# Convex Polyhedra with Regularity Conditions and Hilbert’s Third Problem

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*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.

#### Readership

Advanced undergraduates, graduate students, and research mathematicians interested in geometry.