Vol. 32, No. 2, 1970

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ISSN: 0030-8730
Preassigning the shape of a face

David Wilmot Barnette and Branko Grünbaum

Vol. 32 (1970), No. 2, 299–306
DOI: 10.2140/pjm.1970.32.299
Abstract

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 Fbe a convex n-gon with vertices A1,,An(in cyclic order). Then there exists a 3-polytope P which realizes G, such that Fis a face of P and that the vertex Aiof P corresponds to the node Ai of G for i = 1,2,,n.

Mathematical Subject Classification
Primary: 52.10
Milestones
Received: 8 January 1968
Published: 1 February 1970
Authors
David Wilmot Barnette
Branko Grünbaum