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Wenzel, Walter : Regular Simplices inscribed into the Cube and exhibiting a Group Structure

Wenzel, Walter : Regular Simplices inscribed into the Cube and exhibiting a Group Structure

Author(s):
Wenzel, Walter
Title:
Regular Simplices inscribed into the Cube and exhibiting a Group Structure
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 11, 2002
Mathematics Subject Classification:
52B15 [ Symmetry properties of polytopes ]
20K27 [ Subgroups ]
94B05 [ Linear codes, general ]
Abstract:
For n \in N, we interpret the vertex set W_n of the n-cube as a vector space over the field F_2 and prove that a regular n-simplex can be inscribed into the n-cube such that its vertices constitute a subgroup of W_n if and only if n+1 is a power of 2. Furthermore, a connection to the theory of Hamming Codes will be established.
Keywords:
n-dimensional cube, n-dimensional simplex, abelian groups, congruence maps, reflections, Hamming Codes
Language:
English
Publication time:
10 / 2002