Computer constructions of a regular tetrahedron

This example demonstrates how to construct a regular tetrahedron using computer tools, where the vertices are defined based on the maximum sum of mutual distances among the polyhedron vertices. The core mathematical concepts involved include solid geometry, coordinate geometry, quadratic equations, and sphere intersections. Key GeoGebra commands and objects used in the construction, as listed in the summary, are Intersect, Sphere, Sequence, Join, Sum, Pyramid, and Volume. It is suitable for high school students and teachers for learning and teaching purposes in solid geometry and coordinate geometry.