Parallelohedron

Five types of parallelohedron

Cube

Hexagonal prism

Rhombic dodecahedron

Elongated dodecahedron

Truncated octahedron

In geometry, a parallelohedron is a polyhedron that can be translated without rotations in 3-dimensional Euclidean space to fill space with a honeycomb in which all copies of the polyhedron meet face-to-face. There are five types of parallelohedron, first identified by Evgraf Fedorov in 1885 in his studies of crystallographic systems: the cube, hexagonal prism, rhombic dodecahedron, elongated dodecahedron, and truncated octahedron.[1]

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