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A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., to an n-gon for n an arbitrary positive integer. The above diagrams ...

Baxter's four-coloring constant for a triangular lattice is given by C^2 = product_(j=1)^(infty)((3j-1)^2)/((3j-2)(3j)) (1) = 3/(4pi^2)Gamma^3(1/3) (2) = 1.46099848... (3) ...

Polypons are polyforms obtained from dividing a regular triangular grid into 30-30-120 triangles, illustrated above. The numbers of polypons with n=1, 2, ... components are ...

In statistics, a trial is a single performance of well-defined experiment (Papoulis 1984, p. 25), such as the flipping of a coin, the generation of a random number, the ...

A pyramid with a hexagonal base. The edge length of a hexagonal pyramid of height h is a special case of the formula for a regular n-gonal pyramid with n=6, given by ...

A closed box composed of three pairs of rectangular faces placed opposite each other and joined at right angles to each other, also known as a rectangular parallelepiped. The ...

A cork plug is a three-dimensional solid that can stopper a square, triangular, or circular hole. There is an infinite family of such shapes. The shape with smallest volume ...

There are four strongly regular graphs with parameters (nu,k,lambda,mu)=(28,12,6,4), one of them being the triangular graph of order 8. The other three such graphs are known ...

The dual of a regular tessellation is formed by taking the center of each polygon as a vertex and joining the centers of adjacent polygons. The triangular and hexagonal ...

A Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. Any nilpotent Lie algebra is also solvable. The basic example of a nilpotent Lie ...