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A number of attractive tetrahedron 5-compounds can be constructed. The first (left figures) is one of the icosahedron stellations in which the 5×4 vertices of the tetrahedra ...

A term invented by B. Grünbaum in an attempt to promote concrete and precise polyhedron terminology. The word "coptic" derives from the Greek for "to cut," and acoptic ...

The difference between the sum of face angles A_i at a polyhedron vertex of a polyhedron and 2pi, delta=2pi-sum_(i)A_i.

Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

An augmented polyhedron is a polyhedron formed from a base polyhedron via the augmentation operation on one or more of its faces. Augmentation is implemented under the ...

A construction for the rhombic dodecahedron.

Two cones placed base-to-base. The bicone with base radius r and half-height h has surface area and volume S = 2pirsqrt(r^2+h^2) (1) V = 2/3pir^2h. (2) The centroid is at the ...

Two adjoined cupolas.

Two adjoined rotundas.

A canonical brick is a 1×2×4 cuboid.