Geodesic
Random Realization of Polyhedral Graphs as Deltahedra
Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 227-236 Cet article a éte moissonné depuis la source Heldermann Verlag

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Ee 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.
Classification : 51M20, 05C10, 68R10, 52B05
Mots-clés : Deltahedron, polyhedral graph, geometric realization 
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     author = {N. Tsuruta and J. Mitani and Y. Kanamori and Y. Fukui },
     title = {Random {Realization} of {Polyhedral} {Graphs} as {Deltahedra}},
     journal = {Journal for geometry and graphics},
     pages = {227--236},
     year = {2015},
     volume = {19},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a6/}
}
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N. Tsuruta; J. Mitani; Y. Kanamori; Y. Fukui . Random Realization of Polyhedral Graphs as Deltahedra. Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 227-236. http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a6/