Cone conditions on domains are extensively used in the proof of the Sobolev embedding theorem. Somewhat less common in that respect is the uniform cone condition, which Adams and Fournier (Sobolev spaces, 2001) define as follows
Here, $\Omega_{\delta}$ refers to the set of points in $\Omega$ within $\delta$-distance of the boundary of $\Omega$, i.e., $$\Omega_{\delta} = \{ x \in \Omega: \text{dist}(x, \text{boundary} \{\Omega\} < \delta \} $$
I am having a bit of trouble digesting all these requirements, so my question would be: are there any simple enough examples of open and bounded domains satisfying the uniform cone property? It would seem to me that many domains in $\mathbb{R}^d$, such as the unit squares $(0,1)^d$, do not fulfil these requirements, but the unit ball $\{x:||x|| <1\}$ does. Is my intuition correct?