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Cross Sections of a Cube by nandrews

Cross Sections of a Cube by nandrews
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2016-05-10 02:30
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the cross sections of a cube. It involves the concepts of plane figures and cross sections in solid geometry. Using GeoGebra commands such as Polygon, Prism, Point, etc., various faces and cross sections of the cube can be constructed. Suitable for middle and high school students studying solid geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Prism(poly1, 4) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  3. Point(edgeFG) → I
  4. OrthogonalLine(I, edgeEH, space) → f
  5. OrthogonalLine(I, b, space) → g
  6. Intersect(b, g) → J
  7. OrthogonalLine(J, d, space) → h
  8. Intersect(edgeEH, f) → K
  9. Intersect(h, faceADHE) → L
  10. Polygon(I, K, L, J) → poly2, i, k, l, j
  11. Point(edgeCG) → M
  12. OrthogonalLine(M, edgeBF, space) → n
  13. OrthogonalLine(M, edgeDH, space) → p
  14. Intersect(p, edgeDH) → N
  15. OrthogonalLine(N, edgeAE, space) → q
  16. Point(q) → O
  17. Point(n) → P
  18. Polygon(M, N, O, P) → poly3, m_1, n_1, o, p_1
  19. Point(edgeEH) → Q
  20. Intersect(edgeCG, edgeGH) → R
  21. Point(edgeDH) → S
  22. Plane(Q, R, S) → s
  23. IntersectPath(s, e) → poly4, T, U, V, W, t, a_1, b_1, c_1
  24. Intersect(edgeGH, edgeDH) → Z
  25. Intersect(edgeDH, d) → C_1
  26. Intersect(edgeGH, edgeEH) → A_1
  27. Intersect(edgeFG, edgeBF) → B_1
  28. Segment(A_1, B_1) → d_1
  29. Intersect(edgeBF, a) → D_1
  30. Segment(C_1, D_1) → e_1
  31. Point(d_1) → E_1
  32. Intersect(edgeCG, edgeFG) → F_1
  33. Intersect(edgeEH, edgeAE) → G_1
  34. Segment(G_1, C_1) → f_1
  35. Segment(F_1, C_1) → g_1
  36. Midpoint(g_1) → I_1
  37. Midpoint(f_1) → J_1
  38. Plane(E_1, J_1, I_1) → v
  39. IntersectPath(v, e) → poly5, K_1, l_1, L_1, M_1, N_1, O_1, h_1, i_1, j_1, k_1

AI Drawing Prompt Reference

Draw a cube and show its cross-section perpendicular to the plane FG. First, draw the base ABCD, then construct a prism with edge FG as the axis. Next, take point I on edge FG, draw a perpendicular line f to FG, find its intersection J with the base BCGF, then draw a perpendicular line h from J to edge d, find its intersection K with edge EH, and draw a perpendicular line from K to edge EF, find its intersection L with face ADHE. Finally, connect points I, K, L, and J to form the cross-section polygon.
The prompt above was compiled from the original drawing commands and is for reference only.