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I have recently found myself researching a certain type of convex body in $\mathbb{R}^2$, namely centrally symmetric smooth strictly convex bodies. Instead of repeating such a sentence repetitively I have found myself referring to them as "symmetric bodies", but I was hoping there is a more widely used name for them. I have checked the literature but cannot for the life of me find anything. Any help is appreciated.

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  • $\begingroup$ perhaps you could just say "in this article CSSSCB stands for centrally symmetric smooth strictly convex bodies?" $\endgroup$ – erz May 29 '20 at 10:53
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    $\begingroup$ "symmetric convex body" is widely used to mean "centrally symmetric convex body", so I would add an extra adjective here. Maybe "regular symmetric (convex) body" ? (I have seen "regular" to mean "smooth and strictly convex", but it is not standard terminology) $\endgroup$ – Guillaume Aubrun May 29 '20 at 12:38
  • $\begingroup$ You could try giving them your own name. Call them D-bodies. $\endgroup$ – Deane Yang May 30 '20 at 3:24
  • $\begingroup$ @erz I did originally go with this but I found it isn't very nice to read every time. $\endgroup$ – S. Dewar Jun 2 '20 at 13:22
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Centrally symmetric convex body which is absorbing is called "barrel" in the functional analysis. So I suggest you use this term (probably stating explicitly that the barrels you consider are smooth).

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  • $\begingroup$ This will run into the same issue of me having to call them "strictly convex smooth barrels" which (while better) is still a bit of a mouthful. $\endgroup$ – S. Dewar Jun 2 '20 at 13:21

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