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The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

The Perkel graph is a weakly regular graph on 57 vertices and 171 edges, shown above in several embeddings. It is the unique distance-regular graph with intersection array ...

The truncated icosahedral graph is the cubic Archimedean graph on 60 nodes and 90 edges that is the skeleton of the truncated icosahedron. It is sometimes known as the ...

The truncated tetrahedral graph is the cubic Archimedean graph on 12 nodes and 18 edges that is the skeleton of the truncated tetrahedron. It is implemented in the Wolfram ...

A vertex-transitive graph, also sometimes called a node symmetric graph (Chiang and Chen 1995), is a graph such that every pair of vertices is equivalent under some element ...

The smallest composite squarefree number (2·3), and the third triangular number (3(3+1)/2). It is the also smallest perfect number, since 6=1+2+3. The number 6 arises in ...

Intuitively, a model of d-dimensional percolation theory is said to be a Bernoulli model if the open/closed status of an area is completely random. In particular, it makes ...

In continuum percolation theory, the Boolean-Poisson model is a Boolean model driven by a stationary point process X which is a Poisson process. The Boolean-Poisson model is ...

A graph in which each graph edge is replaced by a directed graph edge, also called a digraph. A directed graph having no multiple edges or loops (corresponding to a binary ...

First-passage percolation is a time-dependent generalization of discrete Bernoulli percolation in which each graph edge e of Z^d is assigned a nonnegative random variable ...