Acronym hexah Name hyperbolic order 3 hexagonal-tiling honeycomb ` ©   ©` Circumradius sqrt(-2) = 1.414214 i Vertex figure ` ©` Dual thon Confer related hyperbolic polytopes: x3o6o3o   o6x3o3o3*b   o3x6o3o   general polytopal classes: partial Stott expansions   regular   noble polytopes Externallinks

This regular non-compact hyperbolic tesselation uses hexat in the sense of an infinite horohedron as its only cell type.

Incidence matrix according to Dynkin symbol

```o3o3o6x   (N,M → ∞)

. . . . | NM ♦   4 |  6 |  4
--------+----+-----+----+---
. . . x |  2 | 2NM |  3 |  3
--------+----+-----+----+---
. . o6x |  6 |   6 | NM |  2
--------+----+-----+----+---
. o3o6x ♦ 2M |  3M |  M | 2N

snubbed forms: o3o3o6s
```

```x3x6o3o   (N,M,K → ∞)

. . . . | 2NMK ♦   1    3 |   3   3 |  3  1
--------+------+----------+---------+------
x . . . |    2 | NMK    * |   3   0 |  3  0
. x . . |    2 |   * 3NMK |   1   2 |  2  1
--------+------+----------+---------+------
x3x . . |    6 |   3    3 | NMK   * |  2  0
. x6o . |    6 |   0    6 |   * NMK |  1  1
--------+------+----------+---------+------
x3x6o . ♦   6M |  3M   6M |  2M   M | NK  *
. x6o3o ♦   2K |   0   3K |   0   K |  * NM

snubbed forms: s3s6o3o
```

```o6x3x6o   (N,M,K → ∞)

. . . . | 6NMK ♦    2    2 |   1    4   1 |   2   2
--------+------+-----------+--------------+--------
. x . . |    2 | 6NMK    * |   1    2   0 |   2   1
. . x . |    2 |    * 6NMK |   0    2   1 |   1   2
--------+------+-----------+--------------+--------
o6x . . |    6 |    6    0 | NMK    *   * |   2   0
. x3x . |    6 |    3    3 |   * 4NMK   * |   1   1
. . x6o |    6 |    0    6 |   *    * NMK |   0   2
--------+------+-----------+--------------+--------
o6x3x . ♦   6M |   6M   3M |   M   2M   0 | 2NK   *
. x3x6o ♦   6K |   3K   6K |   0   2K   K |   * 2NM

snubbed forms: o6s3s6o
```

```o6x3x3x3*b   (N,M,K,L → ∞)

. . . .    | 6NMKL ♦     2     1     1 |    1     2     2    1 |   1   1    2
-----------+-------+-------------------+-----------------------+-------------
. x . .    |     2 | 6NMKL     *     * |    1     1     1    0 |   1   1    1
. . x .    |     2 |     * 3NMKL     * |    0     2     0    1 |   1   0    2
. . . x    |     2 |     *     * 3NMKL |    0     0     2    1 |   0   1    2
-----------+-------+-------------------+-----------------------+-------------
o6x . .    |     6 |     6     0     0 | NMKL     *     *    * |   1   1    0
. x3x .    |     6 |     3     3     0 |    * 2NMKL     *    * |   1   0    1
. x . x3*b |     6 |     3     0     3 |    *     * 2NMKL    * |   0   1    1
. . x3x    |     6 |     0     3     3 |    *     *     * NMKL |   0   0    2
-----------+-------+-------------------+-----------------------+-------------
o6x3x .    ♦    6M |    6M    3M     0 |    M    2M     0    0 | NKL   *    *
o6x . x3*b ♦    6K |    6K     0    3K |    K     0    2K    0 |   * NML    *
. x3x3x3*b ♦    6L |    3L    3L    3L |    0     L     L    L |   *   * 2NMK

snubbed forms: o6s3s3s3*b
```

```x3x3x3x3*a3*c *b3*d   (N,M,K,L,P → ∞)

. . . .             | 6NMKLP ♦      1      1      1      1 |     1     1     1     1     1     1 |    1    1    1    1
--------------------+--------+-----------------------------+-------------------------------------+--------------------
x . . .             |      2 | 3NMKLP      *      *      * |     1     1     1     0     0     0 |    1    1    1    0
. x . .             |      2 |      * 3NMKLP      *      * |     1     0     0     1     1     0 |    1    1    0    1
. . x .             |      2 |      *      * 3NMKLP      * |     0     1     0     1     0     1 |    1    0    1    1
. . . x             |      2 |      *      *      * 3NMKLP |     0     0     1     0     1     1 |    0    1    1    1
--------------------+--------+-----------------------------+-------------------------------------+--------------------
x3x . .             |      6 |      3      3      0      0 | NMKLP     *     *     *     *     * |    1    1    0    0
x . x . *a3*c       |      6 |      3      0      3      0 |     * NMKLP     *     *     *     * |    1    0    1    0
x . . x3*a          |      6 |      3      0      0      3 |     *     * NMKLP     *     *     * |    0    1    1    0
. x3x .             |      6 |      0      3      3      0 |     *     *     * NMKLP     *     * |    1    0    0    1
. x . x       *b3*d |      6 |      0      3      0      3 |     *     *     *     * NMKLP     * |    0    1    0    1
. . x3x             |      6 |      0      0      3      3 |     *     *     *     *     * NMKLP |    0    0    1    1
--------------------+--------+-----------------------------+-------------------------------------+--------------------
x3x3x . *a3*c       ♦     6M |     3M     3M     3M      0 |     M     M     0     M     0     0 | NKLP    *    *    *
x3x . x3*a    *b3*d ♦     6K |     3K     3K      0     3K |     K     0     K     0     K     0 |    * NMLP    *    *
x . x3x3*a3*c       ♦     6L |     3L      0     3L     3L |     0     L     L     0     0     L |    *    * NMKP    *
. x3x3x       *b3*d ♦     6P |      0     3P     3P     3P |     0     0     0     P     P     P |    *    *    * NMKL

snubbed forms: s3s3s3s3*a3*c *b3*d
```