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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Regular triangulations and Steiner points


Authors: M. Yu. Zvagel'skii, A. V. Proskurnikov and Yu. R. Romanovskii
Translated by: Yu. R. Romanovskii
Original publication: Algebra i Analiz, tom 16 (2004), nomer 4.
Journal: St. Petersburg Math. J. 16 (2005), 673-690
MSC (2000): Primary 52B11; Secondary 52B35, 68U05
Published electronically: June 24, 2005
MathSciNet review: 2090852
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Abstract | References | Similar Articles | Additional Information

Abstract: Gel'fand, Zelevinskii, and Kapranov showed that the regular triangulations of a ``primary'' convex polytope can be viewed as the vertices of another convex polytope, which is said to be secondary. Billera, Filliman, and Sturmfels gave a geometric construction of the secondary polytope, based upon Gale transforms. We apply this construction to describing regular triangulations of nonconvex polytopes. We also discuss the problem of triangulating nonconvex polytopes with Steiner points.


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Additional Information

M. Yu. Zvagel'skii
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198904, Russia
Email: zvag@pdmi.ras.ru

A. V. Proskurnikov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198904, Russia
Email: anton@AP9560.spb.edu

Yu. R. Romanovskii
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospekt 28, Staryĭ Peterhof, St. Petersburg 198904, Russia
Email: romanov@YR2008.spb.edu

DOI: https://doi.org/10.1090/S1061-0022-05-00872-1
Keywords: Nonconvex polytopes, regular triangulations, Steiner points
Received by editor(s): December 12, 2003
Published electronically: June 24, 2005
Additional Notes: Supported by the CRDF grant RMO-1296-ST-02
Article copyright: © Copyright 2005 American Mathematical Society