How to count Number different coloring of Tetrahedron with 2 black and 2 white colors by Bernside lemma. first I count the number ways of choosing 2 and 2 faces, it is $\frac{4!}{2!2!}$. second rotation by one face and one vertice, we have 4 that rotation with order 2, and it is have 1 fixed point. And we have rotation by 2 edges, 3 such rotation with order 1, and 0 fixed points. finally $(1*6+ 8*1+3*0)\frac{1}{12}$. where i have a mistake?
2026-02-23 10:49:51.1771843791
Number different coloring of Tetrahedron with 2 black and 2 white colors?
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