General Instructions for building a polyhedron model
This technique is primarily from Mangus Wenninger's Polyhedron book, Polyhedron Models.
What you will need;
- thin cardboard (not corrugated), from back of pads of paper from cereal boxes, shirt cardboard, etc.
- ballpoint pen
- straight edge
- old magazine
- compass point or T-pins to mark vertices
- white glue
- construction paper
- bobby pins or other clamps
For each of the models there is a template to be made of the various faces. Let's begin with one of the Platonic Solids which all have only one template.
A cube (hexahedron) is made of 6 squares. I'll begin by creating one template that will be used to make the six sides.
I use a computer drawing program to create a paper picture of a perfect square.
I cut the square out of the paper but leave lots of extra paper around the border
and then glue that ragged image to a piece of thin cardboard. When the glue is dry, cut the image and the cardboard more carefully. This is an important step. An accurate template is important for a neat and well-aligned polyhedron.
I like to think of the line that defines my square template as having 3 places to cut.
- I could cut the line off.
- I could cut through the line.
- Or I could leave the line on.
I leave the line on but cut close to it in order to achieve a truly square template.
We won't be tracing around this template. We will only be using it to mark the vertices of the square.
Now you are ready to create the faces of your polyhedron.
For my cube I will use 3 different colors of paper. On my model, parallel faces will be the same color.
Put an old magazine on your desk with a piece of construction paper on top of it. Lay your template on the construction paper and allow room in the construction paper for a 1/4 inch border outside of your template. With your compass point or a T pin, poke a hole just outside of your template at the square's vertices and then remove the template.
With your straight edge and ballpoint pen, carefully connect the dots created by your hole punching. These lines that connect the holes will serve as fold lines and their indentation created by the ballpoint pen will help you make a perfect fold. This is called scoring the paper.
Now you must trim the piece and leave on 1/4 inch border that will become the tabs of each face. The tabs of one face will be glued to the tabs of other faces.
Now trim your construction piece so that the corners of your polyhedron will be free from bunched extra material.
After you have made at least two faces, spread white glue thinly on one tab. Connect two of your faces together by aligning the two face tabs perfectly. Make sure that their faces, when viewed from the good side, are in the same plane and that their two sets of vertices align.
Clamp the glued surfaces together with bobby pins or any other small clamp and set the piece aside for 5 minutes to dry.
If you alternate the gluing and cutting parts of this procedure, you won't be just sitting and waiting for pieces to dry before continuing.
All of your pieces are connected in this manner. When you finally get to the last piece you have to connect it differently. You now have only a small space to work within. Think of the last piece as the lid of a box. Glue one remaining edge to the last facial piece. Now your box has a lid with a hinge. Allow it to dry.
Then glue the remaining edges and lower them into place like closing the lid of the box. Hold the finished polyhedron until those last pieces have had time to dry.