Acronym	peat
Name	hyperbolic order 4 pentagonal tiling
	©
Circumradius	sqrt[-(1+sqrt(5))]/2 = 0.899454 i
Vertex figure	[54]
Dual	x4o5o
Confer	more general: xPo3o...o3o4o   combinatorical relatives: {6}-halved x6o4o   {8}-quartered x8o4o   general polytopal classes: regular   noble polytopes
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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 mod-wrap {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.

A further realization of a modwraps thereof is the Leonardo polyhedron of type {5,4;13}.

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