March 9, 2020
By Elaine Wolfe

Elaine Wolfe is a special guest editor. More information on her other projects can be found on her blog.

Rubber band pop-up polyhedrons are intriguing. They are the intersection of mathematics and physics. The process of compressing the figure stores energy in the rubber band inside the figure. When the collapsed two dimensional shape is allowed to be transformed back into a polyhedron, the stored energy makes the figure pop-up. These pop-ups are a fun way to explore mathematics and physics together.

Bifrustums and bicupolas are names given for different types of polyhedrons. For more information about them can be found here.

Materials Needed for this project:

• 65 lb. card stock (This can be found at any craft shop.)
• Aleene’s Tacky Glue. (This is a great quick-drying glue that doesn’t warp the paper when used sparingly.)
• Glue Dots. (Use 3/8 inch Glue Dots rolled into balls and attached to the tail of the rubber band to keep the rubber band from slipping out of the hole with repeated opening and closing of the model.)
• Scotch Tape to anchor the rubber band with the Glue Dot down to the tab.
• 1/16 inch rubber bands. (Please note that different rubber bands may have different tensions. Lengths given here are an estimate.)
• Scissors or an electronic paper cutter like a Silhouette or Cricut.
  

Files:

If you are cutting the models with scissors, here is the PDF.

If you are cutting the models with a Silhouette, here is the .Studio file.

If you are cutting the models with a Cricut, here is the SVG.

The Triangular Bifrustum

Notice in the photo above, the top half of the shape looks like a triangular pyramid without its top. A frustum is a section of an original solid. Since two of these sections are connected, this type of shape is referred to as a bifrustum, with “bi” meaning two.

In this post, we’ll be making a pop-up triangular Bifrustum. Instructions for additional shapes will be linked at the end of this post, and the techniques used here will apply to them as well.

Cut out the triangular bifrustum model and bend the tabs on each section as shown.

Cut and knot a rubber band with approximately 1 inch between the knots. Align the two sections as shown and glue the two pieces together.

Insert one end of the rubber band through the hole in the glued tab. Apply glue to the other folded edge with a round tab on it.

Press the two remaining round tabs together and press along the glued area to make sure the pieces adhere to one another.

Apply a Glue Dot to the tail of the rubber band, then cover both the Glue Dot and the tail with a piece of scotch tape.

Feed the other knotted end of the rubber band through the hole in the opposite round tab.

Repeat the process for gluing and taping on the the second tail of the rubber band.

Apply glue to the remaining tabs and press them together. Press the shape flat and apply pressure to adhere the glue.

After the glue has set, release the shape. The rubber band will pull the sides together, causing the shape to pop back up into a three dimensional object.

More Shapes:

For instructions on how to create additional shapes (as pictured at the beginning of this post), please refer to the document found here.