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A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, ...

The stability index Z^_(G) of a graph G is defined by Z^_=sum_(k=0)^(|_n/2_|)|c_(2k)|, where c_k is the kth coefficient of the characteristic polynomial and |_n_| denotes the ...

The Steinmetz solid is the solid common to two (or three) right circular cylinders of equal radii intersecting at right angles is called the Steinmetz solid. Two cylinders ...

A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given N ...

The tesseract is the hypercube in R^4, also called the 8-cell or octachoron. It has the Schläfli symbol {4,3,3}, and vertices (+/-1,+/-1,+/-1,+/-1). The figure above shows a ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

The Tilley graph is a polyhedral graph that arises in the investigation of Kempe chainsKempe Chain (Tilley 2018). It has 12 vertices, 29 edges, and 19 faces (one of which is ...

The truncated octahedron is the 14-faced Archimedean solid with faces 8{6}+6{4}. It is also the uniform polyhedron with Maeder index 8 (Maeder 1997), Wenninger index 7 ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...