Journal of Graph Algorithms and Applications
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Special Issue on Selected Papers from the Ninth International Workshop on Algorithms and Computation (WALCOM 2015)
Common Unfolding of Regular Tetrahedron and Johnson-Zalgaller Solid
Yoshiaki Araki, Takashi Horiyama, and Ryuhei Uehara
Vol. 20, no. 1, pp. 101-114, 2016. Regular paper.
Abstract In this paper, we investigate the common unfolding between regular tetrahedra and Johnson-Zalgaller solids. More precisely, we investigate the sets of all edge developments of Johnson-Zalgaller solids that fold into regular tetrahedra. We show that, among 92 Johnson-Zalgaller solids, only J17 (gyroelongated square dipyramid) and J84 (snub disphenoid) have some edge developments that fold into a regular tetrahedron, and the remaining Johnson-Zalgaller solids do not have any such edge development.
Submitted: March 2015.
Reviewed: August 2015.
Revised: October 2015.
Accepted: November 2015.
Final: January 2016.
Published: February 2016.