= Simplicial homeomorphism
A simplicial homeomorphism is the <homeomorphism> of <geometric realizations> induced by an <isomorphism> of <simplicial complexes>: a <bijection> of their vertex sets such that a finite vertex set is a <simplex> exactly when its image is a <simplex>. The map acts linearly in each <barycentric coordinate system>. It and its inverse are <continuous> by the realization <topology>. Between the boundaries of two triangles, any <bijection> of the three vertices extends linearly on edges to a simplicial homeomorphism. This ensures that the edge identifications agree at common endpoints.
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