Parametric “Exploding Cube” with Geometric Transformations

This example demonstrates a parametrically controlled “exploding” cube: the cube is decomposed into several faces/parts and then separated by animated movements to create a clear 3D effect. The key mathematical ideas include solid geometry representation using polygonal faces, vector-based displacement, and geometric transformations such as translation, rotation, and mirroring (symmetry). Construction relies on defining direction and offset with Vector objects, generating cube-related faces via Polygon objects (e.g., poly1, poly2), and applying Translate to move each part outward. Mirror and Rotate are used to reorient parts consistently around specified planes or axes. Parameter objects (e.g., t, u, and multiple point/parameter sets) control the motion smoothly while maintaining the shape of each piece. Suitable for middle school to undergraduate geometry visualization, especially for lessons on transformations, parametric animation, and 3D modeling with GeoGebra.