Acronym  peat 
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 though, here are the pentagons regular, while there those would have different edge lengths (being calculated there) but still corner angles of 90° throughout.
Seen as an abstract polytope peat allows for the modwrap {5,4}_{6} (where the index just denotes the size of the corresponding Petrie polygon), realizable when half the pentagons become pentagrams, which then happens to be nothing but did.
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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