Acronym ...
Name hyperbolic x3x3o3o3*a3*c honeycomb
Circumradius sqrt(-2/3) = 0.816497 i

This non-compact hyperbolic tesselation uses both the euclidean tilings that and trat in the sense of infinite horohedra as some of its cells.

Note, this figure can be considered as being s4o3o6s' too. This is quite surprising here, as in general sequential applications of alternated facetings is not commutative! But here we have

(where both end forms are described below, in turn being equivalent with x3x3o3o3*a3*c). So this provides a rare commutative example, which does not base on an additional symmetry of the starting symbol!


Incidence matrix according to Dynkin symbol

x3x3o3o3*a3*c   (N,M,K → ∞)

. . . .       | 4NMK |     6    3 |    6    3    3    3 |   3   3   1   1
--------------+------+------------+---------------------+----------------
x . . .       |    2 | 12NMK    * |    1    1    1    0 |   1   1   1   0
. x . .       |    2 |     * 6NMK |    2    0    0    2 |   2   1   0   1
--------------+------+------------+---------------------+----------------
x3x . .       |    6 |     3    3 | 4NMK    *    *    * |   1   1   0   0
x . o . *a3*c |    3 |     3    0 |    * 4NMK    *    * |   1   0   1   0
x . . o3*a    |    3 |     3    0 |    *    * 4NMK    * |   0   1   1   0
. x3o .       |    3 |     0    3 |    *    *    * 4NMK |   1   0   0   1
--------------+------+------------+---------------------+----------------
x3x3o . *a3*c    3M |    3M   3M |    M    M    0    M | 4NK   *   *   *
x3x . o3*a       12 |    12    6 |    4    0    4    0 |   * NMK   *   *
x . o3o3*a3*c     K |    3K    0 |    0    K    K    0 |   *   * 4NM   *
. x3o3o           4 |     0    6 |    0    0    0    4 |   *   *   * NMK

x3o3o *b6s   (N,M,K → ∞)

demi( . . .    . ) | 4NMK |    3     6 |    3    3    6    3 |   1   3   1   3
-------------------+------+------------+---------------------+----------------
demi( x . .    . ) |    2 | 6NMK     * |    2    0    2    0 |   1   2   0   1
sefa( . o . *b6s ) |    2 |    * 12NMK |    0    1    1    1 |   0   1   1   1
-------------------+------+------------+---------------------+----------------
demi( x3o .    . ) |    3 |    3     0 | 4NMK    *    *    * |   1   1   0   0
      . o . *b6s   |    3 |    0     3 |    * 4NMK    *    * |   0   1   1   0
sefa( x3o . *b6s ) |    6 |    3     3 |    *    * 4NMK    * |   0   1   0   1
sefa( . o3o *b6s ) |    3 |    0     3 |    *    *    * 4NMK |   0   0   1   1
-------------------+------+------------+---------------------+----------------
demi( x3o3o    . )     4 |    6     0 |    4    0    0    0 | NMK   *   *   *
      x3o . *b6s      3M |   3M    3M |    M    M    M    0 |   * 4NK   *   *
      . o3o *b6s       K |    0    3K |    0    K    0    K |   *   * 4NM   *
sefa( x3o3o *b6s )    12 |    6    12 |    0    0    4    4 |   *   *   * NMK

starting figure: x3o3o *b6x

s4o3x3o3*b   (N,M,K → ∞)

demi( . . . .    ) | 4NMK |     6    3 |    3    3    6    3 |   1   3   1   3
-------------------+------+------------+---------------------+----------------
demi( . . x .    ) |    2 | 12NMK    * |    1    1    1    0 |   1   1   0   1
      s4o . .      |    2 |     * 6NMK |    0    0    2    2 |   0   1   1   2
-------------------+------+------------+---------------------+----------------
demi( . o3x .    ) |    3 |     3    0 | 4NMK    *    *    * |   1   1   0   0
demi( . . x3o    ) |    3 |     3    0 |    * 4NMK    *    * |   1   0   0   1
sefa( s4o3x .    ) |    6 |     3    3 |    *    * 4NMK    * |   0   1   0   1
sefa( s4o . o3*b ) |    3 |     0    3 |    *    *    * 4NMK |   0   0   1   1
-------------------+------+------------+---------------------+----------------
demi( . o3x3o3*b )     M |    3M    0 |    M    M    0    0 | 4NK   *   *   *
      s4o3x .         12 |    12    6 |    4    0    4    0 |   * NMK   *   *
      s4o . o3*b       4 |     0    6 |    0    0    0    4 |   *   * NMK   *
sefa( s4o3x3o3*b )    3K |    3K   3K |    0    K    K    K |   *   *   * 4NM

starting figure: x4o3x3o3*b

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