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

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.

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
```