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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 ...

The Tilley graph is a polyhedral graph that arises in the investigation of Kempe chainsKempe Chain (Tilley 2018). It has 12 vertices, 29 edges, and 19 faces (one of which is ...

Three types of n×n matrices can be obtained by writing Pascal's triangle as a lower triangular matrix and truncating appropriately: a symmetric matrix S_n with (S)_(ij)=(i+j; ...

Given a symmetric positive definite matrix A, the Cholesky decomposition is an upper triangular matrix U with strictly positive diagonal entries such that A=U^(T)U. Cholesky ...

A Lie group is called semisimple if its Lie algebra is semisimple. For example, the special linear group SL(n) and special orthogonal group SO(n) (over R or C) are ...

Polysticks, sometimes also known as polyedges, are polyforms obtained from the edges of a regular grid. Square polysticks are polyforms obtained from the edges of a regular ...

A Möbius ladder, sometimes called a Möbius wheel (Jakobson and Rivin 1999), of order n is a simple graph obtained by introducing a twist in a prism graph of order n that is ...

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 ...