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Simplicial geometry of crystals. (English) Zbl 0956.51013
The authors study simplices in the m-dimensional Euclidean space. Two simplices are called $m$-parallel, if all their $\left(m-1\right)$-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.
##### MSC:
 51M20 Polyhedra and polytopes; regular figures, division of spaces 51M25 Length, area and volume (geometry)
##### Keywords:
simplices; volume of simplices; growth of crystals