Three Dimensions
In a polarity of real projective 3-space, PG(3,R), points correspond to planes, and lines correspond to lines. By restriction the duality of polyhedra in solid geometry is obtained, where points are dual to faces, and sides are dual to sides, so that the icosahedron is dual to the dodecahedron, and the cube is dual to the octahedron.
Read more about this topic: Duality (projective Geometry)
Famous quotes containing the word dimensions:
“Is it true or false that Belfast is north of London? That the galaxy is the shape of a fried egg? That Beethoven was a drunkard? That Wellington won the battle of Waterloo? There are various degrees and dimensions of success in making statements: the statements fit the facts always more or less loosely, in different ways on different occasions for different intents and purposes.”
—J.L. (John Langshaw)
“I was surprised by Joe’s asking me how far it was to the Moosehorn. He was pretty well acquainted with this stream, but he had noticed that I was curious about distances, and had several maps. He and Indians generally, with whom I have talked, are not able to describe dimensions or distances in our measures with any accuracy. He could tell, perhaps, at what time we should arrive, but not how far it was.”
—Henry David Thoreau (1817–1862)