Symmetries of Polyhedra
How it works
A polyhedron is a closed 3D shape with flat sides, like a cube. For a given polyhedron, if you can move the polyhedron (by turning it or flipping it over, for example) so it looks the same, you’ve found a symmetry of the polyhedron.
In this activity, students build and determine the symmetries of various polyhedra. In addition, they explore how the symmetries of polyhedra change when their faces are not all the same color.
Polyhedron Symmetries Intro handout
Polyhedron Symmetries Recording handout
Why we like this activity
- It’s fun! Students enjoy building the various polyhedra and finding their symmetries.
- It helps to develop spatial reasoning.
It requires students to engage in mathematical habits of mind:
Comparing and contrasting symmetries of different polyhedra and symmetries of different colorings of the same polyhedron.
Finding and using strategies to quickly count the number of symmetries of different polyhedra.
Finding and using strategies to design colorings that have specific symmetries.
- It has a low floor and a high ceiling: Students can get started finding symmetries by trial and error, but there’s much more to explore and discover.
