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Constructing the cubus simus and the dodecaedron simum via paper folding. (English) Zbl 1285.51018
The purpose of this article is to explain that for general reasons the vertices of the Archimedean solids cubus simus (snub cube) and dodecaedron simum (snub dodecahedron) can be constructed via paper folding on the faces of a cube, respectively dodecahedron. Also, the authors present explicit folding constructions. We shall remember that the Archimedean solids can be obtained by constructing their vertices on the faces of the platonic solids.
After the authors accommodate the readers, in the first section, with the upcoming information to be discussed, they describe the paper folding methods to construct the vertices of the cubus simus on the faces of a cube and of the dodecaedron simum on the faces of a dodecahedron (noting that the construction of the cubus simus is elegant).
For the folding constructions of the dodecaedron simum, the authors use the computer algebra system Maple. In the appendix, the authors review and prove the construction rules of the other Archimedean solids.
51M15 Geometric constructions in real or complex geometry
51M20 Polyhedra and polytopes; regular figures, division of spaces
Full Text: DOI arXiv
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