This article is cited in 5 papers

Volumes of $L$-simplexes of five-dimensional lattices

E. P. Baranovskii

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: We investigate the question of nonbasic Simplexes of an $L$-subdivision of five-dimensional lattices. It is shown that, apart from the Simplexes of volume $2V$ ($V$ is the volume of the basic simplex), no other nonbasic $L$-simplexes exist in these lattices. In primitive lattices the $L$-simplexes of doubled volume abut the basic $L$-simplexes by 4-dimensional faces.

UDC: 513

Received: 21.09.1972

 English version: Mathematical Notes, 1973, 13:5, 460–466

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