On the geometric realization of a finite abstract simplicial complex which is connected, orientable $3$-manifold without boundary

Question

Let $\Delta$ be an abstract simplicial complex on finitely many vertices and $|\Delta|$ be it's geometric realization. (https://en.m.wikipedia.org/wiki/Abstract_simplicial_complex)

If $|\Delta|$ is a connected, orientable, $3$-manifold without boundary, then is $|\Delta|$ Homeomorphic to the sphere $\mathbb S^3$ ?

Answer 1

Any $3$-manifold is triangulable and if it is compact then the triangulation is finite. In particular the $3$-torus is the geometric realization of a finite simplicial complex, so the answer to your question is "no".