Hindustan Book Agency 2001; 120 pp; hardcover ISBN10: 8185931283 ISBN13: 9788185931289 List Price: US$35 Member Price: US$28 Order Code: HIN/8
 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. Readership Advanced undergraduates, graduate students, and research mathematicians interested in geometry. Table of Contents  Introduction
 Definitions and notations
 Theorems of Euler and Descartes
 The regularity restrictions and the five bodies of Plato
 Metrical properties of the five Platonic polyhedra
 The fourteen bodies of Archimedes
 Another method of enumerating the semiregular polyhedra
 The eight Deltahedra
 Finiteness of the number of convex regular faced polyhedra (RFP) and the remaining cases of regularity restrictions
 Star polyhedra and plane tessellations
 A theorem of Johnson and Grunbaum
 Description of the ninetytwo RFP and their derivation from the simple ones
 Hilbert's third problem
 Bibliography
 Index
