Bipyramid Decompositions of Multi-crossing Link Complements
  Generalizing previous constructions, we present a dual pair of decompositions of the complement of a link L into bipyramids, given any multi-crossing projection of L. When L is hyperbolic, this gives new upper bounds on the volume of L given its multi-crossing projection. These bounds are realized by three closely related infinite tiling weaves. 
Colin Adams and Gregory Kehne
math.GT