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A packing of polyhedron in three-dimensional space. A polyhedron which can pack with no holes or gaps is said to be a space-filling polyhedron. Betke and Henk (2000) present ...

The 60-faced dual polyhedron of the truncated dodecahedron A_(10) (Holden 1971, p. 55) and Wenninger dual W_(10). Wenninger (1989, p. 46) calls the small triambic icosahedron ...

The tritetrahedron, also called the "boat polyhedron," is the name given in this work to the concave (non-regular) octahedron formed by joining three regular tetrahedra ...

The truncated pentakis dodecahedron is a polyhedron on 180 vertices, 270 edges, and 92 faces. Its canonical polyhedron has edges of three different lengths and faces ...

The truncated square pyramid is a special case of a pyramidal frustum for a square pyramid. Let the base and top side lengths of the truncated pyramid be a and b, and let the ...

The truncated triangular prism is an undecagon obtained by truncation of a triangular prism. It has 18 vertices, 27 edges, and 11 faces. As a canonical polyhedron with unit ...

Let M be the midpoint of the arc AMB. Pick C at random and pick D such that MD_|_AC (where _|_ denotes perpendicular). Then AD=DC+BC.

The bend of a circle C mutually tangent to three other circles is defined as the signed curvature of C. If the contacts are all external, the signs of the bends of all four ...

The three planes determined by the edges of a trihedron and the internal bisectors of the respectively opposite faces are coaxal, and the common line of these planes is ...

A plane making equal angles with the three edges of a trihedron.