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

Electronic source:

application/pdf

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