Examples of Higher Rank
As stated above, this concept of an abstract polytope is very general, and includes:
- Apeirotopes, i.e. infinite polytopes or tessellations (tilings)
- Decompositions of other manifolds such as the torus or real projective plane
- Many other objects, such as the 11-cell and the 57-cell, that don't fit well into "normal" geometric spaces.
In general, the set of j-faces (−1 ≤ j ≤ n) of a traditional n-polytope form an abstract n-polytope.
Read more about this topic: Abstract Polytope
Famous quotes containing the words examples of, examples, higher and/or rank:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“There is one thing higher than Royalty: and that is religion, which causes us to leave the world, and seek God.”
—Elizabeth I (1533–1603)
“I esteem it the happiness of this country that its settlers, whilst they were exploring their granted and natural rights and determining the power of the magistrate, were united by personal affection. Members of a church before whose searching covenant all rank was abolished, they stood in awe of each other, as religious men.”
—Ralph Waldo Emerson (1803–1882)