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