Woven Fourteenth Stellation of the Icosahedron designed by Daniel Kwan

Some years ago I went to an origami convention, and I thought I’d bring something big and flashy.  So I found this design by Daniel Kwan, decided an appropriate coloring, and the size of the final model surprised me.

No I don’t really know what the “14th Stellation of the Icosahedron is”, I just take Daniel Kwan’s word for it that that’s what it is.  I do know that to “stellate” a polyhedron means to extend the planes of each face outwards, beyond their usual shapes.  Wikipedia has a list of 59 ways to stellate an icosahedron, and this one seems to be arbitrarily designated the 14th stellation.

I always think way too much about how to color these modular origami models.  Most modular origami models have 30 units, each one corresponding to the edge of an icosahedron (or dodecahedron).  You can, of course, choose 30 distinct colors, one for each unit.  Or you could have two colors, one on each hemisphere.  Or you could give it a symmetric coloring–a concept that I rigorously discussed in an old blog series about symmetry in origami.

However, the Woven Fourteenth Stellation of the Icosahedron is different, because it has 60 units, not 30.  Each edge is actually doubled up.  My mind is blown with all the possibilities!  In the end, I used 3 colors of paper: dark green, light green, and the flower pattern, evocative of a floral ball with vines.  The dark green and light green each have with tetrahedral symmetry, 12 units each, but are not interchangeable with one another.  The overall symmetry is secretly cubic.