Space Suggestion
First example of non-normal extremally disconnected space is $\mathbb{N}\cup \{p_A: A\in\mathcal{A}\}$, $\mathcal{A}$ maximal almost disjoint family, $p_A\in \text{cl}_{\beta\mathbb{N}} A\setminus\mathbb{N}$. It's the space witnessing that $\beta\mathbb{N}$ is not $T_5$ so name probably should reflect that.
Define a non-normal $P$-space as $X^2\setminus \{(\omega_2, \omega_2)\}$ where $X = \omega_2+1$ has topology letting $U\subseteq X$ be open iff its a $G_\delta$-set in the order topology. I would like to call it Dow plank since it's a space that appears in the article On F-spaces and F'-spaces by Dow, clearly analogous to something like the Tychonoff plank.
Relationship to other spaces and properties
It's an example of non-normal P-space.
