Teacher resources and professional development across the curriculum

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Platonic Solids

In this lesson on three-dimensional solids, you've seen a lot of polyhedra. But there are five special polyhedra — known collectively as the Platonic solids — that are different from all the others.

What makes the Platonic solids special? Well, two things, actually.

1. They are the only polyhedra whose faces are all exactly the same. Every face is identical to every other face. For instance, a cube is a Platonic solid because all six of its faces are congruent squares.

2. The same number of faces meet at each vertex. Every vertex has the same number of adjacent faces as every other vertex. For example, three equilateral triangles meet at each vertex of a tetrahedron.

No other polyhedra satisfy both of these conditions. Consider a pentagonal prism. It satisfies the second condition because three faces meet at each vertex, but it violates the first condition because the faces are not identical — some are pentagons and some are rectangles.

An illustration of platonic shapes.

Explore Platonic Solids and Input Values

Image of Platonic Flat shapes Print out the foldable shapes to help you fill in the table below by entering the number of faces (F), vertices (V), and edges (E) for each polyhedron. Then, take your examination a step farther by selecting the shape of each polyhedron's faces. As a final step, calculate the number of faces that meet at each vortex of the given polyhedron. Start at blinking cursor in the yellow box and hit the enter key after each answer is inputted. Feedback will be given immediately. As in the other activities, if your calculation is wrong, your answer will appear in red and you will be given two hints and two more chances before the correct answer is displayed.

Depending on the speed of your computer and internet connection,
there may be a wait time of a few seconds before error messages appear.

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