Geodesic
Continuous Flattening of a Regular Tetrahedron with Explicit Mappings
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 6, pp. 127-136

Voir la notice de l'article provenant de la source Math-Net.Ru

We proved in [10] that each Platonic polyhedron $P$ can be folded into a flat multilayered face of $P$ by a continuous folding process of polyhedra. In this paper, we give explicit formulas of continuous functions for such a continuous flattening process in $\mathbb{R}^3$ for a regular tetrahedron. The article is published in the author's wording.
Keywords: Continuous Flattening, Regular Tetrahedra, Polyhedra, Paper Folding. 
@article{MAIS_2012_19_6_a11,
     author = {Jin-ichi Itoh and Chie Nara},
     title = {Continuous {Flattening} of a {Regular} {Tetrahedron} with {Explicit} {Mappings}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {127--136},
     publisher = {mathdoc},
     volume = {19},
     number = {6},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_6_a11/}
}
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Jin-ichi Itoh; Chie Nara. Continuous Flattening of a Regular Tetrahedron with Explicit Mappings. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 6, pp. 127-136. http://geodesic.mathdoc.fr/item/MAIS_2012_19_6_a11/