Unit Cube and Its Diagonals

① This example demonstrates a unit cube (edge length 1) and the geometric relationships among its space diagonals, face diagonals, and related cross-sections. ② Core mathematical concepts include solid geometry of cubes, spatial diagonals, midpoints, polygonal sections, and the roles of linear functions and geometric mean in the construction. ③ Construction highlights: using GeoGebra commands Polygon, Segment, and Midpoint to build vertices, edges, face diagonals, and body diagonals; defining coordinate axes and vectors via objects θ, O, u, v, w; creating auxiliary points (e.g., I_2, G, H) with midpoints; and constructing multiple polygons (poly2, poly6, poly7, poly9) and segments (e, f, g, h, etc.) to reveal diagonal intersections, cross-section shapes, and symmetry. ④ Suitable for high school or early college solid geometry instruction, as well as spatial reasoning training and dynamic geometry exploration, helping students intuitively understand diagonal lengths, intersection points, and section properties of a cube.