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.

[1] It is one of the Johnson solids—a convex polyhedron in which all of the faces are regular polygon—enumerated as 91st Johnson solid

[2] It is known as the elementary polyhedron, meaning that it cannot be separated by a plane into two small regular-faced polyhedra.

[3] The surface area of a bilunabirotunda with edge length

and the volume of a bilunabirotunda is:[1]

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.

[4] Reynolds (2004) discusses the bilunabirotunda as a shape that could be used in architecture.

[5] Six bilunabirotundae can be augmented around a cube with pyritohedral symmetry.

B. M. Stewart labeled this six-bilunabirotunda model as 6J91(P4).

[6] Such clusters combine with regular dodecahedra to form a space-filling honeycomb.