Selim Tezel's 3D Dodecahedron-Icosahedron Duality Simulator

Use the up-down-right-left arrow keys and the "a" and "z" keys to rotate the shape(s) in 3D along the x,y,z axis.
1 key to show/hide Icosahedron
2 key to show/hide Dodecahedron
3 key to show Icosahedron as the dual of Dodecahedron
4 key to show Dodecahedron as the dual of Icosahedron
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Exercises:
Go to myNote   to install the note-taking bookmarklet.
Do some research and answer the following questions, taking your notes with myNote and using the diagram as needed.
-What is meant by "duality" of polyhedra?





-What are the duals of the remaining Platonic solids: Tetrahedron, Cube, Octahedron?





-Verify Euler's famous equation: F-E+V=2 for the icosahedron and the dodecahedron.





-Study Kepler's work on polyhedra. Why did he think Platonic Solids were related to the planetary orbits?