The braid group on $n$ strands is the fundamental group of the configuration space of $n$ points in the plane. As such, it acts on the free group $F_n$, by moving representatives of $\pi_1(\mathbb R^2\setminus \,n\, {\rm points})$. A tetrahedral graph linearly embedded in $\mathbb{R}^3$ has a compliment with $F_3$ its fundamental group. What is $\pi_1$ of the corresponding configuration space? In this talk we review the answer and discuss the generalization to two different indexed families of spaces of skeleta of simplices in some $\mathbb R^n$.