Penultimate Module-Truncated Octahedron

Project taught by Dr. Eva Szillery at the Downtown Education Collaborative in Lewiston, ME.

The project was originally designed by:

For more information:  http://www.cs.utk.edu/~plank/plank/origami/penultimate/intro.html

A truncated octahedron has six square faces and eight hexagonal faces.

36 pieces are required:

12 hexagon-hexagon

24 square-hexagon

Directions to make a square-hexagon unit:

1)  Prepare 36 squares, fold them in 4, then carefully cut off the top

rectangle.  This step is exactly like the preparation of the penultimate

model cube.

2a)  Flatten the square so that you can see a "z" shape when viewing

from the right side.

2b)  Top view shown below:

3)  Fold the lower left corner up, and the upper right corner down to

create a parallelogram as shown below.

4)  Line up a piece of cardboard or note card diagonally across the

middle rectangular piece.  Be sure that the edge of the cardboard piece

creates a straight line from the lower left corner to the upper right corner

of the rectangle.

5)  Pull the top portion down over the card, and create a crease along

the edge of the card.

6)  Remove the cardboard piece, and check to see that there is a sharp

crease that runs diagonally across the middle rectangle.

7)  Open the triangle on the right side, and bisect its angle as shown

below.

8)  In the next step, create a fold to bisect the angle indicated below.

9)  This fold should cause the creases to line up on the upper and lower

layer.

10) Turn over...

11)  The next step is to open the triangle on the right then fold it down as shown in step 12.

12)  Notice that the right corner has a 90 degree angle, while the left

corner has a 120 degree angle.  The shape below is a finished

"square-hexagon" unit. 

Directions to make a hexagon-hexagon unit:

1) Fold the corners as shown below.

2)  Create a diagonal fold as shown below.

3)  Open the triangles on the ends as shown below.

4)  Fold the triangle in half so that the edge lines up with the crease

as shown below.

5)  Now open the small triangle and bisect as shown below.

6)  Turn the shape over and do the same fold on the other side to

create the finished "hexagon-hexagon" unit shown below.

To assemble, be sure you have 24 square-hexagon units and

12 hexagon-hexagon units.  Then use four of the square-hexagon

units to make the first square face of the truncated octahedron.

Off of the first square, you can begin building the first hexagon faces.

The hexagon-hexagon units will be used when you realize that a

square-hexagon unit will not work...