Using points to create a cell inside a voronoi

Hello everyone.

I was hoping someone could help me with a problem I'm facing. 

For an architectual project I'm investigating if I can optimalize a voronoi structure. To do this I'm creating a cell based on the nodes created by the original voroinoi structure. The way I did it for a simple basic structure (3 cells - 1 node) was to;

- Place 3 points

- Create a voronoi cell

- Find the control points

- Select the point in the middle by using 'list item'

- Find the closest points and connect them with a line

- Place a point on those 3 lines and connect them with a polyline

The problem I have is when the structure gets more cells and nodes. I don't know how to find the right points in a quick and easy way (using 'list item' isn't an option anymore). Also I can't use 'closest points' because it gives me the wrong ones. My counselor told me to compare the polylines and find the coinciding lines (and using a vb-script for this as it was easier).

Is there someone who knows how to place those points (around the yellow dot)? Or perhaps how I can acquire the correct lines/points without it becoming real tedious when the structure grows bigger?