%---------------------------Minimum Angle-----------------------------
\section{Minimum Angle\label{s:tet-min-angle}}

The (nonoriented) dihedral angle of two faces of the
tetrahedron that are adjacent along edge $i$ ($0\le{}i\le5$), is,
measured in degrees,
\[
  \alpha_i = \frac{180\dgr}{\pi}
    \arccos{\left(\vec{n_{i1}} \cdot \vec{n_{i2}}\right)},
\]
where $\vec{n_{i1}}$ and $\vec{n_{i2}}$ are unit vectors normal to the
two tetrahedron faces that are adjacent to edge $i$. Subsequently,
the minimum (nonoriented) dihedral angle of the tetrahedron, measured
in degrees, is
\[
  q =
    \min_{i\in\{0,1,2,3,4,5\}}{\alpha_i}.
\]

\tetmetrictable{minimum dihedral angle}%
{$A^1$}%                                              Dimension
{$[40\dgr,\frac{180\dgr}{\pi}\arccos\tfrac{1}{3}]$}%  Acceptable range
{$[0\dgr,\frac{180\dgr}{\pi}\arccos\tfrac{1}{3}]$}%   Normal range
{$[0\dgr,360\dgr]$}%                                  Full range
{$\frac{180\dgr}{\pi}\arccos\tfrac{1}{3}\approx70.528779\dgr$}% Regular tetrahedron value
{--}%                                                 Reference(s)                   
{v\_tet\_minimum\_angle}%                             Verdict function name