Convex 3-polytopes with exactly two types of edges
Abstract We consider convex 3-polytopes with exactly two types of edges. The questions of the existence of such 3-polytopes are solved. The cardinalities of all classes are determined.
5-regular 3-polytopal Graphs with Edges of Only Two Types and Shortness Exponents Less than One
Abstract It is shown that, if q ⩾ 29 and q ≢ 0 (mod 3), the infinite class of 5-regular 3-polytopal graphs whose edges are incident with either two triangles or a triangle and a q -gon contains nonhamiltonian members and even has shortness exponent less than one.
A class of Hamiltonian polytopes
It is shown that any simple 3-polytope, all of whose faces are triangles or hexagons, admits a hamiltonian circuit.