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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.

The collapsoids are a class of non-convex collapsible polyhedra. They can be constructed by replacing each edge of a dodecahedron or icosahedron by the diagonal of a pyramid ...

Construct a 5×5×5 cube from thirteen 1×2×4 blocks, one 2×2×2 block, one 1×2×2, and three 1×1×3 blocks.