Nereis. Interdisciplinary Ibero-American Journal of Methods, Modelling and Simulation.

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A Note on a Very Simple Property about the Volume of a n-Simplex and the Centroids of its Faces

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Abstract

A n–simplex is the convex hull of a set of (n + 1) independent points affine to a n–dimensional Euclidean space. A 0–simplex would be a point, a segment would be a 1–simplex, a 2–simplex would be a triangle and a 3–simplex a tetrahedron. If we connect to each other the centroids of all the (n ? 1) faces of a n–simplex, we will obtain another n-simplex (dual n-simplex). The volume ratio between a n-simplex and its dual is just n?n.

Keywords: n?simplex, centroid.

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