Polyhedron

Symbol-free definition
A topological space is termed a polyhedron if there is a homeomorphism to it from the underlying space (viz, geometric realization) of a (finite) simplicial complex. The simplicial complex, along with the homeomorphism, is termed a triangulation of the topological space.

Definition with symbols
A topological space $$X$$ is termed a polyhedron if there is a (finite) simplicial complex $$K$$ and a homeomorphism $$h:|K| \to X$$. The pair $$(K,h)$$ is termed a triangulation of $$X$$.

Stronger properties

 * Differentiable manifold

Weaker properties

 * CW-space