Acronym ...
Name hyperbolic rhombisquarehexagonal tiling
 
  ©
Circumradius sqrt[-3-2 sqrt(6)]/2 = 1.405256 i
Vertex figure [43,6]
External
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There exists a regular modwrap of this tiling, obtained by identifying every 8th vertex on each hole. Then it allows a representation as infinite skew polyhedron, which happens to be a facial subset of the omnitruncated cubical honeycomb. (The rightmost pictures hint on its relation to x4o6o|4 and x6o4o|4 resp.)


Incidence matrix according to Dynkin symbol

x4o6x   (N → ∞)

. . . | 12N |   2   2 |  1  2  1
------+-----+---------+---------
x . . |   2 | 12N   * |  1  1  0
. . x |   2 |   * 12N |  0  1  1
------+-----+---------+---------
x4o . |   4 |   4   0 | 3N  *  *
x . x |   4 |   2   2 |  * 6N  *
. o6x |   6 |   0   6 |  *  * 2N

snubbed forms: s4o6x, x4o6s, s4o6s'

s4s6x   (N → ∞)

demi( . . . ) | 12N |  1   2  1 |  1  1  2
--------------+-----+-----------+---------
demi( . . x ) |   2 | 6N   *  * |  0  1  1
sefa( s4s . ) |   2 |  * 12N  * |  1  0  1
sefa( . s6x ) |   2 |  *   * 6N |  0  1  1
--------------+-----+-----------+---------
      s4s .   |   4 |  0   4  0 | 3N  *  *
      . s6x   |   6 |  3   0  3 |  * 2N  *
sefa( s4s6x ) |   4 |  1   2  1 |  *  * 6N

starting figure: x4x6x

x4s6s   (N → ∞)

demi( . . . ) | 12N |  1  1   2 |  1  1  2
--------------+-----+-----------+---------
demi( x . . ) |   2 | 6N  *   * |  1  0  1
sefa( x4s . ) |   2 |  * 6N   * |  1  0  1
sefa( . s6s ) |   2 |  *  * 12N |  0  1  1
--------------+-----+-----------+---------
      x4s .   |   4 |  2  2   0 | 3N  *  *
      . s6s   |   6 |  0  0   6 |  * 2N  *
sefa( x4s6s ) |   4 |  1  1   2 |  *  * 6N

starting figure: x4x6x

x4s6x   (N → ∞)

demi( . . . ) | 12N |  1  1  1  1 |  1  1  1  1
--------------+-----+-------------+------------
demi( x . . ) |   2 | 6N  *  *  * |  1  1  0  0
demi( . . x ) |   2 |  * 6N  *  * |  1  0  1  0
sefa( x4s . ) |   2 |  *  * 6N  * |  0  1  0  1
sefa( . s4x ) |   2 |  *  *  * 6N |  0  0  1  1
--------------+-----+-------------+------------
demi( x . x ) |   4 |  2  2  0  0 | 3N  *  *  *
      x4s .   |   4 |  2  0  2  0 |  * 3N  *  *
      . s6x   |   6 |  0  3  0  3 |  *  * 2N  *
sefa( x4s6x ) |   4 |  0  0  2  2 |  *  *  * 3N

starting figure: x4x6x

xx3xx   (N → ∞)

. . . . | 12N |  1  1  1  1 |  1  1  1  1
--------+-----+-------------+------------
x . . . |   2 | 6N  *  *  * |  1  1  0  0
. x . . |   2 |  * 6N  *  * |  0  0  1  1
. . x . |   2 |  *  * 6N  * |  1  0  1  0
. . . x |   2 |  *  *  * 6N |  0  1  0  1
--------+-----+-------------+------------
x . x . |   4 |  2  0  2  0 | 3N  *  *  *
x . . x |   4 |  2  0  0  2 |  * 3N  *  *
. x3x . |   6 |  0  3  3  0 |  *  * 2N  *
. x . x |   4 |  0  2  0  2 |  *  *  * 3N

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