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The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

"Jabulani polyhedron" is a term introduced here to refer to the polyhedron illustrated above which underlies the shape of the soccer ball used in the 2010 World Cup in South ...

The Gömböc (meaning "sphere-like" in Hungarian) is the name given to a class of convex solids which possess a unique stable and a unique unstable point of equilibrium. ...

The regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral ...

Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Pawley (1973) gave a set of restrictions ...

The volume of a solid body is the amount of "space" it occupies. Volume has units of length cubed (i.e., cm^3, m^3, in^3, etc.) For example, the volume of a box (cuboid) of ...

An incircle is an inscribed circle of a polygon, i.e., a circle that is tangent to each of the polygon's sides. The center I of the incircle is called the incenter, and the ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

A (general) dodecahedron is a polyhedron having 12 faces. Examples include the Bilinski dodecahedron, decagonal prism, elongated square dipyramid (Johnson solid J_(15)), ...