Rhombic Hexecontahedron

A procrastination inspired google search of “modular origami blog” lead me to this site which inspired me to fold the rhombic hexecontahedron pictured below. Rhombic hexecontahedron. Doesn’t that have a nice geeky ring to it?

A 30 second math lesson: A rhombus is sort of like a square that someone stepped on and made into a diamond. A special type of rhombus is a golden rhombus in which the ratio of the “width” to the “length” of the rhombus is 1:phi where phi is the golden ratio. The golden ratio is incredibly cool. Anyway, you can make lots of different polyhedra using rhombi as the faces. One such polyhedra is the rhombic triacontahedron which has 30 golden rhombi faces and strong links to more everyday polyhedra like the dodecahedron and icosahedron. Now if you stellate (which sort of means stick a little pyramid on each face) the rhombic triacontahedron you wind up with the 60 face rhombic hexecontahedron. Ta da!

The faces of my model were made from a variation of this unit folded from square paper that was folded and ripped down to a golden rectangle (instructions in pdf). I could have measured and cut the paper down first but I decided to be a purist and make things more challenging. Unfortunately this added another layer of potential for error into the origami process. This is probably why my units didn’t fit together as tightly as I would have liked. It’s still pretty cool though.