sefa( . s3s .    ) |     2 |     * 6NMKL     *     * |    0     1     0    0     1     0     1 |   1   0    1     1
sefa( . s . s3*b ) |     2 |     *     * 6NMKL     * |    0     0     1    0     0     1     1 |   0   1    1     1
sefa( . . s3s    ) |     2 |     *     *     * 3NMKL |    0     0     0    1     0     0     2 |   0   0    2     1
-------------------+-------+-------------------------+-----------------------------------------+-------------------
o6s . .      |     3 |     3     0     0     0 | NMKL     *     *    *     *     *     * |   1   1    0     0
. s3s .      |     3 |     0     3     0     0 |    * 2NMKL     *    *     *     *     * |   1   0    1     0
. s . s3*b   |     3 |     0     0     3     0 |    *     * 2NMKL    *     *     *     * |   0   1    1     0
. . s3s      |     3 |     0     0     0     3 |    *     *     * NMKL     *     *     * |   0   0    2     0
sefa( o6s3s .    ) |     3 |     1     2     0     0 |    *     *     *    * 3NMKL     *     * |   1   0    0     1
sefa( o6s . s3*b ) |     3 |     1     0     2     0 |    *     *     *    *     * 3NMKL     * |   0   1    0     1
sefa( . s3s3s3*b ) |     3 |     0     1     1     1 |    *     *     *    *     *     * 6NMKL |   0   0    1     1
-------------------+-------+-------------------------+-----------------------------------------+-------------------
o6s3s .      ♦    3M |    3M    6M     0     0 |    M    2M     0    0    3M     0     0 | NKL   *    *     *
o6s . s3*b   ♦    3K |    3K     0    6K     0 |    K     0    2K    0     0    3K     0 |   * NML    *     *
. s3s3s3*b   ♦    3L |     0    3L    3L    3L |    0     L     L    L     0     0    3L |   *   * 2NMK     *
sefa( o6s3s3s3*b ) ♦     4 |     1     2     2     1 |    0     0     0    0     1     1     2 |   *   *    * 3NMKL

starting figure: o6x3x3x3*b
```

```s3s3s3s3*a3*c *b3*d   (N,M,K,L,P → ∞)

demi( . . . .             ) | 3NMKLP ♦      2      2      2      2      2      2 |     1     1     1     1     1     1      3      3      3      3 |    1    1    1    1      4
----------------------------+--------+-------------------------------------------+-----------------------------------------------------------------+---------------------------
sefa( s3s . .             ) |      2 | 3NMKLP      *      *      *      *      * |     1     0     0     0     0     0      1      1      0      0 |    1    1    0    0      1
sefa( s . s . *a3*c       ) |      2 |      * 3NMKLP      *      *      *      * |     0     1     0     0     0     0      1      0      1      0 |    1    0    1    0      1
sefa( s . . s3*a          ) |      2 |      *      * 3NMKLP      *      *      * |     0     0     1     0     0     0      0      1      1      0 |    0    1    1    0      1
sefa( . s3s .             ) |      2 |      *      *      * 3NMKLP      *      * |     0     0     0     1     0     0      1      0      0      1 |    1    0    0    1      1
sefa( . s . s       *b3*d ) |      2 |      *      *      *      * 3NMKLP      * |     0     0     0     0     1     0      0      1      0      1 |    0    1    0    1      1
sefa( . . s3s             ) |      2 |      *      *      *      *      * 3NMKLP |     0     0     0     0     0     1      0      0      1      1 |    0    0    1    1      1
----------------------------+--------+-------------------------------------------+-----------------------------------------------------------------+---------------------------
s3s . .               |      3 |      3      0      0      0      0      0 | NMKLP     *     *     *     *     *      *      *      *      * |    1    1    0    0      0
s . s . *a3*c         |      3 |      0      3      0      0      0      0 |     * NMKLP     *     *     *     *      *      *      *      * |    1    0    1    0      0
s . . s3*a            |      3 |      0      0      3      0      0      0 |     *     * NMKLP     *     *     *      *      *      *      * |    0    1    1    0      0
. s3s .               |      3 |      0      0      0      3      0      0 |     *     *     * NMKLP     *     *      *      *      *      * |    1    0    0    1      0
. s . s       *b3*d   |      3 |      0      0      0      0      3      0 |     *     *     *     * NMKLP     *      *      *      *      * |    0    1    0    1      0
. . s3s               |      3 |      0      0      0      0      0      3 |     *     *     *     *     * NMKLP      *      *      *      * |    0    0    1    1      0
sefa( s3s3s . *a3*c       ) |      3 |      1      1      0      1      0      0 |     *     *     *     *     *     * 3NMKLP      *      *      * |    1    0    0    0      1
sefa( s3s . s3*a    *b3*d ) |      3 |      1      0      1      0      1      0 |     *     *     *     *     *     *      * 3NMKLP      *      * |    0    1    0    0      1
sefa( s . s3s3*a3*c       ) |      3 |      0      1      1      0      0      1 |     *     *     *     *     *     *      *      * 3NMKLP      * |    0    0    1    0      1
sefa( . s3s3s       *b3*d ) |      3 |      0      0      0      1      1      1 |     *     *     *     *     *     *      *      *      * 3NMKLP |    0    0    0    1      1
----------------------------+--------+-------------------------------------------+-----------------------------------------------------------------+---------------------------
s3s3s . *a3*c         ♦     3M |     3M     3M      0     3M      0      0 |     M     M     0     M     0     0     3M      0      0      0 | NKLP    *    *    *      *
s3s . s3*a    *b3*d   ♦     3K |     3K      0     3K      0     3K      0 |     K     0     K     0     K     0      0     3K      0      0 |    * NMLP    *    *      *
s . s3s3*a3*c         ♦     3L |      0     3L     3L      0      0     3L |     0     L     L     0     0     L      0      0     3L      0 |    *    * NMKP    *      *
. s3s3s       *b3*d   ♦     3P |      0      0      0     3P     3P     3P |     0     0     0     P     P     P      0      0      0     3P |    *    *    * NMKL      *
sefa( s3s3s3s3*a3*c *b3*d ) ♦      4 |      1      1      1      1      1      1 |     0     0     0     0     0     0      1      1      1      1 |    *    *    *    * 3NMKLP

starting figure: x3x3x3x3*a3*c *b3*d
```