What’s the easiest way to explain why only 5 polyhedrons exist?
In: Mathematics
I think the easiest way to explain is by looking at the corners of the shapes. In order to get a regular polyhedron, we need to construct it entirely out of regular polygons. Looking at the regular polygons, only 3 of them (triangle, square, and pentagon) can actually form a corner, where 3 or more polygons meet. With a hexagon, 3 regular hexagons connected by their corners form a plane and can’t actually fold into a corner. And anything higher than that will overlap.
Likewise, while we can form a corner with 3 squares and regular pentagons, if we try to connect 4 regular pentagons or squares, we will run into the same problem. On the other hand, we can connect up to 5 triangles and still form a corner.
In total, we have 5 regular polyhedrons. 3 formed by triangles with a 3 triangle corner, 4 triangle corner, and 5 triangle corner, one formed by a 3 square corner, and one formed by a 3 pentagon corner.
Latest Answers