Map Projections

### Pseudoglobes on a Rhombic Dodecahedron

Pseudoglobes on rhombic dodecahedra, gnomonic projection.

A rhombic dodecahedron is not a regular polyhedron, since its twelve identical faces are diamonds. It and the cuboctahedron comprise a pair of dual polyhedra: for each face of one there is a corresponding vertex in the other, and vice versa. This solid appears in nature in honeycombs, where every cell consists of half a rhombic dodecahedron topped by a hexagonal prism. A honeycomb has two layers of parallel cells opening in opposite directions, and the bottom of each cell nests between the bottoms of three cells of the opposite layer. Coupled with the choice of hexagonal prisms, this is relevant for efficient use of beeswax, as the rhombic dodecahedron, like the cube and the truncated octahedron, can tesselate three-dimensional space: multiple copies can be juxtaposed to fill any volume.

The rhombic dodecahedron has large faces and can be easily built. However, please read the generic assembly tips before beginning. You might also learn something about polyhedral maps and other map projections.

#### Resolution-3 Maps

 Gnomonic projection on a rhombic dodecahedron, black & white (color it yourself): poles on faces (628 KB PDF), poles on acute vertices (616 KB PDF), poles on obtuse vertices (608 KB PDF), Gnomonic projection on a rhombic dodecahedron, flat colors: poles on faces (1336 KB PDF), poles on acute vertices (1244 KB PDF), poles on obtuse vertices (1252 KB PDF), Gnomonic projection on a rhombic dodecahedron, satellite imagery by NASA's The Blue Marble project: poles on faces, data from December 2004 (1376 KB PDF), poles on acute vertices, data from April 2004, lightened seas (1324 KB PDF), poles on obtuse vertices, data from June 2004 (1308 KB PDF),

www.progonos.com/furuti/MapProj/Normal/ProjPoly/Foldout/RhombicDodecahedron/rhombicdodecahedron.html — June 16, 2018