Find vertices in equilateral triangle mesh originating from a center vertex

Find vertices in equilateral triangle mesh originating from a center vertex

I'd like to ask whether there is code out there or if you can give me some
help in writing some (C#, but I guess the maths is the same everywhere).
I'd like to specify a center point from which an equilateral triangle mesh
is created and get the vertex points of these triangles. The center point
should not be a face center, but a vertex itself. A further input would be
the size of the triangles (i.e side length) and a radius to which triangle
vertices are generated.
The reason behind it is that I want to create a mesh which is centered
nicely on the screen/window center with as little code as possible. I just
find mesh generation code, but not a "radial outward propagation" example.
In the end, I'd like to have the subsequently farther away vertices being
displaced in a logarithmic fashion, but I guess that's just an easy
addition once the mesh code is there.
Can anybody help me with that? Thanks!