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A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

As defined by Gray (1997, p. 201), Viviani's curve, sometimes also called Viviani's window, is the space curve giving the intersection of the cylinder of radius a and center ...

The 24-cell is a finite regular four-dimensional polytope with Schläfli symbol {3,4,3}. It is also known as the hyperdiamond or icositetrachoron, and is composed of 24 ...

The cross polytope beta_n is the regular polytope in n dimensions corresponding to the convex hull of the points formed by permuting the coordinates (+/-1, 0, 0, ..., 0). A ...

Applying the stellation process to the icosahedron gives 20+30+60+20+60+120+12+30+60+60 cells of 11 different shapes and sizes (including the icosahedron itself). The ...

Sangaku problems, often written "san gaku," are geometric problems of the type found on devotional mathematical wooden tablets ("sangaku") which were hung under the roofs of ...

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.