Common Unfolding of Regular Tetrahedron and Johnson-Zalgaller Solid

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 Article type: Regular paper Communicated by: M. S. Rahman and E. Tomita Ryuhei Uehara is supported in part by JSPS KAKENHI Grant Number 26330009 and MEXT KAKENHI Grant Number 24106004. A preliminary version was presented at WALCOM 2015,