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In general, a tetrakis hexahedron is a non-regular icositetrahedron that can be constructed as a positive augmentation of a cube. Such a solid is also known as a ...

Given two positive integers n and k, the bipartite Kneser graph H(n,k) is the graph whose two bipartite sets of vertices represent the k-subsets and (n-k)-subsets of ...

Any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal grid (i.e., the honeycomb, illustrated above). Pappus refers to the ...

A graph G is distance transitive if its automorphism group is transitive on pairs of vertices at each pairwise distance in the graph. Distance-transitivity is a ...

A fusene is a simple planar 2-connected graph embedded in the plane with all vertices of degree 2 or 3, all bounded faces (not necessarily regular) hexagons, and all vertices ...

Percolation theory deals with fluid flow (or any other similar process) in random media. If the medium is a set of regular lattice points, then there are two main types of ...

Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

A septic graph is a regular graph of degree seven. The numbers of (not necessarily connected) simple septic graphs on n=8, 10, 12, ... vertices are 1, 5, 1547, 21609301, ...

A Taylor graph is a distance-regular graph with intersection array {k,mu,1;1,mu,k}. A Taylor graph with these parameters has 2(k+1) vertices. The crown graphs K_2 square ...

A 24-sided polygon. The regular icositetragon is constructible. For side length 1, the inradius r, circumradius R, and area A are given by r = 1/2(2+sqrt(2)+sqrt(3)+sqrt(6)) ...