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There are a number of attractive polyhedron compounds consisting of five cubes. The first of these (left figures) consists of the arrangement of five cubes in the polyhedron ...

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

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 ...

Cubic graphs, also called trivalent graphs, are graphs all of whose nodes have degree 3 (i.e., 3-regular graphs). Cubic graphs on n nodes exists only for even n (Harary 1994, ...

A cubic polyhedral graph is a graph that is both cubic and polyhedral. The numbers of cubical polyhedral graphs on n=2, 4, ... nodes are 0, 1, 1, 2, 5, 14, 50, 233, 1249, ... ...

A cubic semisymmetric graph is a graph that is both cubic (i.e., regular of degree 3) and semisymmetric (i.e., edge- but not vertex-transitive). The four smallest cubic ...

An algebraic surface of order 3. Schläfli and Cayley classified the singular cubic surfaces. On the general cubic, there exists a curious geometrical structure called double ...

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...

Define a cell in R^1 as an open interval or a point. A cell in R^(k+1) then has one of two forms, {(x,y):x in C, and f(x)<y<g(x)} (1) or {(x,y):x in C, and y=f(x)}, (2) where ...