Paper planets, and how to make them

#projections #toys #d3.js

28 September 2017


At the D3.js unconf in San Francisco, in September 2017, Visionscarto brought some paper planets. Nothing like “cut, fold, glue” to understand how map projections work, and how far they are from the true shape of the globe. Here’s how we made them, and the PDF files to download and print if you want to play.

by Philippe Rivière

JPEG - 124.9 KiB
JPEG - 72.7 KiB
JPEG - 89.2 KiB
JPEG - 134.4 KiB

The projections for these paper planets were chosen among those that one can cut and fold back into a polyhedron. They were:

— A gnomonic cube, i.e. a cube holding a gnomonic projection on each face — based on Enrico Spinielli’s work;
— A conformal tetrahedron, our implementation of L. P. Lee’s projection;
— A butterfly projection, based on Steve Waterman’s work (already available in d3);
— The Cahill-Keyes M-shaped projection, based on Mary Jo Graça’s implementation, and ported to javascript by Enrico;
— Buckminster Fuller’s famous Dymaxion Air Ocean map, with a fresh implementation by us (to be published);
— Finally, a “Voronoi” projection, invented and implemented by us (published here).

All these projections are based on d3.js’s geo module by Mike Bostock and Jason Davies. The most recent ones make use of the “clip-polygon” feature, originally created by Jason and adapted to d3v4 by us, that allows more types of polyhedral projections into d3-geo-projection. This work is in the process of being released.

Public domain images of several planets and moons were projected: the Earth, our Moon, Mars, Phobos, Iapetus, Saturn… To compute the actual projections, we used a custom script that, depending on the projection and the size of the images, needs up to 15 minutes to process. (We don’t plan to release this script, but please contact us if you’d like to know more.)

You can find the PDFs below, ready to print. Note however that they were made for large format (11”×17”) paper. Should you want to print them, don’t do it at home — visit a professional print shop (or steal from work), you’ll get much better quality in ink and paper, and it will certainly cost less.

Another option is to print on photo paper, which gives a very nice glossy result that is easy to fold, and the ink doesn’t crack on the edges. However it can quickly become expensive for larger prints. (And if you are in San Francisco, please contact the Unconf organizers, who might be able to give you a few pages from a secret stash.)

View and Download the files from

JPEG - 131.2 KiB
1. Dymaxion Blue and Iapetus
Click to download PDF
JPEG - 117.5 KiB
2. Lee’s tetrahedral projection — Jupiter and Phobos
Click to download PDF
JPEG - 125.7 KiB
3. Cahill-Keyes (schematic) and Voronoi projections
Click to download PDF
JPEG - 131.1 KiB
4. Cahill-Keyes (blue Earth) and Voronoi projections, cubic Luna
Click to download PDF
JPEG - 140.5 KiB
5. Dymaxion gray, Lee’s Luna
Click to download PDF
JPEG - 147.3 KiB
6. Cubic Mars, Butterfly Earth
Click to download PDF

PS: Huge thanks to Ian and Siu-mei!