Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 35 (1994), No. 1, 1-11.

The Dissection of Five-Dimensional Simplices into Orthoschemes

Katrin Tschirpke

Abstract.

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 investgated 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.