Geodesic
On convex hulls of self-similar sets
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 2, pp. 21-27

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Let $S=\{s_1,\dots,s_m\}$ be a system of contraction similitudes in Banach space and $K(S)$ it's invariant set. We obtain the conditions for the convex hull $H(K)$ of the invariant set to be a finite-sided polyhedron and give an exact estimate for the diameter of $K(S)$ in terms of contraction coefficients of $s_i$. 
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     author = {I. B. Davydkin and A. V. Tetenov},
     title = {On convex hulls of self-similar sets},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {21--27},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2005_5_2_a1/}
}
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I. B. Davydkin; A. V. Tetenov. On convex hulls of self-similar sets. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 2, pp. 21-27. http://geodesic.mathdoc.fr/item/VNGU_2005_5_2_a1/