Following my previous question

[How to plot the given graph (irregular tri-hexagonal) with Mathematica?](https://mathematica.stackexchange.com/questions/238649/how-to-plot-the-given-graph-irregular-tri-hexagonal-with-mathematica/238658?noredirect=1#comment602646_238658)

I need a 2D network of the Fig. $a$, something like Fig. $b$ with red points on all vertices. Since I have drawn Fig. $b$ manually, it is not precise and symmetric.
In this case, the blue and the violet edges have different lengths.

[![enter image description here](https://i.stack.imgur.com/i9bpN.png)](https://i.stack.imgur.com/i9bpN.png)