Abstract
Given a triangulated surface, a euclidean or hyperbolic polyhedral surface can be constructed by assigning radii to the vertices of the triangulation. We develop necessary and sufficient conditions for the existence of such a polyhedral surface having specified characteristics.
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The results in this paper are included in the author's doctoral dissertation [12].
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Garrett, B.T. Circle packings and polyhedral surfaces. Discrete Comput Geom 8, 429–440 (1992). https://doi.org/10.1007/BF02293057
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DOI: https://doi.org/10.1007/BF02293057