Directory of Map Projections

What is a projection?

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Cox world in a triangle




Meridians: Central meridian is straight. The 180th meridians are straight lines bent at a southern latitude. Others are complex curves.
Parallels: Complex curves.
Poles: Points, one in a vertex and the other centered on the opposite side of the triangle.
Symmetry: About the central meridian.


Varies along each meridian and parallel.


Great area distortion near the poles and 180th meridians. Conformality fails at each pole and at the corners of the triangle.


Novel whole-world maps.

Similar projections

See note under Adams projection of the world in a square I.
Bernard J.S. Cahill, beginning in 1912, arranged conformal or nonconformal three-sided octants of the world, bounded by the equator and two meridians 90° apart, in a butterfly arrangement, called the “Butterfly Map”. He promoted these interrupted arrangements for weather maps.


J.F. Cox, 1935.

Description adapted from J.P. Snyder and P.M. Voxland, An Album of Map Projections, U.S. Geological Survey Professional Paper 1453. United States Government Printing Office: 1989.