Definition. Automorphisms and regularity [schulte2017regular, Section 2] [frap-000G]
Definition. Automorphisms and regularity [schulte2017regular, Section 2] [frap-000G]
An automorphism of a abstract polytope \(P\) is a bijection \(a:P\to P\) satisfying \(F\leq G\iff a(F)\leq a(G)\). Automorphisms form a group \(\Gamma (P)\) under composition; in \(ab\), the map \(b\) acts first. They preserve ranks and act on flags face by face.
The polytope is regular if this action is transitive on flags. The tetrahedron is regular: a permutation of its four vertices sends any flag to any other.
The underlying order automorphism is represented by
OrderIso with equal source and target. This declaration does
not impose the polytope axioms or assert regularity.