Similarity Classes in the Eight-Tetrahedron Longest-Edge Partition of a Regular Tetrahedron.

A tetrahedron is called regular if its six edges are of equal length. It is clear that, for an initial regular tetrahedron R 0 , the iterative eight-tetrahedron longest-edge partition (8T-LE) of R 0 produces an infinity sequence of tetrahedral meshes, τ 0 = { R 0 } , τ 1 = { R i 1 } , τ 2 = { R i 2 } , ... , τ n = { R i n } , ... . In this paper, it is proven that, in the iterative process just mentioned, only two distinct similarity classes are generated. Therefore, the stability and the non-degeneracy of the generated meshes, as well as the minimum and maximum angle condition straightforwardly follow. Additionally, for a standard-shape tetrahedron quality measure (η) and any tetrahedron R i n ∈ τ n , n > 0 , then η R i n ≥ 2 3 η R 0 . The non-degeneracy constant is c = 2 3 in the case of the iterative 8T-LE partition of a regular tetrahedron. [ABSTRACT FROM AUTHOR]