The hexagons can be made equilateral, or regular depending on the shape of the rhombi.

It can be seen as constructed from a rhombic dodecahedron elongated by a square prism.

Along with the rhombic dodecahedron, it is a space-filling polyhedron, one of the five types of parallelohedron identified by Evgraf Fedorov that tile space face-to-face by translations.

The expanded dodecahedra can be distorted into cubic volumes, with the honeycomb as a half-offset stacking of cubes.

It can also be made concave by adjusting the 8 corners downward by the same amount as the centers are moved up.