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The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

The icosahedral graph is the Platonic graph whose nodes have the connectivity of the regular icosahedron, as well as the great dodecahedron, great icosahedron Jessen's ...

The small stellated dodecahedron is the Kepler-Poinsot polyhedra whose dual polyhedron is the great dodecahedron. It is also uniform polyhedron with Maeder index 34 (Maeder ...

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 ...

In general, a tetrahedron is a polyhedron with four sides. If all faces are congruent, the tetrahedron is known as an isosceles tetrahedron. If all faces are congruent to an ...

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...