Acronym ...
Name hyperbolic truncated infinite-order square tiling
 
  ©
Circumradius sqrt[-(1+sqrt(2))/2] = 1.098684 i
Vertex figure [82,∞]
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Incidence matrix according to Dynkin symbol

x4x∞o   (N,M → ∞)

. . . | 4NM |   1   2 |  2  1
------+-----+---------+------
x . . |   2 | 2NM   * |  2  0
. x . |   2 |   * 4NM |  1  1
------+-----+---------+------
x4x . |   8 |   4   4 | NM  *
. x8o |   M |   0   M |  * 4N

x4x4x∞*a   (N,M → ∞)

. . .    | 8NM |   1   1   1 |  1  1  1
---------+-----+-------------+---------
x . .    |   2 | 4NM   *   * |  1  1  0
. x .    |   2 |   * 4NM   * |  1  0  1
. . x    |   2 |   *   * 4NM |  0  1  1
---------+-----+-------------+---------
x4x .    |   8 |   4   4   0 | NM  *  *
x . x∞*a |  2M |   M   0   M |  * 4N  *
. x4x    |   8 |   0   4   4 |  *  * NM

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