GeoGebra Visualization of the Octahedron-to-Sphere Volume Ratio

This example demonstrates how to construct an octahedron and a corresponding sphere in the same 3D scene, then compute and visualize the ratio of their volumes. It highlights a clear spatial relationship between two classic solid shapes. Key concepts include solid geometry (octahedron and sphere), volume measurement, and center-related constructions such as centroid and midpoints to define the geometry consistently. The construction uses GeoGebra commands like Point, Polygon, and Octahedron to create vertices and faces, Sphere to build the sphere, Centroid and Midpoint to locate the relevant central points, and PointIn and Segment to establish geometric relationships. Finally, Volume is used to compute the individual volumes (e.g., volumec and volumeb), with text/label objects to present the resulting values or ratio. Suitable for advanced secondary students, early undergraduate learners, and exploratory geometry learning.