Classes of Noble Polyhedra
There are four main classes of noble polyhedra:
- Regular polyhedra are also noble.
- Disphenoid tetrahedra. These and the Platonic solids are the only convex noble polyhedra.
- Crown polyhedra or Stephanoids. An infinite series of toroids.
- A variety of miscellaneous examples. It is not known whether there are finitely many, and if so how many might remain to be discovered.
If we allow some of Grünbaum's stranger constructions as polyhedra, then we have two more infinite series of toroids:
- Wreath polyhedra. These have triangular faces in coplanar pairs which share an edge.
- V-faced polyhedra. These have vertices in coincident pairs, and degenerate faces.
Read more about this topic: Noble Polyhedron
Famous quotes containing the words classes of, classes and/or noble:
“Genocide begins, however improbably, in the conviction that classes of biological distinction indisputably sanction social and political discrimination.”
—Andrea Dworkin (b. 1946)
“There were three classes of inhabitants who either frequent or inhabit the country which we had now entered: first, the loggers, who, for a part of the year, the winter and spring, are far the most numerous, but in the summer, except for a few explorers for timber, completely desert it; second, the few settlers I have named, the only permanent inhabitants, who live on the verge of it, and help raise supplies for the former; third, the hunters, mostly Indians, who range over it in their season.”
—Henry David Thoreau (1817–1862)
“A noble person confers no such gift as his whole confidence: none so exalts the giver and the receiver; it produces the truest gratitude. Perhaps it is only essential to friendship that some vital trust should have been reposed by the one in the other. I feel addressed and probed even to the remotest parts of my being when one nobly shows, even in trivial things, an implicit faith in me.... A threat or a curse may be forgotten, but this mild trust translates me.”
—Henry David Thoreau (1817–1862)