We have colored the example above with turquoise stain (intense on the outside and light on the inside) but students may prefer to try their own creative coloring ideas

- 60 pieces laser-cut from 1/8-inch thickness (3 mm) plywood using this template.
- 250 uncolored 4-inch cable ties (example)

- Diagonal wire clippers (example)

- Optional stain and foam brushes if coloring the wood (e.g., ColorCraft Brusho and foam brush)

1. This is the last (and trickiest) of four related geometric sculpture activities. For an introduction to the materials and concepts, students should first do the others.

2. 180 ties are needed for the design, but have extras available because some mistakes will be made, which need to be clipped and discarded.

3. Our example, illustrated above, is stained turquoise on the outside and a light turquoise on the inside. Other colors, a solid color, or no coloring are all options. We also chose to leave the outer cable ties untrimmed for an organic feeling, but feel free to clip yours.

4. We don't advise scaling this design to be any smaller, because it would be difficult for hands to fit through the openings and work inside.

1. Laser-cut the parts. Smoke marks can be minimized by applying tape to the bottom surface before cutting or the surfaces can be lightly sanded afterward. A quick light pass on both sides with an orbital sander (150 grit) removes smoke marks, gives the parts a smooth tactile surface, and prepares them for staining.

3. It is not crucial to bevel the center prong and it is somewhat tricky to do, because the proper angle is very flat. If you do bevel it, be sure to remove material from the

1. Remind students about safety when using cable ties: Cable ties should only be used for the construction and can be dangerous if placed around any part of the body. (See the previous geometric sculpture activities for additional cable tie instructions.)

2. Organize students in groups of two or three. Hand out three pieces to each group.

3. In order to familiarize students with the parts, discuss the following observations: All the parts are identical. There are six connection points in each piece, where a cable tie will be used to connect it to another piece. The connection points at the five straight edges (which includes the central prong) each have a single hole, but the interior connection point has a double hole.

4. Explain that we will initially make a module of three pieces with three-fold rotational symmetry using the prong and the interior double hole. Ask students to figure out what it might be. (They may also discover that 3-fold structures can be made by connecting the parts in other ways, but we want to begin by using the prongs.) When they have a solution, they can hold their three pieces together in position and compare it to the rest of the class. Point out groups with the correct arrangement. The correct assembly is shown above, both from the outside and the inside. Note that the three prongs are hidden on the inside

5. When each group has the parts positioned properly, hand them three cable ties so they can connect the parts. Explain that for the box at the end of the cable tie to be hidden, they should begin on the inside (the lighter color here) which will be more hidden in the final result. A gentle tug while wiggling the tail will snug up the connection.

6. Check each module to ensure the parts are
properly joined and the ties are tight. You can snip off
the tails with the wire cutter as a mark of which modules you
have checked.

9. At this stage, we have added five more modules around one of the groups of five. This view is from the side, with the original 5-fold vertex now at the top. The new five can be added in parallel, with five groups of students working at once on all sides.

11. At this stage, we turn it over and the remaining cycle of five can be added like a hat.

12. When complete, check that all the connections are correct and all the cable ties are tight. You might notice in this closeup view that we inserted all the ties in a consistent manner, so they spiral in the same way around each vertex, but this is a fine point not to worry about the first time doing this assembly.

13. Along the way, students should be able to determine that 180 cable ties are required, since each part has six connection points.

1. Students should locate the 2-fold, 3-fold, and 5-fold axes and see that the sculpture has the same rotational symmetry as a regular icosahedron or dodecahedron. Note that the 2-fold axes pass through openings that are four-sided, but careful examination shows them to have 2-fold, not 4-fold, symmetry.

2. If students sight along the planes to look for co-planar pieces, they should observe that there are none. Each piece lies in its own plane, so the sixty parts lie in sixty different planes.

A. Try all four sculpture activities.

B. Try the Symmetry Search game described here.

C. With some trigonometry, you can calculate what the bevel angle should be, if you start by measuring the angle at the tip of the part.