## The dissection of five-dimensional simplices into orthoschemes.(English)Zbl 0806.52012

Summary: In this paper the dissection of five-dimensional simplices into orthoschemes is shown. Firstly, some general methods for dissecting $$n$$- dimensional Euclidean simplices are described. For this, a description of simplices by graphs is given. All methods for cutting a simplex are investigated with the help of these graphs. The dissection of the five- dimensional Euclidean simplices is thoroughly investigated and it is shown that each of them is decomposable into orthoschemes. Furthermore, the validity of the propositions in spaces of constant curvature is checked and it is proved that every five-dimensional spherical or hyperbolic simplex can be dissected into orthoschemes.

### MSC:

 52B45 Dissections and valuations (Hilbert’s third problem, etc.) 52A55 Spherical and hyperbolic convexity
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