## Dodecagon Edges

#### Problem

A cube (regular hexahedron) consists of 6 faces and 12 edges.

A dodecahedron has 12 faces, how many edges does it have?

#### Solution

If we dismantle a wire frame dodecahedron in the following way:

The top section is made up of 10 edges; a pentagon (5 edges) plus five. The bottom section is made up of exactly the same, plus middle ring of 10 edges. That is, a dodecagon has 30 edges.

How many edges does an icosahedron (20 faces) have?

What about the other Platonic solids?

Can you find a connection between the number of faces, edges and vertices?

Investigate other solids.

Problem ID: 73 (Apr 2002) Difficulty: 2 Star