Acronym o4x4oP*a
Name family of (generally hyperbolic) order 2P square tilings
 
   ©
Vertex figure [42P] = qPq
Confer
more general:
x4oQo (Q not necessary even)  
Especially squat (P=2, euclidean)   x4o6o (P=3)   x4o8o (P=4)   x4o∞o (P→∞)  
External
links
wikipedia

Incidence matrix according to Dynkin symbol

x4o2Po   (P parametrisable, N → ∞)

. . . | 2N |  2P | 2P
------+----+-----+---
x . . |  2 | 2PN |  2
------+----+-----+---
x4o . |  4 |   4 | PN

o4x4oP*a   (P parametrisable, N → ∞)

. . .    | 4N |  2P |  P  P
---------+----+-----+------
. x .    |  2 | 4PN |  1  1
---------+----+-----+------
o4x .    |  4 |   4 | PN  *
. x4o    |  4 |   4 |  * PN

xØoPoØx   (P parametrisable, N → ∞)

. . . . | 2N |  P  P | 2P
--------+----+-------+---
x . . . |  2 | PN  * |  2
. . . x |  2 |  * PN |  2
--------+----+-------+---
x . . x |  4 |  2  2 | PN

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