Parallelogrammatic Pyramid 2: Dynamic Net and Inscribed Ellipse Exploration

This example demonstrates a quadrilateral pyramid with a parallelogram base, termed a parallelogrammatic pyramid, and its dynamic unfolding process. The core mathematical concepts include solid geometry (pyramids, base polygons, lateral triangular faces, edges, and height), plane geometry (parallelograms, inscribed ellipses, arithmetic means), and piecewise functions. Construction highlights: using GeoGebra commands Polygon to construct the base parallelogram ABCD, Pyramid to generate the pyramid, Net to create an unfoldable surface net; OrthogonalLine and Intersect to determine the height and apex, Angle to measure dihedral angles, PointIn and Segment to define points on faces and edges, and Length to compute side lengths. Objects include Height, vertices, faces like faceABF, edges like edgeAF, an OpenClose slider for controlling the unfolding, and auxiliary points E, G, H, I, etc. Suitable for high school solid geometry teaching, this helps students intuitively understand pyramid composition, nets, and spatial reasoning, while also enabling cross-topic exploration with ellipses and functions.