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Cross-Sections of a 3-Cube

Cross-Sections of a 3-Cube
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2020-10-02 00:26
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the cross-sections of a 3-cube. It involves the concept of sections in solid geometry, using GeoGebra commands such as Plane and IntersectPath to visually illustrate the shapes of sections formed by different planes cutting the cube. Suitable for high school or university solid geometry education.

GeoGebra Commands & Parameters

  1. Plane((0, 0, 0), (1, 0, 0), (0, 1, 0)) → p
  2. Cube(A, B, C) → acube, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. IntersectPath(p, acube) → cubsec_{1}, M, r, N, O, Q, U, k, l, m, n

AI Drawing Prompt Reference

Draw a 3D cube and cut it with a plane. The plane passes through the origin along the x and y axes. Show the cross-section shapes formed by the cuts. Make sure the cube and the cutting plane are clear, and highlight the intersecting parts of the cross-section with different colors.
The prompt above was compiled from the original drawing commands and is for reference only.