| Bilunabirotunda | |
|---|---|
 | |
| Type | Johnson J90 –J91 –J92 |
| Faces | 8triangles 2squares 4pentagons |
| Edges | 26 |
| Vertices | 14 |
| Vertex configuration | 4(3.52) 8(3.4.3.5) 2(3.5.3.5) |
| Symmetry group | |
| Properties | convex,elementary |
| Net | |
 | |
Ingeometry, thebilunabirotunda is aJohnson solid with faces of 8 equilateral triangles, 2 squares, and 4 regular pentagons.
The bilunabirotunda is named from the prefixlune, meaning a figure featuring two triangles adjacent to opposite sides of a square. Therefore, the faces of a bilunabirotunda possess 8equilateral triangles, 2squares, and 4regular pentagons as it faces.[1] It is one of theJohnson solids—aconvex polyhedron in which all of the faces areregular polygon—enumerated as 91st Johnson solid.[2]
The surface area of a bilunabirotunda with edge length is:[1]and the volume of a bilunabirotunda is:[1]
The bilunabirotunda is anelementary polyhedron: it cannot be separated by a plane into two small regular-faced polyhedra.[3] One way to construct a bilunabirotunda is by attaching twowedges and twotridiminished icosahedrons.[4]
For edge length is by union of the orbits of thecoordinates, the bilunabirotunda is:under the group action (of order 8) generated by reflections about coordinate planes.[5]
Reynolds (2004) discusses the bilunabirotunda as a shape that could be used in architecture.[6]
Six bilunabirotundae can be augmented around a cube withpyritohedral symmetry.B. M. Stewart labeled this six-bilunabirotunda model as 6J91(P4).[7] Such clusters combine with regulardodecahedra to form a space-filling honeycomb.