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There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...

The smallest cubic graphs with graph crossing number CN(G)=n have been termed "crossing number graphs" or n-crossing graphs by Pegg and Exoo (2009). The n-crossing graphs are ...

As defined in this work, a wheel graph W_n of order n, sometimes simply called an n-wheel (Harary 1994, p. 46; Pemmaraju and Skiena 2003, p. 248; Tutte 2005, p. 78), is a ...

A central angle is an angle ∠AOC with endpoints A and C located on a circle's circumference and vertex O located at the circle's center (Rhoad et al. 1984, p. 420). A central ...

The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

Draw a circle that cuts three given circles perpendicularly. The solution is known as the radical circle of the given three circles. If it lies outside the three circles, ...

A spheric section is the curve formed by the intersection of a plane with a sphere. Excluding the degenerate cases of the plane tangent to the sphere or the plane not ...

The center of the Taylor circle. It has triangle center function alpha_(389)=cosA-cos(2A)cos(B-C) and is Kimberling center X_(389), which is the center of the Spieker circle ...

Every continuous map f:S^n->R^n must identify a pair of antipodal points.

A half-plane is a planar region consisting of all points on one side of an infinite straight line, and no points on the other side. If the points on the line are included, ...