The figure is given by $x^4+y^4\leq\frac1{2^4}$ https://www.wolframalpha.com/input/?i=x%5E4+%2B+y%5E4+%3C1%2F16.
In general is there a name for the figure $x^{2t}+y^{2t}\leq\frac1{2^{2t}}$ or anything resembling it (at $t\rightarrow\infty$ it becomes a square)?
The $\ell^p$ ball in $\mathbb{R}^d$ of radius $r$ centered at the origin is $$\{x \in \mathbb{R}^d : \sum_{i=1}^d |x_i|^p \le r^p\}.$$
Your example is $d = 2$, $p = 2t$, and $r=1/2$.