Random Realization of Polyhedral Graphs as Deltahedra

نویسندگان

  • Naoya Tsuruta
  • Jun Mitani
  • Yoshihiro Kanamori
  • Yukio Fukui
چکیده

In this paper, we propose a method for realizing a polyhedral graph as a deltahedron, i.e., a polyhedron with congruent equilateral triangles as faces. Our experimental result shows that there are graphs that are not realizable as deltahedra. We provide an example of non-realizable graphs which are obtained by trying to construct deltahedra from each of the simple cubic polyhedral graphs with up to 10 vertices. We also show that the infinite families of non-realizable graphs can be obtained by solving the graph isomorphism problem.

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تاریخ انتشار 2015