Max Dehn showed that one type of these figures has a non-zero Dehn invariant in his proof of Hilbert's third problem. The pentachoron contains 5 of these cells in four dimensions, and one subclass of this figure includes disphenoids. The volume of this figure is computed as one-sixth of the scalar triple product of its sides, and its (*) regular type has surface area equal to s squared times the square root of three. It is generalized as a 3-simplex, and its regular variety is the simplest platonic solid. For ten points, identify this polyhedro
Max Dehn showed that one type of these figures has a non-zero Dehn invariant in his proof of Hilbert's third problem. The pentachoron contains 5 of these cells in four dimensions, and one subclass of this figure includes disphenoids. The volume of this figure is computed as one-sixth of the scalar triple product of its sides, and its (*) regular type has surface area equal to s squared times the square root of three. It is generalized as a 3-simplex, and its regular variety is the simplest platonic solid. For ten points, identify this polyhedron with four triangular faces.
Max Dehn showed that one type of these figures has a non-zero Dehn invariant in his proof of Hilbert's third problem.