Convergence of the R1+ tetrahedra family in iterative Longest Edge Bisection

Abstract

We study the similarity classes appearing in the iterative Longest Edge Bisection (LEB), of an improved family of nearly equilateral tetrahedra. We focus here on the R1+ family as a generalization of the family mentioned by Adler in Adler (1983). We characterize the finite convergence of similarity classes using the Similarity Classes Longest Edge Bisection (SCLEB) algorithm. We prove that below the bound of 37 similarity classes, a number n≤37 classes are generated where n∈{4,8,9,13,21,37}. Using a tetrahedra sextuple representation and SCLEB, all the generated classes are clearly delimited, thereby improving the results by Adler and others.