%---------------------------Relative Size Squared---------------------------
\section{Relative Size Squared\label{s:hex-relative-size-squared}}

Consider the ratio $D$ of the hex volume to the average volume of an ensemble of hexahedra:
\[
D = \frac{\sum_{i=0}^7 \alpha_i}{8\overline{V}} = \frac{\alpha_8}{64\overline{V}}.
\]
The relative size the minimum of $D$ and its inverse; and the relative size squared is
\[
  q = \left(\min\left\{ D, \frac {1}{D} \right\}\right)^2 .
\]

Note that if $\overline{V} < DBL\_MIN$ or $D \leq DBL\_MIN$, we set $q = 0$.

\hexmetrictable{relative size squared}%
{$1$}%                                        Dimension
{$[0.5,1]$}%                                  Acceptable range
{$[0,1]$}%                                    Normal range
{$[0,1]$}%                                    Full range
{Dependent on $\overline{V}$}%                Cube
{\cite{knu:03}}%                              Citation
{v\_hex\_relative\_size\_squared}%            Verdict function name
