  Let $B_{x}\subseteq\mathbb{R}^{n}$ denote the Euclidean ball with diameter
$[0,x]$, i.e. with with center at $\frac{x}{2}$ and radius
$\frac{\left|x\right|}{2}$. We call such a ball a petal. A flower $F$ is any
union of petals, i.e. $F=\bigcup_{x\in A}B_{x}$ for any set
$A\subseteq\mathbb{R}^{n}$. We showed in previous work that the family of all
flowers $\mathcal{F}$ is in 1-1 correspondence with $\mathcal{K}_{0}$ - the
family of all convex bodies containing $0$. Actually, there are two essentially
different such correspondences. We demonstrate a number of different non-linear
constructions on $\mathcal{F}$ and $\mathcal{K}_{0}$. Towards this goal we
further develop the theory of flowers.
