©

 | t |  N  | t |N+1/2| 
-+---+-----+---+-----+- e
 |   |  t  |   |  t  | 
-+---+-----+---+-----+- e
 | t |N+1/2| t |  N  | 
 |   |     |   |     | 
-+---+-----+---+-----+- e
 |   |  t  |   |  t  | 
-+---+-----+---+-----+- e
 | t |  N  | t |N+1/2| 
 
 e   e     e   e     e 

where:
e = etrat
t = alternating trip column
N, N+1/2 = relative layer heights of pseudo cube column

Mecejide found this non-convex, non-overlapping honeycomb in spring of 2023. It can be considered as derived from etrat prisms (slabs), pairwise blending out their column of cubes, i.e. the final facets are just those etrats and the trips, coming in alternating wedge columns. Those pseudo cube columns clearly are situated at the vertex positions of a (scaled) squat.

There is a somewhat denser relative: when replacing the roles of the etrat prisms (slabs) by according retrat prisms, then an according retratip-blend could be obtained.

Incidence matrix

(N,M → ∞)

NM |  2  2   4 |   6  4  4 |  6 2
---+-----------+-----------+-----
 2 | NM  *   * |   2  2  0 |  2 2  pseudo cube lacings
 2 |  * NM   * |   0  2  2 |  3 1  pseudo cube base margins
 2 |  *  * 2NM |   2  0  1 |  2 1  wedge lacings
---+-----------+-----------+-----
 3 |  1  0   2 | 2NM  *  * |  1 1
 4 |  2  2   0 |   * NM  * |  1 1
 4 |  0  2   2 |   *  * NM |  2 0
---+-----------+-----------+-----
 6 |  2  3   4 |   2  1  2 | NM *  trip
2M | 2M  M  2M |  2M  M  0 |  * N  etrat