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Extremal antipodal polygons and polytopes | | O. Aichholzer
; L.E. Caraballo
; J. M. Díaz-Báñez
; R. Fabila-Monroy
; C. Ochoa
; P. Nigsch
; | | Date: |
28 Jan 2013 | | Abstract: | Let $S$ be a set of $2n$ points on a circle such that for each point $p in
S$ also its antipodal (mirrored with respect to the circle center) point $p’$
belongs to $S$. A polygon $P$ of size $n$ is called emph{antipodal} if it
consists of precisely one point of each antipodal pair $(p,p’)$ of $S$.
We provide a complete characterization of antipodal polygons which maximize
(minimize, respectively) the area among all antipodal polygons of $S$. Based on
this characterization, a simple linear time algorithm is presented for
computing extremal antipodal polygons. Moreover, for the generalization of
antipodal polygons to higher dimensions we show that a similar characterization
does not exist. | | Source: | arXiv, 1301.6667 | | Services: | Forum | Review | PDF | Favorites | |
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