Is there a theory of isometrically embedded polyhedra on manifolds?

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There is a book that is called embeddings in manifolds that studies topological embeddings and how they relate to each other (by homeomorphisms).

I was wondering if there is a study of isometrically embedded polytopes in manifolds. "Isometric" here would probably mean conservation of the metric (as in metric spaces) rather than the Riemannian structure.

So I would like to ask if there is anything I can find on the topic, if there is such topic, preferably a book but papers will do as well?