What shape are unit balls in $\mathbb R^d$ with the $L_p$ metric for $2 < p < \infty$?

Question

Consider the below figure drawing some examples of unit balls for various $L_p$ metrics.

For $p=1$ and $p=\infty$ we get squares (hyperoctahedra and hypercubes in higher dimensions, respectively), and when $p=2$ we get a circle (spheres in higher dimensions).

For intermediary values of $p$, how would one describe what shape these balls are?

Would they be considered ellipses?