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The Geometry of an Equifacetal Simplex
Author(s) -
Edmonds Allan L.
Publication year - 2005
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300000310
Subject(s) - simplex , mathematics , combinatorics , codimension , set (abstract data type) , type (biology) , group (periodic table) , pure mathematics , computer science , ecology , chemistry , organic chemistry , biology , programming language
Equifacetal simplices, all of whose codimension one faces are congruent to one another, are studied. It is shown that the isometry group of such a simplex acts transitively on its set of vertices and, as an application, equifacetal simplices are shown to have unique centres. It is conjectured that a simplex with a unique centre must be equifacetal. The notion of the combinatorial type of an equifacetal simplex is introduced and analysed, and all possible combinatorial types of equifacetal simplices are constructed in even dimensions.