Acronym  ... 
Name  hyperbolic order 4 pentagonal tiling 
©  
Circumradius  sqrt[(1+sqrt(5))]/2 = 0.899454 i 
Vertex figure  [5^{4}] 
Dual  x4o5o 
Confer 

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Note that x6o4o allows for a consistent halving of hexagons and x8o4o allows for a consistent quartering of octagons, such as to derive a combinatorical variants of x5o4o. Even so, here are the pentagons regular, while there those would have different edge lengths (being calculated there) but still corner angles of 90° throughout.
Incidence matrix according to Dynkin symbol
o4o5x (N → ∞) . . .  5N  4  4 +++ . . x  2  10N  2 +++ . o5x  5  5  4N
o5x5o (N → ∞) . . .  5N  4  2 2 +++ . x .  2  10N  1 1 +++ o5x .  5  5  2N * . x5o  5  5  * 2N
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