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
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—Bernard Mandeville (1670–1733)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
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