\begin{section}{Cone}
The dual cone of $K$ is $\dual{K}$. Some familiar symmetric cones
are $\Rnplus$, $\Lnplus$, $\Snplus$, and $\Hnplus$. If cones
\begin{section}{Cone}
The dual cone of $K$ is $\dual{K}$. Some familiar symmetric cones
are $\Rnplus$, $\Lnplus$, $\Snplus$, and $\Hnplus$. If cones
The conic hull of a set $X$ is $\cone{X}$; its affine hull is
$\aff{X}$, and its convex hull is $\conv{X}$. If $K$ is a cone,
then its lineality space is $\linspace{K}$, its lineality is
The conic hull of a set $X$ is $\cone{X}$; its affine hull is
$\aff{X}$, and its convex hull is $\conv{X}$. If $K$ is a cone,
then its lineality space is $\linspace{K}$, its lineality is
- $\lin{K}$, and its extreme directions are $\Ext{K}$.
+ $\lin{K}$, and its extreme directions are $\Ext{K}$. The fact that
+ $F$ is a face of $K$ is denoted by $F \faceof K$; if $F$ is a
+ proper face, then we write $F \properfaceof K$.