Acronym ...
Name hyperbolic o8o4x *b3x tesselation
Circumradius sqrt[1-sqrt(2)]/2 = 0.321797 i
Confer
uniform relative:
lamina-trunc( o8o4x *b3x )  

This hypercompact hyperbolic tesselation uses the order 8 triangle tiling and the order 8 square tiling in the sense of infinite bollohedra as some of its cell types.

As the order 8 square tiling here are hemi-choral (have same curvature resp. intersect the sphere of infinity orthogonally) those could be replaced by mirror images of the remainder each. Further the order 8 triangle tiling allow for an attaching layer of trips. The magic then would be, that the bollo-surface through their center points again happens to be hemi-choral, thus there too a second type of mirror can be placed. Accordingly we thus would produce the lamina-trunc( o8o4x *b3x ), built from sircoes and trips only.


Incidence matrix according to Dynkin symbol

o8o4x *b3x   (N,M,K → ∞)

. . .    . | 3NMK |     8     8 |    8    8    8 |   1  1   8
-----------+------+-------------+----------------+-----------
. . x    . |    2 | 12NMK     * |    2    1    0 |   1  0   2
. . .    x |    2 |     * 12NMK |    0    1    2 |   0  1   2
-----------+------+-------------+----------------+-----------
. o4x    . |    4 |     4     0 | 6NMK    *    * |   1  0   1
. . x    x |    4 |     2     2 |    * 6NMK    * |   0  0   2
. o . *b3x |    3 |     0     3 |    *    * 8NMK |   0  1   1
-----------+------+-------------+----------------+-----------
o8o4x    .     M |    4M     0 |   2M    0    0 | 3NK  *   *
o8o . *b3x    3K |     0   12K |    0    0   8K |   * NM   *
. o4x *b3x    24 |    24    24 |    6   12    8 |   *  * NMK

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