Hindustan Book Agency
Volume: 8; 2001; 120 pp; Hardcover
MSC: Primary 13; 14;
Print ISBN: 978-81-85931-28-9
Product Code: HIN/8
List Price: $35.00
Individual Member Price: $28.00
Convex Polyhedra with Regularity Conditions and Hilbert’s Third ProblemShare this page
A R Rajwade
A publication of Hindustan Book Agency
Since antiquity, people knew that there are only five regular solids, i.e. polyhedra whose all faces are regular polygons and all solid angles are also regular. These solids are, of course, the tetrahedron, the octahedron, the cube, the icosahedron, and the dodecahedron. Later, much attention was drawn to the question of how to describe polyhedra with other types of regularity conditions. The author puts together many facts known in this direction. He formulates four regularity conditions (two for faces and two for solid angles) and for any combination of their conditions lists all the corresponding polyhedra. In this way, he obtains such very interesting classes of solids as 13 semiregular solids, or 8 deltahedra, or 92 regularly faces polyhedra, etc. In later chapters the author presents some related topics of geometry of solids, like star polyhedra and plane tessellations. In the concluding chapter, a complete solution of the Hilbert 3rd problem is given.
Supplied with many figures, the book can be easily read by anyone interested in this beautiful classical geometry.
A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.
Table of Contents
Table of Contents
Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem
Advanced undergraduates, graduate students, and research mathematicians interested in geometry.