4-polytope

English

A Schlegel diagram of a 16-cell, an example of a 4-polytope

Etymology

From 4-dimensional + polytope.

Noun

4-polytope (plural 4-polytopes)

1. (geometry) A four-dimensional polytope.
   • 1984, London Mathematical Society lecture note series, numbers 88-90, page 101:

     Perhaps the most obvious next step is to investigate 4-polytopes with respect to symmetry equivalence.

   • 2004, Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler, “16: Basic properties of convex polytopes”, in Joseph O'Rourke, Jacob E. Goodman, editors, Handbook of Discrete and Computational Geometry, 2nd edition, page 369:

     The situation for 4-polytopes is fundamentally different from that for 3-dimensional polytopes. One reason is that there is no similar reduction of 4-polytope theory to a combinatorial (graph) problem.

   • 2011, Felix Effenberger, Hamiltonian Submanifolds of Regular Polytopes‎^[1], page 40:

     For d = 4, Hamiltonian cycles in the regular 4-polytopes are known to exist. However, it seems that so far no decision about the existence or non-existence of 1-Hamiltonian surfaces in the 2-skeleton of any of the three sporadic regular 4-polytopes can be made, compare [120].

Synonyms

• (4-dimensional polytope): polycell, polychoron, polyhedroid

Translations

4-dimensional polytope

• Italian: policoro m