Another view of my piece ...

Here are the images of my final piece:

Finally! A Dodecahedron-shaped Flowery Ball Thing!

Finally, after about two hours of folding and 5 hours of assembling the thing over and over again (until I got fed up and hot-glued it), I have a dodecahedron-shaped flowery ball thing.

It looks pretty much like it was supposed to, except it's a little bit crooked.

Next I'm going to try and make a dodecahedron using modular units from a pattern that I found and modified slightly. It should end up looking sort of floral, like a hydrangea or an agapanthus, hopefully ...

Fingers crossed.

Tetrahedron Form

Here's a tetrahedron form that I'm using in my art work:

It's made from three pieces of thick paper to hold the shape.

Each piece of paper is formed into a modular unit that has pockets and tabs that are able to be interlocked into other units in order to assemble a geometric shape.

Here's one of the parts for my Math & Art work. It's a pinwheel-shaped piece made with eight modular units.

A more successful butterfly ...

An experiment at making a butterfly ....

I don't think it worked particularly well.

Kusudama Piece Unfolded

This is the kusudama when it's unfolded back to a sheet of flat paper.

Kusudama Piece Side View

Kusudama Piece

This piece is called a kusudama.

Math & Art Essay

Here's the link to my Math & Art essay:

Math & Art Essay

The Huzita-Hatori Axioms:

1. Given two lines L1 and L2, a line can be folded placing L1 onto L2.
2. Given two points P1 and P2, a line can be folded placing P1 onto P2. Line equation is F(s) = P1 + s(P2 - P1).
3. Given two points P1 and P2, a line can be folded passing through both P1 and P2.
4. Given a point P and a line L, a line can be folded passing through P and perpendicular to L.
5. Given two points P1 and P2 and a line L, a line can be folded placing P1 onto L and passing through P2.
6. Give two points P1 and P2 and two lines L1 and L2, a line can be folded placing P1 onto L1 and placing P2 onto L2.
7. Given a point P and two lines L1 and L2, a line can be folded placing P onto L1 and perpendicular to L2.

These rules are also known as the Huzita-Justin Axioms, named for Humiaki Huzita and Jacques Justin, and Humiaki Huzita and Koshiro Hatori respectively. They are a set of rules related to the mathematical principles of origami.

Apparently, because these axioms have several solutions, the resulting geometries are stronger than those resulting from compass and straightedge geometries.