Improper element

From Polytope Wiki
Jump to navigation Jump to search
The Hasse diagram (right) of a square pyramid. U and Ø are the improper elements.

An element of a polytope is called improper whenever it's the minimal or maximal element of the polytope. These elements can be thought of as the empty set and the entire polytope. All other elements are said to be proper.[1]

Traditionally, these elements aren't considered. Nevertheless, taking them into account is mathematically convenient in a lot of circumstances. If we were to ignore them, the following annoyances would occur:

Despite all of this, one can generalize polytopes in a way that completely ignores the improper elements, as hypertopes.

References[edit | edit source]

  1. McMullen, Peter; Schulte, Egon (2002). Abstract Regular Polytopes. Cambridge University Press. p. 23.