Solution: Let the three given vertices be $A = (1,0,0)$, $B = (0,1,0)$, $C = (0,0,1)$, and let $D = (x,y,z)$ be the fourth vertex of a regular tetrahedron, so that all edges have equal length.

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**Unearthing Geometry: How D Lies the Tetrahedron Straight Among Vertices A, B, and C** When exploring 3D shapes in mathematical and design contexts, a cool question arises: if you place three points in space—$A = (1,0,0)$, $B = (0,1,0)$, and $C = (0,0,1)$—what shape forms with a fourth point $D$ such that all sides are equal? This isn’t just for math nerds—it’s a fundamental problem in geometry with quiet relevance across fields from architecture to computer graphics. Users searching for keys to understanding spatial design, symmetry, or structural balance often stumble here. Understanding how to find $D = (x,y,z)$ completes a *regular tetrahedron*, offering insight into balance, proportion, and hidden harmony in space. --- ### Why This Tetrahedral Puzzle Is gaining Momentum in the US