This paper presents an approach to the theory of Riemannian manifolds that avoids the use of coordinates. Instead, curved spaces are approximated by higher-dimensional analogs of polyhedra. The authors develop the theory of intrinsic curvature on polyhedra, following the work of Aleksandrov. They define the Gaussian curvature for geodesic triangles and show how to approximate any surface by a sequence of polyhedra with an increasing number of faces. The local curvature is defined as a measure rather than a function, and the integral curvature theorem is derived, connecting it to Euler's formula for the genus of the polyhedron. This approach provides a simplified model that captures essential features of topologies like Wheeler's wormhole and offers deeper geometrical insights.This paper presents an approach to the theory of Riemannian manifolds that avoids the use of coordinates. Instead, curved spaces are approximated by higher-dimensional analogs of polyhedra. The authors develop the theory of intrinsic curvature on polyhedra, following the work of Aleksandrov. They define the Gaussian curvature for geodesic triangles and show how to approximate any surface by a sequence of polyhedra with an increasing number of faces. The local curvature is defined as a measure rather than a function, and the integral curvature theorem is derived, connecting it to Euler's formula for the genus of the polyhedron. This approach provides a simplified model that captures essential features of topologies like Wheeler's wormhole and offers deeper geometrical insights.