Triangulation of 1/8 Sphere with Angle and Distance Calculations

This example demonstrates how to triangulate 1/8 of a sphere. The core mathematical concepts involve solid geometry, spherical surface subdivision, polygon construction, and precise angle and distance measurements. Construction key points: ①Use the Sphere command to create a sphere, determine key intersection points using Point and Intersect commands; ②Apply the Polygon command to construct triangular and quadrilateral faces on the spherical surface; ③Use the Angle command to measure dihedral angles at vertices; ④Calculate distances between key points using the Distance command and label results with Text commands. This example is suitable for high school and college students learning solid geometry and spherical trigonometry, helping them understand the relationship between polyhedra and spherical geometry, and can be used for teaching the geometric principles of spherical subdivision.