Rotation and Perspective of a Regular Hexagonal Pyramid

This example demonstrates the 3D geometric construction of a regular hexagonal pyramid with both solid and perspective views. Using the Rotate command, the pyramid can be dynamically rotated in space, allowing students to observe its structure from any angle. The regular hexagonal base and triangular lateral faces are constructed systematically with the Sequence and Polygon commands, while the altitude and orthogonal auxiliary lines are drawn to highlight the internal geometric relationships. Trigonometric functions such as cosine and tangent are applied to analyze edge lengths, angles, and other geometric properties of the pyramid. This interactive visualization is well suited for solid geometry instruction, helping students develop a deeper understanding of spatial figures, their structural characteristics, and projection transformations. By manipulating the rotation and examining the associated measurements and constructions in real time, learners can connect abstract mathematical concepts with concrete visual intuition, reinforcing key ideas in three-dimensional geometry.