Research output: Contribution to journal › Article › peer-review
Recognition of Affine-Equivalent Polyhedra by Their Natural Developments. / Alexandrov, V. A.
In: Siberian Mathematical Journal, Vol. 64, No. 2, 03.2023, p. 269-286.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Recognition of Affine-Equivalent Polyhedra by Their Natural Developments
AU - Alexandrov, V. A.
N1 - The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).
PY - 2023/3
Y1 - 2023/3
N2 - The classical Cauchy rigidity theorem for convex polytopes reads that iftwo convex polytopes have isometric developments then they are congruent.In other words, we can decide whether two convex polyhedra are isometricor not by only using their developments.We study a similar problem of whether it is possible to understand thattwo convex polyhedra in Euclidean 3-space are affine-equivalent by onlyusing their developments.
AB - The classical Cauchy rigidity theorem for convex polytopes reads that iftwo convex polytopes have isometric developments then they are congruent.In other words, we can decide whether two convex polyhedra are isometricor not by only using their developments.We study a similar problem of whether it is possible to understand thattwo convex polyhedra in Euclidean 3-space are affine-equivalent by onlyusing their developments.
KW - 514.12
KW - Cauchy rigidity theorem
KW - Cayley–Menger determinant
KW - Euclidean 3-space
KW - affine-equivalent polyhedra
KW - convex polyhedron
KW - development of a polyhedron
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85151091280&origin=inward&txGid=f004194e4fea1d0c11d7275945ae2b1c
UR - https://www.mendeley.com/catalogue/6e8306aa-74fe-3a2f-b33e-d7899a679373/
U2 - 10.1134/S0037446623020027
DO - 10.1134/S0037446623020027
M3 - Article
VL - 64
SP - 269
EP - 286
JO - Siberian Mathematical Journal
JF - Siberian Mathematical Journal
SN - 0037-4466
IS - 2
ER -
ID: 59243022