On the existence of a combinatorial Schlegel diagram of a simplical unstacked 3-polytope with a prescribed set of vertices

✍ Scribed by Yaakov S. Kupitz

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 791 KB
• Volume: 120
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90570-j

✦ Synopsis

Kupitz, Y.S., On the existence of a combinatorial Schlegel diagram of a simplicial unstacked 3-polytope with a prescribed set of vertices, Discrete Mathematics 120 (1993) 121-134. It is shown that, except for two well defined configurations, any finite set V c Rz with exactly three points on I? V is the vertex set of a triangulation of [V] which is combinatorially the Schlegel diagram of a simplicial unstacked 3-polytope. line segments, and) whose union is a (euclidean) triangle s.t. the O-skeleton (= vertex set) of T lies entirely inside the triangle, except for the three boundary vertices, is