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Rubik's Clock is a puzzle consisting of 18 small clocks, 14 of which are independent, each of which may be set to any 12-hour position. There are therefore 12^(14) possible ...

Let k>=0 and n>=2 be integers. A SOMA, or more specifically a SOMA(k,n), is an n×n array A, whose entries are k-subsets of a kn-set Omega, such that each element of Omega ...

A symbol of the form {p,q,r,...} used to describe regular polygons, polyhedra, and their higher-dimensional counterparts. The symbol {p} denotes a regular polygon for integer ...

The Schroeder stairs, also called Schouten's staircase (Bool et al. 1982, p. 147), are an ambiguous figure that depicts two different staircases at the same time: one going ...

While early soccer balls were constructed in a number of ways, a fairly stadard 32-panel ball was designed by Danish national team goalkeeer Eigil Nielsen in 1962. This was ...

The maximal number of regions into which space can be divided by n planes is f(n)=1/6(n^3+5n+6) (Yaglom and Yaglom 1987, pp. 102-106). For n=1, 2, ..., these give the values ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In ...

In general, an unresolved nth root, commonly involving a radical symbol RadicalBox[x, n], is known as a surd. However, the term surd or "surd expression" (e.g., Hardy 1967, ...

A Taylor graph is a distance-regular graph with intersection array {k,mu,1;1,mu,k}. A Taylor graph with these parameters has 2(k+1) vertices. The crown graphs K_2 square ...