Prove that the tetrahedron with vertices at the points* O*(0, 0, 0), *A*(0, 1, 1), *B*(1, 0, 1) and *C*(1, 1, 0) is a regular one.

Take triangle OAB

So OA = $\sqrt{(0-0{)}^{2}+(0-1{)}^{2}+(0-1{)}^{2}}=\sqrt{2}\phantom{\rule{0ex}{0ex}}$

OB = $\sqrt{2}$

AB = $\sqrt{2}$

Hence this face is equilateral .

Similarly take other faces, you will get all faces as equilateral triangles .

Hence the tetrahedron is regular

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