Examples
All 1-dimensional polyhedral spaces are just metric graphs. A good source of 2-dimensional examples constitute triangulations of 2-dimensional surfaces. The surface of a convex polyhedron in is a 2-dimensional polyhedral space.
Any PL-manifold (which is essentially the same as a simplicial manifold, just with some technical assumptions for convenience) is an example of a polyhedral space. In fact, one can consider pseudomanifolds, although it makes more sense to restrict the attention to normal pseudomanifolds.
Read more about this topic: Polyhedral Space
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