Skip to content
Register Sign in Wishlist

Geometric Regular Polytopes

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: March 2020
  • availability: In stock
  • format: Hardback
  • isbn: 9781108489584


Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available for inspection. However, if you are interested in the title for your course we can consider offering an inspection copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.

    • Provides the first comprehensive coverage of the modern geometric theory
    • Uses an elementary approach to topics and collects basic theory in one place, making it suitable for graduate students
    • Introduces new techniques for the use of researchers
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: March 2020
    • format: Hardback
    • isbn: 9781108489584
    • dimensions: 240 x 160 x 32 mm
    • weight: 1.1kg
    • contains: 43 b/w illus. 19 colour illus. 3 tables
    • availability: In stock
  • Table of Contents

    Part I. Regular Polytopes:
    1. Euclidean space
    2. Abstract regular polytopes
    3. Realizations of symmetric sets
    4. Realizations of polytopes
    5. Operations and constructions
    6. Rigidity
    Part II. Polytopes of Full Rank:
    7. Classical regular polytopes
    8. Non-classical polytopes
    Part III. Polytopes of Nearly Full Rank:
    9. General families
    10. Three-dimensional apeirohedra
    11. Four-dimensional polyhedra
    12. Four-dimensional apeirotopes
    13. Higher-dimensional cases
    Part IV. Miscellaneous Polytopes:
    14. Gosset–Elte polytopes
    15. Locally toroidal polytopes
    16. A family of 4-polytopes
    17. Two families of 5-polytopes
    Symbol index
    Author index
    Subject index.

  • Author

    Peter McMullen, University College London
    Peter McMullen is Professor Emeritus of Mathematics at University College London. He was elected a foreign member of the Austrian Academy of Sciences in 2006 and is also a member of the London Mathematical Society and the European Mathematical Society. He was elected a Fellow of the American Mathematical Society in 2012. He has co-edited several books and co-authored Abstract Regular Polytopes (Cambridge, 2002). His work has been discussed in the Encyclopaedia Britannica and he was an invited speaker at the International Congress of Mathematicians in 1974.

Sign In

Please sign in to access your account


Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.