Abstract Polytopes
The abstract polytopes arose out of an attempt to study polytopes apart from the geometrical space they are embedded in. They include the tessellations of spherical, euclidean and hyperbolic space, tessellations of other manifolds, and many other objects that do not have a well-defined topology, but instead may be characterised by their "local" topology. There are infinitely many in every dimension. See this atlas for a sample. Some notable examples of abstract polytopes that do not appear elsewhere in this list are the 11-cell and the 57-cell.
Read more about this topic: List Of Regular Polytopes
Famous quotes containing the word abstract:
“One of the fundamental reasons why so many doctors become cynical and disillusioned is precisely because, when the abstract idealism has worn thin, they are uncertain about the value of the actual lives of the patients they are treating. This is not because they are callous or personally inhuman: it is because they live in and accept a society which is incapable of knowing what a human life is worth.”
—John Berger (b. 1926)