The dodecahedron is one of the 5 platonic solids. It is a regular
convex polyhedra with each of its 12 sides being a regular
pentagon. Using trigonometry and/or vector geometry, can you
find the angle between two adjacent sides of the dodecahedron?
To help, the applet below attempts to show a method of constructing a dodecahedron around a cube. Click "Draw cube" and then "Draw dodecahedron" or the other way around.
A roof like structure is formed on each face of the cube. The roof
itself is constructed from the pentagons as shown in the following diagrams:
For a brief introduction to the five Platonic polyhedra with a much better applet which also illustrates dual shapes and other inclusions, try this link to Gian Marco Todesco's page.Home