Cattani, Carlo; Laserra, Ettore Simplicial geometry of crystals. (English) Zbl 0956.51013 J. Interdiscip. Math. 2, No. 2-3, 143-151 (1999). The authors study simplices in the m-dimensional Euclidean space. Two simplices are called \(m\)-parallel, if all their \((m-1)\)-faces are parallel. Mappings which fix one vertex and keep this kind of parallelism are applied. Then the change of the volume of this simplex is being studied. The result of these considerations is applied to the theory of crystal growth. Reviewer: O.Röschel (Graz) Cited in 1 Document MSC: 51M20 Polyhedra and polytopes; regular figures, division of spaces 51M25 Length, area and volume in real or complex geometry Keywords:simplices; volume of simplices; growth of crystals PDFBibTeX XMLCite \textit{C. Cattani} and \textit{E. Laserra}, J. Interdiscip. Math. 2, No. 2--3, 143--151 (1999; Zbl 0956.51013) Full Text: DOI References: [1] Cattani C., Workshop on numerical applications of Regge calculus an related topics (1990) [2] C. Cattani Variational method and Regge equations, Proceedings of the M08, Eighth Marcel Grossmann Meeting T. Piran R. Ruffini 1999 753 755 [3] Cattani C., Dip. di Matematica, Univ. di Roma ”La Sapienza” (1997) [4] Cattani C., di Roma ”La Sapienza” (1988) [5] Cattani C., CAD (Computer Aided Design) 22 (2) pp 130– (1990) · Zbl 0697.65004 · doi:10.1016/0010-4485(90)90007-Y [6] Cattani C., EWC (Engineering with computers) 6 pp 17– (1990) · doi:10.1007/BF01200201 [7] Iannece D., Meccanica 25 (1990) · Zbl 0703.76084 · doi:10.1007/BF02015029 [8] Sorkin R., Journal of Mathematical Physics 16 (12) pp 2432– (1975) · doi:10.1063/1.522483 [9] Strickland-Constable R. F., Kinetics and Mechanism of crystallization (1968) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.