A wallpaper map is a conformal projection of a spherical earth onto regular polygons with which the plane can be tiled continuously. A complete set of distinct wallpaper maps that satisfy certain natural symmetry conditions is derived and illustrated. Though all of the projections have been published before, some generalize to one-parameter families in which the sphere is pre-transformed by a conformal automorphism.
Keywordsconformal projection elliptic integral spherical tiling planar tiling
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