In geometry, the bilunabirotunda is a Johnson solid with faces of 8 equilateral triangles, 2 squares, and 4 regular pentagons.

Properties

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 J_{91}. It is known as the elementary polyhedron, meaning that it cannot be separated by a plane into two small regular-faced polyhedra. The surface area of a bilunabirotunda with edge length a is: and the volume of a bilunabirotunda is:

Cartesian coordinates

One way to construct a bilunabirotunda with edge length is by union of the orbits of the coordinates under the group's action (of order 8) generated by reflections about coordinate planes.

Applications

discusses the bilunabirotunda as a shape that could be used in architecture.

Related polyhedra and honeycombs

Six bilunabirotundae can be augmented around a cube with pyritohedral symmetry. B. M. Stewart labeled this six-bilunabirotunda model as 6J91(P4). Such clusters combine with regular dodecahedra to form a space-filling honeycomb.