High Quality Content by WIKIPEDIA articles! In geometry, Schlafli orthoscheme is a type of simplex. They are defined by a sequence of edges (v0v1), (v1v2), … , (vd ? 1vd) which are mutually orthogonal. These were introduced by Ludwig Schlafli, who called them orthoschemes and studied their volume in the Euclidean, Lobachevsky and the spherical geometry. H.S.M. Coxeter later named them after Schlafli. J.-P. Sydler and B rge Jessen studied them extensively in connection with Hilbert's third problem. Orthoschemes are a special case of a more general class of simplices studied by Fiedler (1957), and later rediscovered by Coxeter (1991). These simplices are the convex hulls of trees in which all edges are mutually perpendicular. In the orthoscheme, the underlying tree is a path.

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