4-polytope

English right|thumb|A Schlegel diagram of a 16-cell, an example of a 4-polytope Etymology From en 4-dimensional + en polytope. Noun en geometry A four-dimensional polytope. en Higher-dimensional geometry en 1984 London Mathematical Society lecture note series 88-90 https://books.google.com.au/books?id=FIJLAQAAIAAJ&q=%224-polytope%22%7C%224-polytopes%22&dq=%224-polytope%22%7C%224-polytopes%22&hl=en&sa=X&ved=0ahUKEwi685_5zN7MAhXG6aYKHWVtD1AQ6AEI1QEwJA 101 Perhaps the most obvious next step is to investigate 4-polytopes with respect to symmetry equivalence. en 2004 Martin Henk; Jürgen Richter-Gebert; Günter M. Ziegler 16: Basic properties of convex polytopes Joseph O'Rourke; Jacob E. Goodman Handbook of Discrete and Computational Geometry 2nd https://books.google.com.au/books?id=QS6vnl8WlnQC&pg=PA369&dq=%224-polytope%22%7C%224-polytopes%22&hl=en&sa=X&ved=0ahUKEwi685_5zN7MAhXG6aYKHWVtD1AQ6AEIbjAP#v=onepage&q=%224-polytope%22%7C%224-polytopes%22&f=false 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. en 2011 Felix Effenberger Hamiltonian Submanifolds of Regular Polytopes 40 https://books.google.com.au/books?id=RolxQhYPubkC&pg=PA40&dq=%224-polytope%22%7C%224-polytopes%22&hl=en&sa=X&ved=0ahUKEwi685_5zN7MAhXG6aYKHWVtD1AQ6AEIgQEwEw#v=onepage&q=%224-polytope%22%7C%224-polytopes%22&f=false 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: it policoro m