A delta-complex is obtained by gluing standard simplexes along affine face maps, allowing different vertices or faces of one simplex to acquire the same image. Every simplex interior is mapped injectively, and the topology is determined simplexwise. Unlike an abstract simplicial complex, its simplexes need not be determined by their sets of global vertices. A circle built from one edge with its two endpoints identified is a basic example. Subdivisions remove these repeated-vertex and repeated-simplex obstructions.
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