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:
““I couldn’t afford to learn it,” said the Mock Turtle with a sigh. “I only took the regular course.”
“What was that?” inquired Alice.
“Reeling and Writhing, of course, to begin with,” the Mock Turtle replied; “and then the different branches of Arithmetic—Ambition, Distraction, Uglification, and Derision.”
“I never heard of ‘Uglification,’” Alice ventured to say.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)