Application of polyhedrons as image surface in cartographic projections has a tradition of more than 200 years. The first maps relying on polyhedrons appeared in the 19th century. One of the first maps which based on an original polyhedral projection using a regular octahedron was constructed by the Californian architect Bernard Cahill in 1909. Other well known polyhedral projections and maps included Buckminster Fuller’s projection and map into icosahedron from 1954 and S. Waterman’s projection into truncated octahedron from 1996, which resulted in the “butterfly” map. Polyhedrons as image surface have the advantage of allowing a continuous image of continents of the Earth with low projection distortion. Such maps can be used for many purposes, such as presentation of tectonic plates or geographic discoveries.
The article presents most well known polyhedral maps, describes cartographic projections applied in their preparation, as well as contemporary examples of polyhedral maps. The method of preparation of a polyhedral map and a virtual polyhedral globe is also presented.
If the inline PDF is not rendering correctly, you can download the PDF file here.
Andrews K. 2013 Buckminster Fuller’s Dymaxion world map redesigned. http://www.dezeen.com/2013/08/07/buckminster-fuller-dymaxion-world-map-reimagined/ (access 10.11.2016).
Cahill B.J.S. 1909 An account of a new land map of the World. “The Scottish Geographical Magazine” no. 09 pp. 449-469.
Catalan M.E. 1865 Memoire sur la theorie des polyedres. „Journal de l’Ecole Polytechnique” vol. 24 pp. 25-71.
Copleston F. 1998 Historia filozofii. Warszawa.
D’Andrea J. 2011 Fundamental transversals on the complexes of polyhedra. A thesis for the degree of Master of Arts Department of Mathematics College of Arts and Sciences University of South Florida http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=4941&context=etd.
Doroziński T. Pogoda Z. 2009 Wielościany Catalana. „Delta” nr 12 pp. 1-3 http://mimuw.edu.pl/delta/artykuly/delta1209/20091201-wielosciany.pdf (access 10.11.2016).
Flynn D. 2014 Emirates route map puts Dubai at the centre of the world. http://www.ausbt.com.au/emirates-new-route-map-puts-dubai-at-the-centre-of-the-world (access 10.11.2016).
Fuller R.B. 1943 Life presents R. Buckminster Fuller’s Dymaxion World. “Life” vol. 14 no. 9 pp. 41-55.
Gurba S. 1970 Ortofroma na globusie dwunastościennym. „Polski Przegląd Kartograficzny” T. 2 nr 4 pp. 160-168.
Heinz A. 2008 Development of mathematical imagination of 3-dimensional polyhedra throughout history and inversion phenomena. 13th International Conference on Geometry and Graphics 4-10.08.2008 Dresden.
Jędrzejewicz J. 1887 Globus składany. „Wszechświat” T. VI no. 27 pp. 427.
Kepler J. 1619 Harmonices Mundi. http://posner.library.cmu.edu/Posner/books/book.cgi?call=520_K38PI (access 10.11.2016).
Maling D.H. 1992 Coordinate systems and map projections. Exeter: Pergamon Press.
Piasecka J. 2004 Polskie globusy Ziemi z XIX i XX wieku. Lublin: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej.
Schuricht S. 2001 Exhibition of the buckymap puzzle at Buckminster Fuller - Your Private Sky exhibition Bauhaus Dessau Germany http://www.sushu.de/buckymap/fuller-sat_13.htm (access 10.11.2016).
Snyder J. 1993 Flattening the earth. Two thousand years of map projections. Chicago: University of Chicago Press.
Szurek M. 2000 Matematyka dla humanistów. Warszawa: Wydawn. RTW.
van Leeuwen D. Strebe D. 2006 A “Slice-and-Dice” approach to area equivalence in polyhedral map projections. “Cartography and Geographic Information Science” Vol. 33 no. 4 pp. 269-286.
van Wijk J. 2008 Unfoolding the Earth: Myriahedral projections. “The Cartographic Journal” Vol. 45 no 1 pp. 32-42.