What is this mutant tetrahedron and how do i make a lined up one?

Question

I have written a program that arranges stars stars into polyhedra, for example tetrahedron. here is a mutant tetrahedron, i dont know why the sides dont line up, and how to correct it. please help.

Answer 1

I had to rotate the stars by +/- 90' and it lined up symetrically. i was confused because the points of the triads were touching, and it gave the illusion that only half the sides could be aligned. actually, by rotating all sides equally by +/- 30 or by 90 degrees produced 2 different classes of symmetrical shapes.