Sesquitruncated rhombic dodecahedron

The decagonal-faced polyhedron is a near-miss Johnson solid. It has 6 squares, 8+24 triangles and 12 decagons which are not regular but equilateral.

It is one of the near-misses with only one edge length.

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



Alternatively it can be constructed as a truncation of chamfered cube.

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.