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Martini, Horst; Wenzel, Walter : Simplices with Congruent k-faces

Martini, Horst ; Wenzel, Walter : Simplices with Congruent k-faces

Author(s):
Martini, Horst
Wenzel, Walter
Title:
Simplices with Congruent k-faces
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 3, 2002
Mathematics Subject Classification:
05A15 [ Exact enumeration problems, generating functions ]
05A15 [ Exact enumeration problems, generating functions ]
05B05 [ Block designs ]
26B05 [ Continuity and differentiation questions ]
51E05 [ General block designs ]
Abstract:
We prove that a non-degenerate simplex S in R^n is regular if, for some k with 1 < k < n - 2, all its k-dimensional faces are congruent. On the other hand, there are non-regular simplices with the property that all their (n-1-dimensional faces are congruent.
Keywords:
(regular) simplices, faces of simplices, congruence, inverse mapping, theorem
Language:
English
Publication time:
8 / 2002