Continuous Flattening of the 2-Dimensional Skeleton of the Square Faces in a Hypercube

The surface of a 3-dimensional cube can be continuously flattened onto any of its faces, by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. Let C n be an n -dimensional cube with n ≥ 4 , and S be the set of its 2-dimensional faces, i.e.,...

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Bibliographic Details
Published in:Graphs and combinatorics 2020-03, Vol.36 (2), p.331-338
Main Authors: Itoh, Jin-ichi, Nara, Chie
Format: Article
Language:English
Subjects:
Combinatorics
Engineering Design
Flattening
Hypercubes
Mathematics
Mathematics and Statistics
Original Paper
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Summary:The surface of a 3-dimensional cube can be continuously flattened onto any of its faces, by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. Let C n be an n -dimensional cube with n ≥ 4 , and S be the set of its 2-dimensional faces, i.e., the 2-dimensional skeleton of the square faces in C n . We show that S can be continuously flattened onto any face F of S , such that the faces of S that are parallel to F , do not have any crease, that is, they are rigid during the motion.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-019-02100-8