Geodesic
Some properties of self-similar convex polytopes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 48-52

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We show that for each semigroup $\mathrm G$ of similarities defining the self-similarity structure on a convex self-similar polytope $K$ there is an edge $A$ of $K$ such that the fixed points of homotheties $g\in G$ are dense in $A$.
Keywords: self-similar set, convex polytope, graph-directed IFS, homothety, semigroup.
Mots-clés : fractal 
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     author = {A. V. Tetenov and I. B. Davydkin},
     title = {Some properties of self-similar convex polytopes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {48--52},
     publisher = {mathdoc},
     volume = {8},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2011_8_a33/}
}
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A. V. Tetenov; I. B. Davydkin. Some properties of self-similar convex polytopes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 48-52. http://geodesic.mathdoc.fr/item/SEMR_2011_8_a33/