TY  - GEN
AU  - Brondsted, Arne
TI  - Introduction to convex polytopes
SN  - 9781461270232
U1  - 514​.223 BRO 
PY  - 1982///
CY  - New York
PB  - Springer
KW  - Convex Polytopes
KW  - Geometry
KW  - Combinatorial Analysis
KW  - Mathematics
KW  - Physical Sciences &​ Mathematics
KW  - Combinatorics
N2  - The aim of this book is to introduce the reader to the fascinating world of convex polytopes. The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. All the background information on convex sets and convex polytopes which is m~eded to under­ stand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects of polytope theory. The Dehn-Sommerville Relations are classical, whereas the proofs of the Upper Bound Theorem and the Lower Bound Theorem are of more recent date: they were found in the early 1970's by P. McMullen and D. Barnette, respectively. A famous conjecture of P. McMullen on the charac­ terization off-vectors of simplicial or simple polytopes dates from the same period; the book ends with a brief discussion of this conjecture and some of its relations to the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. However, the recent proofs that McMullen's conditions are both sufficient and necessary go beyond the scope of the book
ER  -