Geometric Construction of a Truncated Cube

This example demonstrates how a truncated cube is constructed in 3D geometry: by locating division points along the edges of a cube at specified proportions and then connecting the corresponding points, the model forms a truncated polyhedron with triangular and hexagonal faces. Key mathematical ideas include solid geometry, segment division on edges (midpoint/ratio-type reasoning), and the combinatorial face-joining rules that determine the resulting polyhedron. Construction approach in GeoGebra: the scene is built primarily from the commands Polygon, Plane, and Point. A set of 3D points (e.g., a, b, c, d and multiple indexed variants) represents the edge-division and intersection/connection locations; Plane provides reference planes for organizing the spatial setup; Polygon is used to draw the different face outlines (such as poligon1, poligon2, poligon3) and assemble them into the complete truncated cube. Suitable for advanced secondary school and early university learners, especially for teaching geometric construction, spatial visualization, and ratio-based reasoning in solid geometry.