Introduction; 1. Indivisible, inexpressible and unavoidable; 2. Rules and regularity; 3. Decline and rebirth of polyhedral geometry; 4. Fantasy, harmony and uniformity; 5. Surfaces, solids and spheres; 6. Equality, rigidity and flexibility; 7. Stars, stellations, and skeletons; 8. Symmetry, shape and structure; 9. Counting, colouring and computing; 10. Combination, transformation and decoration; Appendices.
This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics.
'The topic itself … is easily visualised and it has a long history
as part of our culture, interacting with philosophy, art and
chemistry. Cromwell's treatment admirably exploits all these
opportunities, with many interesting digressions and a lively
historical commentary … popular exposition at a high level.' Sir
Michael Atiyah, The Times Higher Education Supplement
'… plenty to fascinate.' New Scientist
'… Peter Cromwell has done us a great service by writing this
handsome, scholarly and beautifully illustrated book.' Peter
Giblin, The London Mathematical Society Newsletter
'This remarkable book goes far beyond the superficial, providing a
solid and fascinating account of the history and mathematics of
polyhedra, especially regular polyhedra. It is likely to become the
classic book on the topic.' MAA Online
' … a fascinating book … the book holds many surprises and will
find rich use among students of both mathematics and computer
science.' Choice
' … a well got-up book with an abundant and beautiful material of
illustration. The study of polyhedra, as the author explicitly
states, 'is currently enjoying something of a renaissance'. This
work itself will surely help this renaissance, and may be an
enjoyable reading for a very wide audience.' Acta. Sci. Math.
' … the book should have a wide and appreciative audience of all
ages.' The Times Higher Education Supplement
' … this book contains a thorough treatment of all that is known
about polyhedra … A very interesting and detailed account.'
European Mathematical Society
' … well-illustrated throughout with line diagrams, as well as
several colour plates of the author's own superb models. The
writing is clear and entertaining, and reassuringly anticipates
many of the reader's questions.' Thomas Bending, The Mathematical
Gazette
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