  Goldberg & Gott (2008) developed six error measures to rate flat map
projections on their verisimilitude to the sphere: Isotropy, Area, Flexion,
Skewness, Distances, and Boundary Cuts. The first two depend on the metric of
the projection, the next two on its first derivatives. By these criteria, the
Winkel Tripel (used by National Geographic for world maps) was the best scoring
of all the known projections with a sum of squares of the six errors of 4.563,
normalized relative to the Equirectangular in each error term. We present here
a useful Gott-Wagner variant with a slightly better error score of only 4.497.
We also present a radically new class of flat double-sided maps (like
phonograph records) which have correct topology and vastly improved error
scores: 0.881 for the azimuthal equidistant version. We believe it is the most
accurate flat map of Earth yet. We also show maps of other solar system objects
and sky maps.
