“The regular 4-dimensional 57-cell” by Séquin and Hamlin

  • ©Carlo H. Séquin and James F. Hamlin

Conference:


Type(s):


Title:

    The regular 4-dimensional 57-cell

Session/Category Title:   The Viz Biz

Presenter(s)/Author(s):


Abstract:


    Besides the six regular four-dimensional “Platonic” polytopes, there exist two fascinating, highly symmetrical 4D objects with 11 and 57 non-orientable cells, respectively. This sketch summarizes an attempt to visualize these objects through stepwise construction.

References:


    1. Coxeter, H. S. M. 1982. Ten toroids and fifty-seven hemi-dodecahedra. Geometriae Dedicata, 13, pp 87–99.
    2. Grünbaum, B. 1977. Regularity of Graphs, Complexes and Designs. Colloque Intern. C.N.R.S., Vol. 260, pp 191–197.
    3. Séquin, C. H. and Lanier, J. 2007. Hyperseeing the Regular Hendecachoron. Proc ISAMA 2007, Texas A&M, pp 159–166.
    4. Lanier, J. 2007. Jaron’s World: Shapes in Other Dimensions. Discover Magazine, April 2007, pp 28–29.

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