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Definition: Let X be a compact Hausdorff space. A triangulation of X is a collection of curved triangles A_1, ... , A_n in X whose union is X such that for i not equal to j, the intersection of A_i and A_j is either empty, or a vertex of both A_i and A_j, or an edge of both.
Source: Topology (second edition) by James R. Munkres