As many antipodes as vertices on convex polyhedra
نویسندگان
چکیده
An earlier result states that, on the surface of a convex polyhedron with vertices endowed with its intrinsic metric, a point cannot have more than antipodes (farthest points). In this paper we produce examples of polyhedra with vertices, on which some suitable point admits exactly antipodes. We also proved that, for any positive number 1, there exist (in the closure of the set of these polyhedra) some convex surfaces on which some point have a set of antipodes of Hausdor dimension . MSC (2000): 52B10, 53C45.
منابع مشابه
As many antipodes as vertices on some convex polyhedra
An earlier result states that a point of the surface of a convex polyhedron with n vertices, endowed with its intrinsic metric, cannot have more than n antipodes (farthest points). In this paper we produce examples of polyhedra with n vertices, on which some suitable point admits exactly n antipodes. MSC (2000): 52B10, 53C45.
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