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If I take a finite collection of polyhedra and glue their faces together (potentially gluing two faces of the same polyhedron together) to get a closed 3-manifold, is this always a CW-complex? Can I use the Euler characteristic on the number of vertices, edges, faces and polyhedra?

zyx123
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  • If I ensure that I get a manifold, can I use the Euler characteris #vertices -#edges +#faces - #polyhedra – zyx123 Oct 13 '22 at 03:30
  • Gluing pairs of faces of polyhedra to each other, and potentially gluing faces of polyhedra tofaces of the same polyhedron. – zyx123 Oct 13 '22 at 03:31

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