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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

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