Gift to the 2013 Origami USA annual Holiday Tree at the American Museum of Natural History in New York. Based on my lizard hex base.

The third in a series of Penrose tessellations, with seventy cells, made by subdividing the layout of the second tessellation. Folded from a pentagonal sheet.

The second in a series of Penrose tessellations, with thirty-five cells, made by subdividing the layout of the first tessellation. Folded from a pentagonal sheet.

The first in a series of Penrose tessellations, with ten cells. Folded from a pentagonal sheet.

The shape is based on the regular dodecahedron, a platonic solid composed of twelve regular pentagons. The stellated version replaces each face with a five-sided pyramid, resulting in a star-like shape composed of sixty triangles. My Stellated Dodecahedron is the result of a long and arduous quest. I made several attempts at it a few years back, but it was beyond my skill at the time, and I only barely managed to make one out of a giant sheet of foil, and it didn't hold together too well. For the new attempt I began with a pentagon sheet of paper rather than a square. When I got to the end I had a nice array of identical flaps that made perfect tabs, and I was able to use a twist-lock to finish the model.

The shape is a complement to the Stellated Dodecahedron. Both are composed of sixty triangles and form star shapes out of sets of coplanar faces. With the Great Dodecahedron, the coplanar faces form a pentagon with the star rising out of the middle in the negative space. This model is a development of my previous version, folded one from a square. The new is folded from a pentagon, and has a refined CP so the corners provide nice flaps and the model goes together well and holds its shape quite strongly.

Cats and dogs are challenging subjects because they're so familiar to humans. This model was inspired by the animal adoption service Timber's Legacy. Having the subject in a sitting posture allowed me to focus more on the overall shape and sculptural aspects rather than worrying much about the base and where the points for all the legs would come from. This dog has pointy ears, which is rare in origami dogs.

Once I had my dog worked out, I figured the cat would be a simple variation, but it turned out the pretty different. Not only is the head and face totally different, but the long tail required a whole new geometry and base. Finally, the body posture, neck and shoulders were different enough to have to come up with a new treatment. It took quite a few iterations before I had the details refined enough to attempt one out of good paper.

A 3-D evolution my Penfractal Tessellation. Each face of the dodecahedron is subdivided into six smaller pentagons. The model also makes a reasonable representation of the dodecahedral analog of the tesseract, albeit in 3-d hyperbolic space rather than true 4-d space (trust me on this; I looked it up). This model was the beginning of a whole series folded from pentagonal sheets of paper.