  This paper is concerned with achieving optimal coherence for highly redundant
real unit-norm frames. As the redundancy grows, the number of vectors in the
frame becomes too large to admit equiangular arrangements. In this case, other
geometric optimality criteria need to be identified. To this end, we use an
iteration of the embedding technique by Conway, Hardin and Sloane. As a
consequence of their work, a quadratic mapping embeds equiangular lines into a
simplex in a real Euclidean space. Here, higher degree polynomial maps embed
highly redundant unit-norm frames to simplices in high-dimensional Euclidean
spaces. We focus on the lowest degree case in which the embedding is quartic.
