IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-5648-9_14.html
   My bibliography  Save this book chapter

Two Quaternionic 4-Polytopes

In: The Geometric Vein

Author

Listed:
  • S. G. Hoggar

    (University of Glasgow, Department of Mathematics)

Abstract

One property of a (convex) polytope in ℝ n is that the vertex set defines the actual subdivision into edges, triangles, etc. The cells (dimension n − 1) are the intersections of the convex hull of the vertices with its bounding hyperplanes. The cells intersect in (n − 2)-dimensional elements, and so on. All these are finite. But for a polytope in ℂ n convexity is not available; there is some latitude as to the various elements (now subspaces), subject to suitable conditions on their incidences. For example the fractional polytope $$ \frac{1}{3}\gamma _3^3 $$ and generalized cross polytope $$ \beta _3^3 $$ [10] agree as to vertices and “edges,” but the first has 18 “triangles” whereas the second has 27.

Suggested Citation

  • S. G. Hoggar, 1981. "Two Quaternionic 4-Polytopes," Springer Books, in: Chandler Davis & Branko Grünbaum & F. A. Sherk (ed.), The Geometric Vein, pages 219-230, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5648-9_14
    DOI: 10.1007/978-1-4612-5648-9_14
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4612-5648-9_14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.