ON THE SHAPE OF TETRAHEDRA FROM BISECTION

We present a procedure for bisecting a tetrahedron T successively into an infinite sequence of tetrahedral meshes T0, T1, T2, ... , which ha s the following properties: (1) Each mesh T(n) is conforming. (2) Ther e are a finite number of classes of similar tetrahedra in all the T(n) , n greater-than-or-equal-to 0. (3) For any tetrahedron T(i)n in T(n) , eta(T(n)) greater-than-or-equal-to c1eta(T), where eta is a tetrahed ron shape measure and cl is a constant. (4) delta(T(i)n) less-than-or- equal-to c2(1/2)n/3delta(T), where delta(T') denotes the diameter of t etrahedron T' and c2 is a constant. Estimates of c1 and c2 are provide d. Properties (2) and (3) extend similar results of Stynes and Adler, and of Rosenberg and Stenger, respectively, for the 2-D case. The diam eter bound in property (4) is better than one given by Kearfott.