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 -