Introduction: Rhombic Triacontahedron
Make an origami polyhedron. The rhombic triacontahedron is easy to make because it is both face uniform and edge uniform. I came up with this folding scheme by modifying some instructions for a rhombic dodecahedron (http://www.ii.uib.no/~arntzen/kalender/), (http://www.paperfolder.info/diagrams/a4unit.htm).
Step 1: Paper Size
Pick a piece of paper with aspect ratio as close to the golden ratio as possible. You can do this by picking two consecutive numbers in the fibonacci sequence. (Shown here is a 8.5"x5.5" sheet, the aspect ratio of 17:11 isn't very close to the golden ratio.) You will need 30 sheets. Experiment with different colors and patterns.
Step 2: Folding
Fold in half, and then into quarters.
Step 3: Folding
Fold in half the other direction
Step 4: Folding
Fold the corners to the center so that the fold goes from the midpoint on the side to the opposite corner. Repeat for all four corners to make a grid pattern.
Step 5: Folding
Open up the sheet to show the grid of golden rhombi. Fold the corners up in toward the center to make pockets on the sides and tabs at the end. A piece of tape across the center helps to keep the pockets tight.
Step 6: Assembly
Put tabs into pockets, alternating three and five rhombi.
Step 7: Examples
The pink triacontahedron was made from 5.5"x8.5" sheets (aspect ratio of 17:11), and is too loose to stay together. The white triacontahedron was made from readily available 5"x8" index cards and is very sturdy. The multicolored triacontahedron was made from sheets cut to 4.25"x2.625" (aspect ratio of 34:21) and is very tight.
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