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Truncated Cube by Patrick Clément

Truncated Cube by Patrick Clément
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2016-02-09 14:46
Solid GeometryTransformationGeometric Construction
This example demonstrates the construction of a truncated cube. It involves the concept of a truncated polyhedron in solid geometry. Using GeoGebra commands such as Point, Cube, Rotate, Polygon, etc., the faces and edges of the truncated cube can be constructed. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, arêteAD, arêteAB, arêteBC, arêteCD, arêteAE, arêteDH, arêteEH, arêteEF, E, arêteBF, arêteFG, arêteCG, arêteGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Point(arêteAE, 1 - p) → Ka
  4. Point(arêteAB, p) → Ia
  5. Point(arêteAD, 1 - p) → Ja
  6. Rotate(Ja, 90°, zAxis) → Jb
  7. Rotate(Ka, 90°, zAxis) → Kb
  8. Pyramid(Polygon[Ia, Ja, Ka], A) → pyrA, faceAIaJa, faceAJaKa, faceAIaKa, arêteAIa, arêteAJa, arêteAKa
  9. Polygon(Ia, Ja, Ka) → triA, ka, ia, ja
  10. Plane(xAxis, yAxis) → o
  11. Mirror(Ka, o) → Ke
  12. Mirror(Ia, o) → Ie
  13. Mirror(Jb, o) → Jf
  14. Mirror(Kb, o) → Kf
  15. Polygon(Ia, Jb, Kb, Kf, Jf, Ie, Ke, Ka) → fab, ia_1, jb_1, kb_1, kf, jf, ie, ke_1, ka_2
  16. Rotate(fab, 90°, zAxis) → fbc
  17. Rotate(fab, 180°, zAxis) → fcd
  18. Rotate(fab, -90°, zAxis) → fda
  19. Rotate(fab, -90°, arêteAB) → fsous
  20. Rotate(fab, 90°, arêteEF) → fsur
  21. CircumcircleArc(A, I, J) → c
  22. Translate(Rotate[pyrA, (t * α), arêteAE], Vector[A, Point[c, t]]) → pyramA
  23. Rotate(triA, 90°, zAxis) → triB
  24. Rotate(triA, 180°, zAxis) → triC
  25. Rotate(triA, -90°, zAxis) → triD
  26. Mirror(triA, o) → triE
  27. Rotate(triE, 90°, zAxis) → triF
  28. Rotate(triE, 180°, zAxis) → triG
  29. Rotate(triE, -90°, zAxis) → triH
  30. CircumcircleArc(B, K, J) → d
  31. Translate(Rotate[Rotate[pyrA, 90°, zAxis], (t * α), arêteBF], Vector[B, Point[d, t]]) → pyramB
  32. CircumcircleArc(C, L, J) → e
  33. CircumcircleArc(D, M, J) → f
  34. Translate(Rotate[Rotate[pyrA, 180°, zAxis], (t * α), arêteCG], Vector[C, Point[e, t]]) → pyramC
  35. Translate(Rotate[Rotate[pyrA, -90°, zAxis], ((-t) * α), arêteDH], Vector[D, Point[f, t]]) → pyramD
  36. Mirror(pyramD, o) → pyramH
  37. Mirror(pyramA, o) → pyramE
  38. Mirror(pyramB, o) → pyramF
  39. Mirror(pyramC, o) → pyramG

AI Drawing Prompt Reference

Draw a truncated cube by constructing a cube first, then perform cutting and rotation on its faces to form the faces and edges of the truncated cube. Identify the vertices and faces of the cube, then use rotations and reflections to obtain the various parts of the truncated cube, and finally combine these parts to form the complete model.
The prompt above was compiled from the original drawing commands and is for reference only.