In geometry, the bilunabirotunda is a Johnson solid with faces of 8 equilateral triangles, 2 squares, and 4 regular pentagons.
The bilunabirotunda is named from the prefix lune, meaning a figure featuring two triangles adjacent to opposite sides of a square. Therefore, the faces of a bilunabirotunda possess 8 equilateral triangles, 2 squares, and 4 regular pentagons as it faces. It is one of the Johnson solids—a convex polyhedron in which all of the faces are regular polygon—enumerated as 91st Johnson solid .
The surface area of a bilunabirotunda with edge length is:
and the volume of a bilunabirotunda is:
The bilunabirotunda is an elementary polyhedron: it cannot be separated by a plane into two small regular-faced polyhedra. One way to construct a bilunabirotunda is by attaching two wedges and two tridiminished icosahedrons.
For edge length is by union of the orbits of the coordinates, the bilunabirotunda is:
under the group action (of order 8) generated by reflections about coordinate planes.
discusses the bilunabirotunda as a shape that could be used in architecture.
Six bilunabirotundae can be augmented around a cube with pyritohedral symmetry. B. M. Stewart labeled this six-bilunabirotunda model as 6J<sub>91</sub>(P<sub>4</sub>). Such clusters combine with regular dodecahedra to form a space-filling honeycomb.