Polystroma

Polystromata are combinatorial objects introduced by Branko Grünbaum. They are considered a precursor to the modern concept of abstract polytopes.

Definition
A polystroma is a partially ordered set with a single minimum element.

Regular polystromata
A flag of a polystroma is a totally ordered subset of  which is not a proper subset of any other totally ordered subset of.

The automorphism group of a polystroma is the group of order preserving bijections on the elements of

A polystroma is regular iff its automorphism group acts transitively on its flags.

Comparison to abstract polytopes
The definition of polystromata is much weaker than that of abstract polytopes. Polystromata are not required to be connected, meet the diamond condition, or have a maximal element, among other considerations. This specificity of abstract polytopes has made them richer objects of study.