/ A.V. Timofeenko // St. Petersburg Mathematical Journal. - 2012. - Vol. 23, Is. 4. - P779-780, DOI 10.1090/S1061-0022-2012-01217-3
. - ISSN 1061-0022
Scopus
Доп.точки доступа:
Тимофеенко, Алексей Викторович
Труды сотрудников ИВМ СО РАН
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Найдено документов в текущей БД: 6
JUNCTION OF NONCOMPOSITE POLYHEDRA
[Text] / A.V. Timofeenko // St. Petersb. Math. J. - 2010. - Vol. 21, Is. 3. - pp. 483-512. - Cited References: 12. - Supported by grant 09-09-1/NSh from the V.P. Astafev Krasnoyarsk State Pedagogical University, and also by grants 09-01-00395-a and 09-01-00717-a from RFBR.
. - ISSN 1061-0022
РУБ Mathematics
Аннотация: 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.
Доп.точки доступа:
Тимофеенко, Алексей Викторович
Рубрики:
CONVEX POLYHEDRA
REGULAR FACES
Кл.слова (ненормированные):
Regular-hedra -- concomposite polyhedra -- symmetry groups -- superfundamental faces
CONVEX POLYHEDRA
REGULAR FACES
Кл.слова (ненормированные):
Regular-hedra -- concomposite polyhedra -- symmetry groups -- superfundamental faces
Аннотация: 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.
Доп.точки доступа:
Тимофеенко, Алексей Викторович
On Mazurov triples of the sporadic group B and Hamiltonian cycles of the Cayley graph
[Text] : статья / A. I. Makosi, A. V. Timofeenko // Discrete Mathematics and Applications. - 2008. - Vol. 18, Iss. 2. - p. 199-205, DOI 10.1515/DMA.2008.016
. - ISSN 0924-9265
Аннотация: A system of generators of a group consisting of three involutions, two of which commute, is called a Mazurov triple. We describe algorithms for finding in an explicit form the Mazurov triples of one of the sporadic Monsters, the finite simple group B, and for constructing a Hamiltonian cycle in the Cayley graph of the finite group with Mazurov triple. We give examples of Hamiltonian cycles in the Cayley graphs of some groups.
Доп.точки доступа:
Timofeenko, A.V.; Тимофеенко, Алексей Викторович
Аннотация: A system of generators of a group consisting of three involutions, two of which commute, is called a Mazurov triple. We describe algorithms for finding in an explicit form the Mazurov triples of one of the sporadic Monsters, the finite simple group B, and for constructing a Hamiltonian cycle in the Cayley graph of the finite group with Mazurov triple. We give examples of Hamiltonian cycles in the Cayley graphs of some groups.
Доп.точки доступа:
Timofeenko, A.V.; Тимофеенко, Алексей Викторович
To thre Theory of Convex Regular-hedra
[Text] : статья / A. V. Timofeenko, A. M. Gurin // Doklady Mathematics. - 2008. - Vol. 77, № 2. - p. 234–237, DOI 10.1134/S1064562408020208
. - ISSN 1064-–562
Полный текст на сайте правообладателя
Доп.точки доступа:
Gurin, A.M.; Тимофеенко, Алексей Викторович
Полный текст на сайте правообладателя
Доп.точки доступа:
Gurin, A.M.; Тимофеенко, Алексей Викторович
Convex polyhedra with parquet faces
[Text] / A. V. Timofeenko // Dokl. Math. - 2009. - Vol. 80, Is. 2. - P720-723, DOI 10.1134/S1064562409050238. - Cited References: 10. - The work was supported by the Krasnoyarsk State Pedagogical University (project no. 09-09-1/NSh) and by the Russian Foundation for Basic Research (project nos. 09-01-00395-a and 09-01-00717-a).
. - ISSN 1064-5624
РУБ Mathematics
Доп.точки доступа:
Тимофеенко, Алексей Викторович; Krasnoyarsk State Pedagogical University [09-09-1/NSh]; Russian Foundation for Basic Research [09-01-00395-a, 09-01-00717-a]
Рубрики:
REGULAR FACES
REGULAR FACES
Доп.точки доступа:
Тимофеенко, Алексей Викторович; Krasnoyarsk State Pedagogical University [09-09-1/NSh]; Russian Foundation for Basic Research [09-01-00395-a, 09-01-00717-a]
The non-Platonic and non-Archimedean noncomposite polyhedra
[Text] : статья / A. V. Timofeenko // Journal of Mathematical Sciences. - 2008. - Vol. 162, № 5. - p. 710-729, DOI 10.1007/s10958-009-9655-0
. - ISSN 1072-3374
Аннотация: If a convex polyhedron with regular faces cannot be divided by any plane into two polyhedra with regular faces, then it is said to be noncomposite. We indicate the exact coordinates of the vertices of noncomposite polyhedra that are neither regular (Platonic), nor semiregular (Archimedean), nor their parts cut by no more than three planes. Such a description allows one to obtain a short proof of the existence of each of the eight such polyhedra (denoted by M 8, M 20–M 25, M 28) and to obtain other applications.
Полный текст на сайте правообладателя
Доп.точки доступа:
Тимофеенко, Алексей Викторович
Аннотация: If a convex polyhedron with regular faces cannot be divided by any plane into two polyhedra with regular faces, then it is said to be noncomposite. We indicate the exact coordinates of the vertices of noncomposite polyhedra that are neither regular (Platonic), nor semiregular (Archimedean), nor their parts cut by no more than three planes. Such a description allows one to obtain a short proof of the existence of each of the eight such polyhedra (denoted by M 8, M 20–M 25, M 28) and to obtain other applications.
Полный текст на сайте правообладателя
Доп.точки доступа:
Тимофеенко, Алексей Викторович