Acronym	...
Name	hyperbolic alternated small prismated order-4 square tiling honeycomb
Circumradius	1/sqrt[-sqrt(8)] = 0.594604 i
Vertex figure	qxo4oxq&#xt = ©
Confer	more general: s4oPo4s   uniform relative: s4o4o4s + x4x4o4o4*a blend
External links

This non-Wythoffian but still uniform non-compact hyperbolic tesselation uses the squat in the sense of an infinite horohedron for some of its cells. – Its vertex figure is qxo4oxq&#xt.

Incidence matrix according to Dynkin symbol

s4o4o4s   (N,M → ∞)

demi( . . . . )    | NM |   8   8 |   8  24 |  2   8  8
-------------------+----+---------+---------+----------
      s4o . .    & |  2 | 4NM   * |   2   2 |  1   1  2
      s . . s      |  2 |   * 4NM |   0   4 |  0   2  2
-------------------+----+---------+---------+----------
sefa( s4o4o . )  & |  4 |   4   0 | 2NM   * |  1   0  1
sefa( s4o . s )  & |  3 |   1   2 |   * 8NM |  0   1  1
-------------------+----+---------+---------+----------
      s4o4o .    & ♦  M |  2M   0 |   M   0 | 2N   *  *
      s4o . s    & ♦  4 |   2   4 |   0   4 |  * 2NM  *
sefa( s4o4o4s )    ♦  8 |   8   8 |   2   8 |  *   * NM

starting figure: x4o4o4x