  We construct and study a family of toric degenerations of the algebra of
conformal blocks for a stable marked curve $(C, \vec{p})$ with structure group
$SL_3(\mathbb{C}).$ We find that this algebra is Gorenstein. For the genus $0,
1$ cases we find the level of conformal blocks necessary to generate the
algebra. In the genus 0 case we also find bounds on the degrees of relations
required to present the algebra. Along the way we recover polyhedral rules for
counting conformal blocks originally due to Senechal, Mathieu, Kirillov, and
Walton.
