Abstract
We provide a constructive proof of a face-to-face simplicial partition of a d-dimensional space for arbitrary d by generalizing the idea of Sommerville, used to create space-filling tetrahedra out of a triangular base, to any dimension. Each step of construction that increases the dimension is determined up to a positive parameter, d-dimensional simplicial partition is, therefore, parameterized by d parameters. We show the shape optimal value of those parameters and reveal that the shape optimal partition of d-dimensional space is constructed over that of \((d-1)\)-dimensional space.
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