DEVELOPMENTS OF POLYHEDRA USING OBLIQUE COORDINATES

J. Akiyama; C. Nara

doi:10.22342/jims.13.1.77.99-114

J. Akiyama ⁽¹⁾ , C. Nara ⁽²⁾

(1) The Research Institute of the Educational Development, Tokai University, 2-28-4 Tomi- gaya, Shibuya, Tokyo 151-8677, Japan., Japan,

(2) Department of General Education, Kyushu Tokai Univershity, Kawayo, Minami-Aso, Aso, Kumamoto, 869-1404, Japan., Japan

https://doi.org/10.22342/jims.13.1.77.99-114

Issue
Volume 13 Number 1 (April 2007)

Submitted
May 25, 2012

Accepted
July 24, 2012

Published
July 24, 2012

Keywords:

tetrahedron, development, tiling, convexity

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Abstract

This paper is an exposition of the results in the paper entitled "Convex Development of a Regular Tetrahedron" by J. Akiyama, et. al. [1]. We fill in the detail which have been omitted in the paper. We determine all convex developments of a regular tetrahedron V using a tiling generated by V and we arrive at conditions for convex polygons to be convex develpments of V . Moreover, we identify all convex polyhedra whose convex developments can be determined by the method used for V .

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Authors

J. Akiyama

The Research Institute of the Educational Development, Tokai University, 2-28-4 Tomi- gaya, Shibuya, Tokyo 151-8677, Japan.

penulis@jims-a.org (Primary Contact)

C. Nara

Department of General Education, Kyushu Tokai Univershity, Kawayo, Minami-Aso, Aso, Kumamoto, 869-1404, Japan.

Akiyama, J., & Nara, C. (2012). DEVELOPMENTS OF POLYHEDRA USING OBLIQUE COORDINATES. Journal of the Indonesian Mathematical Society, 13(1), 99–114. https://doi.org/10.22342/jims.13.1.77.99-114