Map Projections: Polyhedron Maps

Map Fold-outs


Tetrahedron	Octahedron


Cube	Dodecahedron


Icosahedron	Cuboctahedron


Truncated icosahedron	Truncated octahedron

Practice folding these blank models: the "real" maps have no red crease lines. Preferably score all crease lines with a dull blade before cutting, and paste the shaded face last.
	Rhombicuboctahedron

Assembling

in the map fold-outs, folding lines separating polygon faces are absent; they are included in the crease patterns available here for practice

precision and patience matter most. Small errors can accumulate and prevent fitting the last faces

using a dull blade (or a spent ballpoint pen) guided by ruler or straightedge, lightly and carefully score all folding lines before cutting. This will make creasing easier and more precise

if you prefer scoring the paper's reverse side to avoid scratching the inked surface, use a needle or pin to punch tiny guide holes at every vertex

a utility knife guided by a straightedge is more precise than scissors, but please be careful! To keep better alignment, score or cut as many lines as possible without moving the straightedge; also, use the extra alignment ticks included in several maps

check every white tab's fit before applying glue

a single face (shaded in the preview pattern) should be glued last; it has no tabs, so must be aligned by sight

as a rule of thumb, polyhedra with more (and smaller) faces are harder to assemble. If you take the punch-score-cut-fold approach, expect to spend 7-10 minutes on the tetrahedron, and almost two hours on the truncated icosahedron

Fold-outs

World maps on a regular tetrahedron (5 high-resolution maps, 8 low-resolution)

World maps on a cube (10 high-resolution maps, 7 low-resolution)

World maps on a regular octahedron (5 high-resolution maps, 5 low-resolution)

World maps on a regular dodecahedron (8 new high-resolution maps, 9 low-resolution)

World maps on a regular icosahedron (8 high-resolution maps, 12 low-resolution)

World maps on a truncated octahedron (3 high-resolution maps, 5 low-resolution)

World maps on a truncated icosahedron (2 high-resolution maps, 7 low-resolution maps)

World maps on a cuboctahedron (3 high-resolution maps, 8 low-resolution)

World maps on a rhombicuboctahedron (4 high-resolution maps, 9 low-resolution)

Disclaimers

Although I have carefully programmed my mapping algorithms, I offer no warranty about the precision of these images. The data sets used may be outdated, especially those with country borders.

PDF files included here require Adobe^® Reader^® ("Acrobat Reader"), version 5.0 or more recent, or compatible software like Xpdf, version 3, or Evince, version 0.5.