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 the regular tetrahedron with integer coordinates. In a regular tetrahedron, all edges are equal.

Fri, 17 Apr 2026 11:00:58 +0000

**Discover the Geometry Behind the Regular Tetrahedron: Where Math Meets Precision** Ever wondered how three points can structure a perfect four-dimensional balance in 3D space? The regular tetrahedron—where every edge is equal—has sparked quiet interest across scientific, educational, and technological circles. Now, a precise challenge: given three vertices at $ A(1,0,0) $, $ B(0,1,0) $, and $ C(0,0,1) $, where does the fourth point $ D(x,y,z) $ with integer coordinates lie to complete this symmetrical shape? Recent conversations around spatial design, equal-edge structures, and advanced geometry visualization in digital environments have reignited curiosity about this shape. This configuration isn’t just theoretical—it fuels practical applications in architecture, crystallography, and even coding and simulation environments. Understanding how to calculate such a point reveals deeper insights into spatial symmetry and distances in mathematics. **Why This Geometry Puzzle Is Trending in the US**