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Mecejide found this non-convex, self-overlapping honeycomb in spring of 2023. It can be considered as derived from retrat prisms (slabs), pairwise blending out their column of cubes, i.e. the final facets are just those retrats 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 sparser relative: when replacing the roles of the retrat prisms (slabs) by according etrat prisms, then an according etratip-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  retrat