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Preassigning the shape
of a face
David Wilmot Barnette and Branko Grünbaum |
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Vol. 32 (1970), No. 2, 299–306
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Abstract |
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THEOREM. Let G be a 3-connected planar graph, F a nonseparating n-circuit of G with nodes A1,⋯,An (in a cyclic order of F), and let F′ be a convex n-gon with vertices A1′,⋯,An′ (in cyclic order). Then there exists a 3-polytope P which realizes G, such that F′ is a face of P and that the vertex Ai′ of P corresponds to the node Ai of G for i = 1,2,⋯,n. |
Mathematical Subject Classification
Primary: 52.10
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Milestones
Received: 8 January 1968
Published: 1 February 1970
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Authors |
| David Wilmot Barnette | |
| Branko Grünbaum | |
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