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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).

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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.

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.

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.

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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Equation wise, this would be X = 1 + 1/X, where X can be found to be 1+sqrt(5) all divided by 2 or 1.6180339... The Golden Ratio is also key to the Pentagon and Pentagram but that's another story.

All of this is meant only for added information but not meant to improve on the fine work of the author here...

Your first shape doesn't have a specific name it's a kind of penrose tiling

http://www.josephwu.com/Files/PDF/silver-gold.pdf