Put the faces of the polyhedra so that the colors of the faces in contact match
- Location: Martin Gardner Room
- Minimum age: from 6 years old.
- Required time: 5 minutes each
- Number of participants: One or more people
- Keywords: permutations, cube, dodecahedron
- Taxonomy: Geometry, Combinatorics
Color matching is at vertices
The color match is on the edges
How to combine colors on faces?
In the case of the cube, it turns out that the circular permutations of 4 elements are precisely 6. You can put the 6 faces on the table with a color always on the top to see that there is indeed no different way of these 6 to order the 4 colors.
It coincides that the cube also has six faces and that it is possible to reconstruct it with these six squares so that the colors match.
Once resolved, look at: What are the opposite faces like?
In the case of the dodecahedron, the circular permutations of 5 elements are 24, but since the dodecahedron has 12 faces, half of them have been chosen to make this module.
By working methodically in an orderly manner it is possible to reconstruct the dodecahedron in a few minutes. Once resolved notice how the opposite faces are symmetrical. Thus, the 12 chosen faces can each be paired with their symmetry.
