It is known that the bottom of honeycombs are rhombic dodecahedra (part of).


The rhombic dodecahedron is one of the convex polyhedra that tessellates the space; see [Weisstein].

Tessellation of rhombic dodecahedra made by Antonio Zarauz (May 2018, NeoTrie VR).

In the video below we construct this cell of the honeycomb (which is flat on the top part) from a rhombic dodecahedron, using the tools of “middle point”, “intersection”, and “copy seal” in NeoTrie VR.

This video was made in the congress #17CEAMTHALES (, with Ana García López and Manuel Martínez Díaz, after a communication about their project “ALLAN POE O EL SECRETO DE LAS ABEJAS”.


Ibáñez R., El rombododecaedro estrellado: arte, abejas y puzzles, Cuaderno de Cultura Científica, 2014. Universidad del País Vasco.

Cangas D., Crespo D., Grazyna M., Rodríguez J. L., Zarauz A., CONSTRUYENDO Y APRENDIENDO GEOMETRÍA 3D EN REALIDAD VIRTUAL, Actas de XVII Congreso de Enseñanza y Aprendizaje de las Matemáticas. Almería 2018 (en prensa).

Weisstein, Eric W. “Space-Filling Polyhedron.” From MathWorld–A Wolfram Web Resource.