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This non-compact hyperbolic tesselation blends out the horocells squat from either its pre-images, thereby providing a double cover by the respective remainder regions. It still uses tosquats in the sense of an infinite horohedron as one of its cell types.

Its toroidal vertex figure in fact is just the set-theoretic subtraction of qo4oq&#k from qxo4oxq&#xt.

Incidence matrix

(N,M → ∞)

NM |  8  8 |  24   8  8 |   8  8 8
---+-------+------------+---------
 2 | 4N  * |   2   2  2 |   1  2 3  acc. to verf's pol. vert.
 2 |  * 4N |   4   0  0 |   2  2 0  acc. to verf's equ. vert.
---+-------+------------+---------
 3 |  1  2 | 8NM   *  * |   1  1 0
 4 |  4  0 |   * 2NM  * |   0  1 1
 8 |  8  0 |   *   * NM |   0  0 2
---+-------+------------+---------
 4 |  2  4 |   4   0  0 | 2NM  *  *  tet
 8 |  8  8 |   8   2  0 |   * NM  *  squap
4M | 6M  0 |   0   M  M |   *  * 2N  tosquat