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The regular dodecahedron, often simply called "the" dodecahedron, is the Platonic solid composed of 20 polyhedron vertices, 30 polyhedron edges, and 12 pentagonal faces, ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

Consider a two-dimensional tessellation with q regular p-gons at each polygon vertex. In the plane, (1-2/p)pi=(2pi)/q (1) 1/p+1/q=1/2, (2) so (p-2)(q-2)=4 (3) (Ball and ...

Regular tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround each polygon vertex are called semiregular ...

A regular graph that is edge-transitive but not vertex-transitive is called a semisymmetric graph (Marušič and Potočnik 2001). In contrast, any graph that is both ...

The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...

The Shrikhande graph is a strongly regular graph on 16 nodes. It is cospectral with the rook graph L_(4,4), so neither of the two is determined by spectrum. The Shrikhande ...

The Suetake graph is a weakly regular Hamiltonian graph on 231 vertices with parameters (nu,k,lambda,mu)=(72,(12),(0),(0,4)). It is distance-regular with intersection array ...

The Suzuki graph is an edge-transitive strongly regular graph on 1782 vertices with parameters (nu,k,lambda,mu)=(1782,416,100,96) and automorphism group Suz.2. It is an ...

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 ...