Non-axial Mirroring - Mirroring every 60 degrees for a tetrahedron?

Hi,

I was trying to add a mirror every 60 degrees on a teterahedron so everything I do to one side of a vertex on the bottom triangular face will mirror to the other side of the vertex and to every other vertex.

I tried to find this on the forums/google, but was unable. I know how to do mirroring on the three axis, and I read that I might be able to do it with arrays, but what is the easiest way to do it?

Thanks!

alt+d to get a linked copy and rotate it 60, and the parent all parts to first with ctrl+p. and note making the 1st’s center in the mirrored point.