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 $.

Tue, 05 May 2026 23:30:54 +0000

Write the article as informational and trend-based content, prioritizing curiosity, neutrality, and user education over promotion. --- ### A Regular Tetrahedron in 3D Space: Finding the Hidden Vertex $ D $ What if a trio of points in 3D space suddenly raises the question: where is the fourth vertex? This isn’t a sci-fi scenario—it’s a geometric puzzle with real relevance in fields like architecture, computer graphics, and advanced design. The specific question on many minds: given regular tetrahedron vertices at $ A(1, 1, 1) $, $ B(1, -1, -1) $, and $ C(-1, 1, -1) $, where is the fourth vertex $ D $, assumed to have integer coordinates? This query reflects growing curiosity in spatial reasoning and precision design, especially as STEM fields and digital modeling demand exact geometric solutions. Now, the search for $ D $ reveals both elegant math and unexpected depth—not just a coordinate, but an exploration of symmetry and spatial logic.