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Define a valid "coloring" to occur when no two faces with a common edge share the same color. Given two colors, there is a single way to color an octahedron (Ball and Coxeter ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

Sphere tetrahedron picking is the selection of quadruples of of points corresponding to vertices of a tetrahedron with vertices on the surface of a sphere. n random ...

The ditrigonal icosidodecahedral graph is the skeleton of the cube 5-compound, ditrigonal dodecadodecahedron, great ditrigonalIcosidodecahedron, and small ditrigonal ...

The dodecadodecahedral graph is the skeleton of the dodecadodecahedron, great dodecahemicosahedron, and small dodecahemicosahedron. It is illustrated above in several ...

Polynomials b_n(x) which form a Sheffer sequence with g(t) = t/(e^t-1) (1) f(t) = e^t-1, (2) giving generating function sum_(k=0)^infty(b_k(x))/(k!)t^k=(t(t+1)^x)/(ln(1+t)). ...

A type of abstract space which occurs in spline and rational function approximations. The Besov space B_(p,q)^alpha is a complete quasinormed space which is a Banach space ...

The Borwein integrals are the class of definite integrals defined by I_n=1/piint_0^inftyx^(-(n+1)/2)product_(k=1,3,...)^nsin(x/k)dx for odd n. The integrals are curious ...

Each Cartan matrix determines a unique semisimple complex Lie algebra via the Chevalley-Serre, sometimes called simply the "Serre relations." That is, if (A_(ij)) is a k×k ...

A generalization of Grassmann coordinates to m-D algebraic varieties of degree d in P^n, where P^n is an n-dimensional projective space. To define the Chow coordinates, take ...