Trouble with Delaunay Mesh [Grasshopper]

Hello All,
I’m trying to make a triangulation pattern, similar to the image shown.
I used the random component to list out random points from the 4 vertices of the quad panels.
Even after shift paths, I’m unable to form a triangulation pattern, where I get the same error of “Insufficient vertices”

Del (9.2 KB)

I’m not sure I follow exactly, but here is an example using a couple of different methods.

Del (10.9 KB)

Thank you Adam for your fast reply.
The thing is, I only want a random point from the 4 vertices of the scaled down quad panel.
The same need to be extruded as well.
The issue comes up as soon as I introduce a random component.
If, I define the index value, the Mesh gets generated without any issues. Check the attached pic.

I’m still unclear. Like this?

Del (11.2 KB)

Yes! That’s exactly what I wanted.
Thank you so much Adam.
It’s really helpful.
Also, just one minor tweak, I had to change the move command from unit Z to unit Y.
Thanks a lot!

No problem.

You didn’t internalise the input curve in your original definition (if you’re not sure how, see point 3 in the link below), so I just created a new one on the XY plane.