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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