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Consider a two-dimensional tessellation with q regular p-gons at each polygon vertex. In the plane, (1-2/p)pi=(2pi)/q (1) 1/p+1/q=1/2, (2) so (p-2)(q-2)=4 (3) (Ball and ...

A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes (n dimensions) is called a tessellation. Tessellations can be specified using a ...

A block diagonal matrix, also called a diagonal block matrix, is a square diagonal matrix in which the diagonal elements are square matrices of any size (possibly even 1×1), ...

A figurate number which is constructed as an octahedral number with a square pyramid removed from each of the six graph vertices, TO_n = O_(3n-2)-6P_(n-1)^((4)) (1) = ...

A hexagonal grid is a grid formed by a tessellation of regular hexagons. Boards made of hexagonal grids are often found in strategy and role-playing games because of the lack ...

The straight polyomino of order n is the n-polyomino in which all squares are placed along a line.

A bundle or fiber bundle is trivial if it is isomorphic to the cross product of the base space and a fiber.

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

With three cuts, dissect an equilateral triangle into a square. The problem was first proposed by Dudeney in 1902, and subsequently discussed in Dudeney (1958), and Gardner ...

A board is a subset of the polygons determined by a number of (usually regularly spaced and oriented) lines. These polygons form the spaces on which "pieces" can be placed ...