Acronym ...
Name family of (generally hyperbolic) s4oPo4s tesselation
Especially hex (P=2, spherical)   octet (P=3, euclidean)   s4o4o4s (P=4, paracompact hyperbolean)  

This will be a non-Wythoffian but still uniform (generally non-compact hyperbolic for P>3) snub tesselation. – Its vertex figure is pxoPoxp&#xt.


Incidence matrix according to Dynkin symbol

s4oPo4s   (N,M → ∞)

demi( . . . . )    | 2NM |   2P   2P |  2P   6P |  2  2P  2P
-------------------+-----+-----------+----------+-----------
      s4o . .    & |   2 | 2PNM    * |   2    2 |  1   1   2
      s . . s      |   2 |    * 2PNM |   0    4 |  0   2   2
-------------------+-----+-----------+----------+-----------
sefa( s4oPo . )  & |   P |    P    0 | 4NM    * |  1   0   1
sefa( s4o . s )  & |   3 |    1    2 |   * 4PNM |  0   1   1
-------------------+-----+-----------+----------+-----------
      s4oPo .    &   2M |   PM    0 |  2M    0 | 2N   *   *
      s4o . s    &    4 |    2    4 |   0    4 |  * PNM   *
sefa( s4oPo4s )      2P |   2P   2P |   2   2P |  *   * 2NM

starting figure: x4oPo4x

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