More About the Height of Faces in 3-Polytopes

Abstract

The height of a face in a 3-polytope is the maximum degree of its incident vertices, and the height of a 3-polytope, h, is the minimum height of its faces. A face is pyramidal if it is either a 4-face incident with three 3-vertices, or a 3-face incident with two vertices of degree at most 4. If pyramidal faces are allowed, then h can be arbitrarily large, so we assume the absence of pyramidal faces in what follows.

Keywords

• plane map
• planar graph
• 3-polytope
• structural properties
• height of face
• 05c15