Sesquitruncated rhombic dodecahedron

The decagonal-faced octahedral polyhedron is a near-miss Johnson solid. Its faces are 12 snub triangles, 4 triangles, and 12 rectangular-symmetric equilateral decagons. It is one of the near-miss Johnson solids with only one edge length. Nevertheless, it is considered a near-miss because the internal angles of the decagons are not identical.

To construct it, one needs to inscribe an equilateral decagon in each face of the rhombic dodecahedron and fill all the remaining gaps with triangles and squares.



If all rhombic dodecahedra in the rhombic dodecahedral honeycomb are replaced with these solids, the remaining gaps can be filled with cuboctahedra and two types of regular tetrahedra forming an equilateral near-miss CRF honeycomb.