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.

$\begingroup$ perhaps you could just say "in this article CSSSCB stands for centrally symmetric smooth strictly convex bodies?" $\endgroup$– erzMay 29, 2020 at 10:53

1$\begingroup$ "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 AubrunMay 29, 2020 at 12:38

$\begingroup$ You could try giving them your own name. Call them Dbodies. $\endgroup$– Deane YangMay 30, 2020 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. DewarJun 2, 2020 at 13:22
1 Answer
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).

$\begingroup$ 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. DewarJun 2, 2020 at 13:21