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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Junction of noncomposite polyhedra


Author: A. V. Timofeenko
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 21 (2009), nomer 3.
Journal: St. Petersburg Math. J. 21 (2010), 483-512
MSC (2000): Primary 52B10
Published electronically: March 2, 2010
Erratum: St. Petersburg Math. J. 23 (2012), 779--780
MathSciNet review: 2588767
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Abstract | References | Similar Articles | Additional Information

Abstract: All 3-dimensional convex regular-hedra are found, i.e., the convex polyhedra having positive curvature of each vertex and such that every face is either a regular polygon or is composed of two regular polygons. The algorithm for constructing such solids is based on calculation of the corresponding symmetry groups and gives a listing of all possible adjoins along entire faces of convex regular-hedra that cannot be cut by any plane into smaller regular-hedra.


References [Enhancements On Off] (What's this?)

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Additional Information

A. V. Timofeenko
Affiliation: Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Academgorodok 50/44, Krasnoyarsk 660036, Russia
Email: A.V.Timofeenko62@mail.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-10-01105-2
PII: S 1061-0022(10)01105-2
Keywords: Regular-hedra, concomposite polyhedra, symmetry groups, superfundamental faces
Received by editor(s): August 31, 2008
Published electronically: March 2, 2010
Additional Notes: Supported by grant 09-09-1/NSh from the V. P. Astaf′ev Krasnoyarsk State Pedagogical University, and also by grants 09-01-00395-a and 09-01-00717-a from RFBR
Dedicated: To my son’s coming of age
Article copyright: © Copyright 2010 American Mathematical Society