Geocart Projections

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Peirce quincuncial


Geocart menu class: Miscellaneous


Meridians: Every 90th meridian is straight but bent at the Equator. Other meridians are complex curves.
Parallels: Equator is a square, bent at the straight meridians. Other parallels are complex curves.
Poles: Points at the center of each hemispherical map
Symmetry: About the central meridian or the Equator


Varies considerably along each meridian and parallel


Great distortion of area, especially near each 90th meridian at the Equator, where conformality fails

Other features

Actually a “star” projection in the normal aspect. Shows a polar hemisphere conformally in a square and the world in a larger square. The first use of elliptic functions for a map projection.


Novelty whole-world maps


Presented by Charles Sanders Peirce (1839–1914) of the U.S. Coast and Geodetic Survey in 1879


In normal form, the pole is at the center of a square. In transverse form, placing the pole at the midpoint of one side of a square results in the Guyou projection. Placing the pole at the corner of the square results in the Adams projection of a hemisphere in a square.

Other names

Quincuncial; name applied by Peirce, because there are normally five parts within a square (the Northern Hemisphere is in the center, and four parts of the Southern Hemisphere are in the corners)

Similar projections

Listed under Aspects above

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.