Search Results for ""

The great dodecahedron is the Kepler-Poinsot polyhedron whose dual is the small stellated dodecahedron. It is also uniform polyhedron with Maeder index 35 (Maeder 1997), ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...

In algebraic topology, a p-skeleton is a simplicial subcomplex of K that is the collection of all simplices of K of dimension at most p, denoted K^((p)). The graph obtained ...

Tutte's wheel theorem states that every polyhedral graph can be derived from a wheel graph via repeated graph contraction and edge splitting. For example, the figure above ...

A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...

The Kepler-Poinsot polyhedra are four regular polyhedra which, unlike the Platonic solids, contain intersecting facial planes. In addition, two of the four Kepler-Poinsot ...

A heptahedral graph is a polyhedral graph on seven nodes. There are 34 nonisomorphic heptahedral graphs, as first enumerated by Kirkman (1862-1863) and Hermes (1899ab, 1900, ...

The Faulkner-Younger graphs (Faulkner and Younger 1974) are the cubic polyhedral nonhamiltonian graphs on 42 and 44 vertices illustrated above that are counterexamples to ...

The skeleton graphs of the Johnson solids are polyhedral graphs. The Johnson skeleton graphs J_3 and J_(63) are minimal unit-distance forbidden graphs. The skeleton of the ...