  We classify all edge-to-edge spherical isohedral 4-gonal tilings such that
the skeletons are pseudo-double wheels. For this, we characterize these
spherical tilings by a quadratic equation for the cosine of an edge-length. By
the classification, we see: there are indeed two non-congruent, edge-to-edge
spherical isohedral 4-gonal tilings such that the skeletons are the same
pseudo-double wheel and the cyclic list of the four inner angles of the tiles
are the same. This contrasts with that every edge-to-edge spherical tiling by
congruent 3-gons is determined by the skeleton and the inner angles of the
skeleton. We show that for a particular spherical isohedral tiling over the
pseudo-double wheel of twelve faces, the quadratic equation has a double
solution and the copies of the tile also organize a spherical non-isohedral
tiling over the same skeleton.
