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

StackOverflow https://stackoverflow.com/questions/21075262

Question

enter image description here

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.

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Solution

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.enter image description here

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