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A regular local ring is a local ring R with maximal ideal m so that m can be generated with exactly d elements where d is the Krull dimension of the ring R. Equivalently, R ...

A k-regular simple graph G on nu nodes is strongly k-regular if there exist positive integers k, lambda, and mu such that every vertex has k neighbors (i.e., the graph is a ...

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 ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...

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, ...

The regular icosahedron (often simply called "the" icosahedron) is the regular polyhedron and Platonic solid illustrated above having 12 polyhedron vertices, 30 polyhedron ...

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 quasi-regular graph is a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 (Bozóki et al. 2020). ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

A regular skew polyhedron is a polyhedron whose faces and vertex figures are regular skew polygons. There are only three regular skew polyhedra in Euclidean three-space ...