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The 57-cell, also called the pentacontaheptachoron, is a regular self-dual locally projective polytope with 57 hemidodecahedral facets described by Coxeter (1982) and also ...

The term discrete percolation is used to describe models of percolation theory whose media are discrete sets like sets of regular lattice points (e.g., bond percolation and ...

Guy's conjecture, which has not yet been proven or disproven, states that the graph crossing number for a complete graph K_n is ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...

Given a regular tetrahedron of unit volume, consider the lengths of line segments connecting pairs of points picked at random inside the tetrahedron. The distribution of ...

An n-trapezohedron, also called an antidipyramid, antibipyramid, or deltohedron (not to be confused with a deltahedron), is a solid composed of interleaved symmetric ...

A graph is a forbidden (vertex-)induced subgraph if its presence as a vertex-induced subgraph of a given graph means it is not a member of some family of graphs. For example, ...

Two graphs are homeomorphic if there is a graph isomorphism from some graph subdivision of one to some subdivision of the other.