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Four or more points P_1, P_2, P_3, P_4, ... which lie on a circle C are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a ...

The hat polykite is an aperiodic monotile discovered by Smith et al. (2023). It is illustrated above in an aperiodic tiling (Smith et al. 2023).

A polyiamond composed of six equilateral triangles. The 12 hexiamonds are illustrated above. They are given the names bar, crook, crown, sphinx, snake, yacht, chevron, ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

Let L denote the partition lattice of the set {1,2,...,n}. The maximum element of L is M={{1,2,...,n}} (1) and the minimum element is m={{1},{2},...,{n}}. (2) Let Z_n denote ...

An N-cluster is a point lattice configuration in which the distance between every pair of points is an integer, no three points are collinear, and no four points are ...

A polyabolo is an analog of the polyomino composed of n isosceles right triangles joined along edges of the same length. Polyaboloes are sometimes also called polytans ...

A polyare is a polyform formed from a polyomino by removing of half of each square such that at least half of the original join between squares is retained. The first few ...

A polyform of 30-60-90 triangles. The name was coined by Ed Pegg, Jr. because of the 30-60-90 triangle's use in mechanical drawing and drafting. The Eternity puzzle is based ...

A plane figure or solid compound consisting of multiple connected copies of a given base shape. For example, affixing n equal squares gives an n-polyomino, while affixing n ...