Junction of noncomposite polyhedra
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A. V. Timofeenko
Translated by: A. Plotkin - St. Petersburg Math. J. 21 (2010), 483-512
- DOI: https://doi.org/10.1090/S1061-0022-10-01105-2
- Published electronically: March 2, 2010
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Erratum: St. Petersburg Math. J. 23 (2012), 779-780.
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
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Bibliographic 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
- 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
- © Copyright 2010 American Mathematical Society
- Journal: St. Petersburg Math. J. 21 (2010), 483-512
- MSC (2000): Primary 52B10
- DOI: https://doi.org/10.1090/S1061-0022-10-01105-2
- MathSciNet review: 2588767
Dedicated: To my son’s coming of age