  The conventional formulation of the Fresnel wave and ray surfaces typically
involves the implicit use of Euclidian metrics in order to justify treating
vectors and covectors as indistinguishable. This tends to disguise the fact
that one of the surfaces lives in the cotangent spaces to the spatial (or
space-time) manifold, while the other lives in the tangent spaces. Moreover, no
mention is made of how to get from tangent spaces to cotangent spaces in the
absence of a metric. The following analysis shows how to resolve those issues
within the framework of pre-metric electromagnetism. The way that
electromagnetic waves imply spatial frames, coframes, and metrics will be
explained.
