Platonic Solids
Eagle House = 408/449-9039
Plato was not the first to find the set of all regular convex polyhedrons but his name has become attached to them. There are exactly five and they appear and reappear in branch after branch of math, science, tech, art, and nature.
We'd like students to have a firm, intuitive understanding of Platonic Solids but flat drawings are only informative to those who already have the abstract background we wish to build. Young students especially have difficulty forming any sort of good mental picture without handling solid models directly.
If we have a set of models available, well and good. Here we offer a set of printable templates which can be used to build these models with students. Perhaps even if we have models already, we'll find that students benefit from the activity.
Contents |
Project
Download the highest-resolution versions:
Each image is 1575 x 1200 pixels. Print each one at 150 dpi to produce an image 10.5 x 8 inches. This should be adequate for most inkjet printers.
Materials
- Scissors
- Glue
- Toothpicks
- Scrap newspaper
White glue seems to be easiest to use in this project.
Action
Cover entire worktable with newspaper for easy cleanup later.
Cut on the light blue dotted lines. It's easiest to cut out the general shape of each piece first, then make the detailed cuts. The precise shape of each glue tab (colored white) is unimportant but be careful with any cut that touches the piece itself -- any solid black line. Cut away all gray-colored waste paper.
Crease each piece along each solid black line, then unfold.
Glue matching tabs together, making sure all tabs are pushed into the model interior.
A difficulty is that as we complete the assembly of a given solid, the interior becomes inaccessible. We can't reach inside to press the glue tabs together. It's important that the glue tabs press against each other naturally, so unfolding them is critical. Letting the glue get slightly dry and tacky seems to help. Don't use too much glue! Apply small amounts with toothpicks.
Even young students can generally assemble the low-order models; they may need hand-help with dodecahedron and icosahedron.
Note that the dodecahedron comes in two pieces. Assemble each half and let it dry a bit before mating the two halves. It's easiest to "roll up" the icosahedron.
Toothpicks come in handy not only for glue application but also to rescue models about to come to grief because something is stuck too far inside. Take a clean toothpick and pry out the offender.
Another minor crisis arises when, during construction, the paper rips, due to rough handling, too much glue, or a cut taken beyond a black line. The quick fix is to flatten the piece, turn it over, and glue a small patch over the rip. Let dry, restore the crease, and all will be well; the patch is hidden in the interior of the completed model.
Of course, there's no harm at all in bringing several sets to session.
Discussion
- What makes these things special?
- What do we mean by regular and polyhedron?
- Why is the sphere not included in this set? Why not the cylinder? Why not the pyramid?
- Why are there exactly five Platonic Solids and no more?
- There are, after all, an infinite number of regular polygons.
- All these models are the same "size". In what way?
- Each model has been constructed to the same circumradius. Let students visualize each circumsphere.
- Would models in which all edges were equal be the same "size"? Why? Why not?
