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A graph Gamma is locally Petersen if, for each point t of Gamma, the graph induced by Gamma on all points adjacent to t (i.e., the neighborhood graph) is isomorphic to the ...

A polytope in four dimensions. Polychora are bounded by polyhedra.

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

A triangle-replaced graph T(G) is a cubic graph in which each vertex is replaced by a triangle graph such that each vertex of the triangle is connected to one of the ...

A convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities mx<=b, where m is a real s×3 matrix and b is a real s-vector. ...

The Foster cage is one of the four (5,5)-cage graphs. Like the other (5,5)-cages, the Foster cage has 30 nodes. It has 75 edges, diameter 3, girth 5, chromatic number 4, and ...

The Frucht graph is smallest cubic identity graph (Skiena 1990, p. 185). It is implemented in the Wolfram Language as GraphData["FruchtGraph"]. It has 12 vertices and 18 ...

A generalized octagon GO(n,k) is a generalized polygon of order 8. GO(1,2) is the (3,8)-cage graph, the incidence graph of the Cremona-Richmond configuration, the cubic ...

The Meredith graph is a quartic nonhamiltonian graph on 70 nodes and 140 edges that is a counterexample to the conjecture that every 4-regular 4-connected graph is ...

The Robertson-Wegner graph is of the four (5,5)-cage graphs, also called Robertson's cage (Read and Wilson 1998, p. 273). Like the other (5,5)-cages, the Robertson-Wegner ...