Acronym ...
Name hyperbolic o3x:s3s4s honeycomb,
hyperbolic rectified x3o:s3s4s honeycomb
Circumradius ... i
Confer
more general:
o3x:s3sPs  
uniform relative:
x3o:s3s4s   x3x:s3s4s  

Incidence matrix according to symbol extension

o3x:s3s4s = rect( x3o:s3s4s )   (N → ∞)

12N |   2   4   4 |   3  2  2   6  2 |  4 1 2
----+-------------+------------------+-------
  2 | 12N   *   * |   1  0  2   0  0 |  2 0 1  underneath tips of former lacing trigs of 3pyrs
  2 |   * 24N   * |   1  0  0   2  0 |  2 0 1  underneath base-vertex of former lacing trigs of 3pyrs
  2 |   *   * 24N |   0  1  0   1  1 |  1 1 1  underneath vertices of other trigs
----+-------------+------------------+-------
  3 |   1   2   0 | 12N  *  *   *  * |  2 0 0  rect of former lacing trigs of 3pyrs
  3 |   0   0   3 |   * 8N  *   *  * |  1 1 0  rect of former other trigs
  3 |   3   0   0 |   *  * 8N   *  * |  1 0 1  underneath tip of former 3-pyr
  3 |   0   2   1 |   *  *  * 24N  * |  1 0 1  underneath base-vertex of former 3-pyr
  4 |   0   0   4 |   *  *  *   * 6N |  0 1 1  underneath vertex of former oct
----+-------------+------------------+-------
  6 |   3   6   3 |   3  1  1   3  0 | 8N * *  oct
 12 |   0   0  24 |   0  8  0   0  6 |  * N *  co
 24 |  12  24  24 |   0  0  8  24  6 |  * * N  snic

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