This regular hypercompact hyperbolic tesselation uses the order 5 pentagonal tiling in the sense of an infinite bollohedron as its only cell type.

Incidence matrix according to Dynkin symbol

o3o5o5x   (N,M → ∞)

. . . . | NM ♦   20 |  30 | 12
--------+----+------+-----+---
. . . x |  2 | 10NM |   3 |  3
--------+----+------+-----+---
. . o5x |  5 |    5 | 6NM |  2
--------+----+------+-----+---
. o5o5x ♦ 2M |   5M |  2M | 6N