Appendix 1. Minor Hypotheses

Let octavor0(Q)=0.5( vor0(Q)+ vor0( hat Q)), and octavor(Q) = 0.5( vor(Q)+ vor( hat Q)). kappa(S) is defined in Section 3.4. We let taunu, tauV, tau0, and tauGamma be f- sol zeta pt, where f= nu, vor, vor0, and Gamma, respectively. betapsi is defined in Section 2.8.

Each calculation is accompanied by one or more reference numbers. These identification numbers are needed to find further details about the calculation in cite{H}.

The numbering that follows reflects the sections from which the hypotheses are drawn. Edge lengths whose bounds are not specified are assumed to be between 2 and 2.51.

Section 2


Section 3

In Inequalities 3.23.1 -- 3.23.12, the domain is the set of upright quarters. The dihedral angle is measured along the diagonal. In Inequalities 3.23.13-- 3.23.25, y1 in[2.51,2 sqrt{2}] and y4 in[2.51,2 sqrt{2}] and dih<2.46. Let vorx = vor if the simplex has type C and vorx= vor0 otherwise. Set taux = sol zeta pt - vorx.

In the Inequalities 3.23.26 -- 3.23.38, we assume y1 in[2.51,2 sqrt{2}], y4 in[2 sqrt{2},3.2], and dih<2.46.


Section 4
Section 5 Define sigmaMax as in Section 3.32.
Section 6