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Bilunabirotunda

91st Johnson solid (14 faces) From Wikipedia, the free encyclopedia

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

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3D model of a bilunabirotunda
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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.[1] It is one of the Johnson solidsa convex polyhedron in which all of the faces are regular polygonenumerated as 91st Johnson solid .[2]

The surface area of a bilunabirotunda with edge length is:[1] and the volume of a bilunabirotunda is:[1]

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Construction

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The bilunabirotunda is an elementary polyhedron: it cannot be separated by a plane into two small regular-faced polyhedra.[3] One way to construct a bilunabirotunda is by attaching two wedges and two tridiminished icosahedrons.[4]

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.[5]

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Applications

Reynolds (2004) discusses the bilunabirotunda as a shape that could be used in architecture.[6]

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Six bilunabirotundae around a cube

Six bilunabirotundae can be augmented around a cube with pyritohedral symmetry. B. M. Stewart labeled this six-bilunabirotunda model as 6J91(P4).[7] Such clusters combine with regular dodecahedra to form a space-filling honeycomb.

References

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