On the volume and the Chern-Simons invariant for the $2$-bridge knot   orbifolds
  We extend some part of the unpublished paper written by Mednykh and Rasskazov. Using the approach indicated in this paper we derive the Riley-Mednykh polynomial for some family of the $2$-bridge knot orbifolds. As a result we obtain explicit formulae for the volume of cone-manifolds and the Chern-Simons invariant of orbifolds of the knot with Conway's notation $C(2n,4)$. 
Ji-Young Ham, Joongul Lee, Alexander Mednykh, and Aleksey Rasskazov
math.GT