Acronym ...
Name hyperbolic tetragonal-horocyclic tiling,
hyperbolic square-apeirogon tiling
 
Circumradius 1/sqrt(-2) = 0.707107 i
Vertex figure [(4,∞)2]
Confer
topological relatives:
x3xØx∞xØ*a3*c   o4o6x  
External
links
wikipedia  

Having the same curvature (resp. circumradius) as o4o6x, both having even numbered polygons only and both having tetravalent vertex figures with inversional symmetry, these allow for resp. alternating layers, i.e. an corresponding laminat. That one then would have the vertex configuration [4,6,6,∞] and could be described by the generalized Dynkin diagram x3xØx∞xØ*a3*c.


Incidence matrix according to Dynkin symbol

o4x∞o   (N,M → ∞)

. . . | 2NM |   4 |  2  2
------+-----+-----+------
. x . |   2 | 4NM |  1  1
------+-----+-----+------
o4x . |   4 |   4 | NM  *
. x∞o |   M |   M |  * 4N

x∞o∞x   (N,M → ∞)

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

x∞x4o4*a   (N,M → ∞)

. . .    | 4NM |   2   2 |  2  1  1
---------+-----+---------+---------
x . .    |   2 | 4NM   * |  1  1  0
. x .    |   2 |   * 4NM |  1  0  1
---------+-----+---------+---------
x∞x .    |  2M |   M   M | 4N  *  *
x . o4*a |   4 |   4   0 |  * MN  *
. x4o    |   4 |   0   4 |  *  * MN

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