Two-fold branched cover of Hexagon - Which map is meant

Question

I am trying to understand an obvious example in a paper but do not get what is meant by:

"X is a hexagon and $f:X \rightarrow \sigma^2$ is a two-fold branched cover (branched at the center of $\sigma^2$)."

Here $\sigma^2$ denotes the standard two-dimensional simplex and $f$ is a simplicial map.

What does the map $f$ precisely look like?

Answer 1

I presume that, identifying $X$ with the regular hexagon centered at the origin of the complex plane with vertices at $\exp(i2\pi k/6)$ for $k=0,1,\dots,5$, and $\sigma^2$ with the triangle with vertices $\exp(i2\pi k/3)$ for $k=0,1,2$, then $f:X\to \sigma^2$ is the map given by $$ f(re^{i\theta})=re^{i2\theta}, $$ or $f(x) = x^2/|x|$.

Here is an animation illustrating the map: