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

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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. 
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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/

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