Robert M. Erdahl

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A lattice Delaunay polytope is perfect if its Delaunay sphere is its only circumscribed ellip-soid. A perfect Delaunay polytope naturally corresponds to a positive quadratic function on Z n that can be recovered uniquely from the data consisting of its minimum and all points of Z n where this minimum is achieved – a quadratic function with this uniqueness(More)
A polytope D, whose vertices belong to a lattice of rank d, is Delaunay if it can be circumscribed by an ellipsoid E with interior free of lattice points, and so that the vertices of D are the only lattice points on the quadratic surface E. If in addition E is uniquely determined by D, we call D a perfect Delaunay polytope. Thus, in the perfect case, the(More)
We show how a d-stress on a piecewise-linear realization of an oriented (non-simplicial, in general) d-manifold in R d naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the analysis of self-stresses in spatial frameworks. The mappings we construct are not linear, but polynomial. In the 1860–70s(More)
A lattice Delaunay polytope D is called perfect if it has the property that there is a unique circumscribing ellipsoid with interior free of lattice points, and with the surface containing only those lattice points that are the vertices of D. An inhomogeneous quadratic form is called perfect if it is determined by such a circumscribing " empty ellipsoid "(More)