  We provide a constructive proof of a face-to-face simplical partition of a
d-dimensional space for arbitrary d by generalizing the idea of Sommerville,
used to create space-filling tetrahedra out of triangular base, to any
dimension. Each step of construction that increases the dimension is determined
up to a positive parameter, d-dimensional simplical partition is therefore
parametrized by d parameters. We show the shape optimal value of those
parameters.
