Acronym ...
Name hyperbolic rhombisquareapeirogonal tiling
 
 ©
Circumradius sqrt[-1-2 sqrt(2)]/2 = 0.978318 i
Vertex figure [43,∞]
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Incidence matrix according to Dynkin symbol

x4o∞x   (N,M → ∞)

. . . | 4NM |   2   2 |  1   2  1
------+-----+---------+----------
x . . |   2 | 4NM   * |  1   1  0
. . x |   2 |   * 4NM |  0   1  1
------+-----+---------+----------
x4o . |   4 |   4   0 | NM   *  *
x . x |   4 |   2   2 |  * 2NM  *
. o∞x |   M |   0   M |  *   * 4N

xx∞xx   (N,M → ∞)

. . . . | 4NM |   1   1   1   1 |  1  1  1  1
--------+-----+-----------------+------------
x . . . |   2 | 2NM   *   *   * |  1  1  0  0
. x . . |   2 |   * 2NM   *   * |  0  0  1  1
. . x . |   2 |   *   * 2NM   * |  1  0  1  0
. . . x |   2 |   *   *   * 2NM |  0  1  0  1
--------+-----+-----------------+------------
x . x . |   4 |   2   0   2   0 | NM  *  *  *
x . . x |   4 |   2   0   0   2 |  * NM  *  *
. x∞x . |  2M |   0   M   M   0 |  *  * 2N  *
. x . x |   4 |   0   2   0   2 |  *  *  * NM

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