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The associahedron is the n-dimensional generalization of the pentagon. It was discovered by Stasheff in 1963 and it is also known as the Stasheff polytope. The number of ...

A set in Euclidean space R^d is convex set if it contains all the line segments connecting any pair of its points. If the set does not contain all the line segments, it is ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...

The great dodecahemidodecahedron is the uniform polyhedron with Maeder index 70 (Maeder 1997), Wenninger index 107 (Wenninger 1989), Coxeter index 86 (Coxeter et al. 1954), ...

The great icosihemidodecahedron is the uniform polyhedron with Maeder index 71 (Maeder 1997), Wenninger index 106 (Wenninger 1989), Coxeter index 85 (Coxeter et al. 1954), ...

In the field of functional analysis, the Krein-Milman theorem is a result which characterizes all (nonempty) compact convex subsets K of "sufficiently nice" topological ...

The Lemoine hexagon is a cyclic hexagon with vertices given by the six concyclic intersections of the parallels of a reference triangle through its symmedian point K. The ...

If one looks inside a flat origami without unfolding it, one sees a zigzagged profile, determined by an alternation of "mountain-creases" and "valley-creases." The numbers of ...

The octahemioctahedron, also called the octatetrahedron, is the uniform polyhedron with Maeder index 3 (Maeder 1997), Wenninger index 68 (Wenninger 1989), Coxeter index 37 ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...