Duality of The Regular Polyhedra
The regular polyhedra come in natural pairs, with each twin being dual to the other (i.e. the vertices of one polyhedron correspond to the faces of the other, and vice versa):
- The tetrahedron is self-dual, i.e. it pairs with itself.
- The cube and octahedron are dual to each other.
- The icosahedron and dodecahedron are dual to each other.
- The small stellated dodecahedron and great dodecahedron are dual to each other.
- The great stellated dodecahedron and great icosahedron are dual to each other.
The Schläfli symbol of the dual is just the original written backwards, for example the dual of {5, 3} is {3, 5}.
For further information please see the individual articles or the general polyhedron article.
Read more about this topic: Regular Polyhedron
Famous quotes containing the word regular:
“It was inspiriting to hear the regular dip of the paddles, as if they were our fins or flippers, and to realize that we were at length fairly embarked. We who had felt strangely as stage-passengers and tavern-lodgers were suddenly naturalized there and presented with the freedom of the lakes and woods.”
—Henry David Thoreau (1817–1862)