What do we call well-founded posets whose elements have a unique height?

What do we call those well-founded posets $P$ with the property that for every $x \in P$, all maximal chains in the lowerset generated by $x$ have the same length? Examples:

  • The set of all finite subsets of a (possibly infinite) set.
  • The set of all finite-dimensional vector subspaces of a (possibly infinite-dimensional) vector space.
  • The set of all finite-dimensional affine subspaces a (possibly infinite-dimensional) affine space.
  • Any set-theoretic tree.
  • Any poset that could reasonably be construed as an “abstract polytope.”

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