Solution: Let the fourth vertex be $D = (x, y, z)$. In a regular tetrahedron, all six edges must be equal. First, compute the distance between known points:

Sun, 03 May 2026 03:32:58 +0000

Title: Solving for Vertex $D = (x, y, z)$ in a Regular Tetrahedron: Equal Edge Lengths Explained --- Introduction
Creating a regular tetrahedron in 3D space requires all six edges to be equal in length—this presents a classic geometric challenge. In this article, we explore a key solution approach: solving for the unknown fourth vertex $D = (x, y, z)$ when several vertices are already defined. By computing distances between known points and enforcing uniform edge lengths, we establish equations that determine the precise coordinates of $D$, ensuring symmetry and regularity. Let’s dive into the details. ---