  Discontinuous Galerkin (DG) methods discretized under the method of lines
must handle the inverse of a block diagonal mass matrix at each time step.
Efficient implementations of the DG method hinge upon inexpensive and
low-memory techniques for the inversion of each dense mass matrix block. We
propose an efficient time-explicit DG method on meshes of pyramidal elements
based on the construction of a semi-nodal high order basis, which is orthogonal
for a class of transformations of the reference pyramid, despite the non-affine
nature of the mapping. We give numerical results confirming both expected
convergence rates and discuss efficiency of DG methods under such a basis.
