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What is N – Simplex

Chapter 3
The Geometry of Higher-Dimensional Polytopes
Convex polytope of dimension n , all vertices of which have connections with an edge to all other vertices of the vertices of this polytope.
Published in Chapter:
The Number of Symmetry Transformation of Convex Regular Polytopes in the n - Space
Copyright: © 2019 |Pages: 29
DOI: 10.4018/978-1-5225-6968-8.ch003
Abstract
The number of symmetry transformations of regular polytopes of dimension n (n - cubes, n - simplexes, n - cross polytopes) are considered, using symmetry transformation of their facets. In this chapter, it is investigated how a certain symmetry transformation of the facet leads to the transformation of the symmetry of the polytope, under the condition of continuity of the polytope as a whole. It is established that the number of symmetry transformations of a regular n - polytope is equal to the product of the number of symmetry transformations of the facet of the corresponding polytope by the number of facets in this polytope.
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