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📰 Question: A regular tetrahedron is embedded in 3D space with three of its vertices at $ A(1, 1, 1) $, $ B(1, -1, -1) $, and $ C(-1, 1, -1) $. The fourth vertex $ D $ has integer coordinates. Find the coordinates of $ D $.
📰 Let the fourth vertex be $ D(x, y, z) $. Since the tetrahedron is regular, all edges must have equal length.
📰 First, compute the squared distance between $ A $ and $ B $:
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