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Triangle on a Cube

Triangle on a Cube
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2017-07-19 13:57
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates constructing a triangle on the surface of a cube, involving core concepts in solid geometry, geometric construction, vectors, and coordinate geometry. It utilizes commands like Point, Cube, PointIn, Rotate, Segment, Intersect, and If, along with objects such as points, faces, edges, and segments. Suitable for high school and above students learning spatial geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(Circle[B_2, Distance[A_2, B_2], Segment[A_2, B_2]]) → C_2
  2. Cube(A_2, B_2, C_2) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. PointIn(faceEFGH) → B
  4. PointIn(faceABFE) → A
  5. PointIn(faceCDHG) → C
  6. Rotate(B, 90°, edgeEF) → I'
  7. Segment(A, I') → f
  8. Intersect(f, edgeEF) → L
  9. Rotate(B, 90°, edgeFG) → I'_1
  10. Rotate(A, (-(90°)), edgeBF) → J'
  11. Segment(I'_1, J') → g
  12. Intersect(g, edgeFG) → M
  13. Intersect(g, edgeBF) → N
  14. Rotate(C, 90°, edgeCG) → K'
  15. Segment(J', K') → i
  16. Rotate(C, (-(90°)), edgeGH) → K'_1
  17. Rotate(C, 90°, edgeDH) → K'_2
  18. Rotate(C, 90°, edgeCD) → K'_3
  19. Rotate(A, -90°, edgeEF) → J'_1
  20. Rotate(A, 90°, edgeAB) → J'_2
  21. Rotate(A, 90°, edgeAE) → J'_3
  22. Segment(J'_1, K'_1) → j
  23. Segment(J'_3, K'_2) → k
  24. Segment(J'_2, K'_3) → l
  25. Intersect(i, edgeBF) → O
  26. Intersect(i, edgeCG) → P
  27. Intersect(edgeEF, j) → Q
  28. Intersect(edgeGH, j) → R
  29. Intersect(edgeDH, k) → S
  30. Intersect(k, edgeAE) → T
  31. Intersect(edgeCD, l) → U
  32. Intersect(edgeAB, l) → V
  33. If(ii, PolyLine[A, O, P, C], If[ll, PolyLine[A, V, U, C], If[jj, PolyLine[A, Q, R, C], PolyLine[A, T, S, C]]]) → m
  34. Rotate(B, 90°, edgeGH) → I'_2
  35. Segment(C, I'_2) → n
  36. Rotate(B, 90°, edgeFG) → I'_3
  37. Rotate(C, 90°, edgeCG) → K'_4
  38. Segment(I'_3, K'_4) → p
  39. Rotate(C, 90°, edgeDH) → K'_5
  40. Rotate(B, 90°, edgeEH) → I'_4
  41. Segment(I'_4, K'_5) → q
  42. Intersect(edgeEH, q) → W
  43. Intersect(edgeDH, q) → Z
  44. Intersect(edgeGH, n) → A_1
  45. Intersect(p, edgeFG) → B_1
  46. Intersect(edgeCG, p) → C_1
  47. If(nn, PolyLine[C, A_1, B], If[pp, PolyLine[C, C_1, B_1, B], PolyLine[C, Z, W, B]]) → r
  48. Rotate(B, 90°, edgeEH) → I'_5
  49. Segment(I'_5, J'_3) → s
  50. Intersect(edgeEH, s) → D_1
  51. Intersect(edgeAE, s) → E_1
  52. If(ff, PolyLine[A, L, B], If[gg, PolyLine[A, N, M, B], PolyLine[A, E_1, D_1, B]]) → h