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:
“This is the frost coming out of the ground; this is Spring. It precedes the green and flowery spring, as mythology precedes regular poetry. I know of nothing more purgative of winter fumes and indigestions. It convinces me that Earth is still in her swaddling-clothes, and stretches forth baby fingers on every side.”
—Henry David Thoreau (1817–1862)