This regular hypercompact hyperbolic tesselation uses the order 4 pentagonal tiling in the sense of an infinite bollohedron as its only cell type.

Incidence matrix according to Dynkin symbol

o3o4o5x   (N,M → ∞)

. . . . | 5NM ♦    8 |   12 |  6
--------+-----+------+------+---
. . . x |   2 | 20NM |    3 |  3
--------+-----+------+------+---
. . o5x |   5 |    5 | 12NM |  2
--------+-----+------+------+---
. o4o5x ♦  5M |  10M |   4M | 6N