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Truncated Cube Construction

Truncated Cube Construction
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2020-04-09 01:19
PolygonSolid GeometryGeometric Construction
This example demonstrates the geometric construction and properties of a truncated cube. It involves core concepts like solid geometry, polygons, distance calculations, and transformations (rotation, reflection). GeoGebra commands used include Point, Cube, Segment, OrthogonalPlane, IntersectPath, OrthogonalLine, Rotate, Mirror, Polygon, and Distance. Suitable for high school and above students learning solid geometry, geometric construction, and spatial reasoning.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → 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. Tool1(E, H, C, G) → b, I
  4. Segment(H, I) → f
  5. Point(f) → J
  6. OrthogonalPlane(J, f) → c
  7. IntersectPath(c, a) → poly1, K, k, l, m, L, M, T, U, V, g, h, i
  8. OrthogonalLine(I, faceABCD) → j
  9. Rotate(poly1, 90°, j) → poly1'
  10. Rotate(poly1, 180°, j) → poly1'_1
  11. Rotate(poly1, 270°, j) → poly1'_2
  12. Mirror(M, j) → M'
  13. Mirror(L, j) → L'
  14. Mirror(K, j) → K'
  15. Rotate(L, 90°, j) → L'_1
  16. Rotate(M, 90°, j) → M'_1
  17. Rotate(K, 90°, j) → K'_1
  18. Mirror(M'_1, j) → N
  19. Mirror(K'_1, j) → O
  20. Mirror(L'_1, j) → P
  21. OrthogonalPlane(I, j) → d
  22. Mirror(poly1'_1, d) → t1
  23. Mirror(poly1', d) → poly1''
  24. Mirror(poly1, d) → poly1'_3
  25. Mirror(poly1'_2, d) → t2
  26. Mirror(L, d) → L'_2
  27. Mirror(K, d) → K'_2
  28. Mirror(M, d) → M'_2
  29. Mirror(P, d) → P'
  30. Mirror(O, d) → O'
  31. Mirror(N, d) → N'
  32. Mirror(L', d) → L''
  33. Mirror(M', d) → M''
  34. Mirror(K', d) → K''
  35. Mirror(K'_1, d) → Q
  36. Mirror(M'_1, d) → R
  37. Mirror(L'_1, d) → S
  38. Polygon(L, M'_1, K'_1, Q, R, L'_2, K'_2, K) → poly2, l_1, m'_1, k'_1, q, r, l'_2, k'_2, k_1
  39. Polygon(L'_1, M', K', K'', M'', S, Q, K'_1) → poly3, l'_1, m', k', k'', m'', s, q_1, k'_3
  40. Polygon(P, M, K, K'_2, M'_2, P', O', O) → poly4, p, m_1, k_2, k'_4, m'_2, p', o', o
  41. Polygon(L', N, O, O', N', L'', K'', K') → poly5, l', n, o_1, o'_1, n', l'', k''_1, k'_5
  42. Polygon(L', M', L'_1, M'_1, L, M, P, N) → poly6, l'_3, m'_3, l'_4, m'_4, l_2, m_2, p_1, n_1
  43. Polygon(L'', M'', S, R, L'_2, M'_2, P', N') → poly7, l''_1, m''_1, s_1, r_1, l'_5, m'_5, p'_1, n'_1
  44. Distance(H, J) → e