Duality of Regular Solids

Continue to the duality example

Two polyhedra are dual if:

1. The faces of one correspond to the vertices of the other, and vice versa.
2. Each edge separating adjacent faces in one corresponds to the edge joining the corresponding vertices in the other.

The five classic regular polyhedra (Platonic solids) include three dual pairs.

• Tetrahedron is dual to tetrahedron.
• Cube is dual to octahedron.
• Dodecahedron is dual to icosahedron.

Navigation:

1. To rotate a dual pair, drag the mouse over it while holding the LEFT button down.
2. To bring a dual pair closer to or farther from the camera, hold the mouse WHEEL (MIDDLE button) down and move the mouse up or down. (Due to a fit of sloth, I haven't implemented this for turning the mouse wheel.)
3. To bring the camera closer to or farther from a dual pair, hold the SHIFT key down and either
   • rotate the mouse WHEEL or else
   • hold it down and move the mouse up or down.
4. To move a dual pair around, drag the mouse over it while holding the RIGHT mouse button down.
5. To roll a dual pair around, drag the mouse over it while either:
   • holding the LEFT button and the SHIFT key down; or
   • holding bother LEFT and RIGHT mouse buttons down.
   We get this effect by invoking two controls, the rotate control from (1) and the move control from (3).
6. To zoom the camera, drag the mouse (anywhere) while holding down the LEFT and MIDDLE (WHEEL) mouse buttons.
7. To move the camera in a plane relative to an object, drag the mouse on that object while holding down the MIDDLE (WHEEL) and RIGHT mouse buttons.

I realize that not all possible combinations will work on all platforms. For example, touchpads and Apple-type mice don't have an equivalent for pressing the mouse wheel (A.K.A. the middle button). I may look at this in the future, but meanwhile, if you want to fiddle with it…