Abstract
In this paper, we consider geometric structures on a simplicial complex. Rivin considered geometric structures on a 2-simplicial complex which is homeomorphic to an orientable surface when some values are assigned to the edges of the simplicial complex and the assigned values are distributed to the vertices of the 2-faces as their angles. We extend his results to the case where a 2-simplicial complex is not homeomorphic to a surface and also discuss geometric structures on a 3-simplicial complex which is homeomorphic to a 3-manifold.
