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Cube + Tetrahedron Slice 3 Demo

Cube + Tetrahedron Slice 3 Demo
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2017-11-17 03:13
Solid GeometryTransformationGeometric Construction
This example demonstrates the geometric relationship and spatial distribution between a cube and a tetrahedron slice. It involves core mathematical concepts such as solid geometry, geometric construction, and spatial geometric transformations. The construction utilizes commands and objects like Rotate, Angle, Circle, Line, OrthogonalLine, Intersect, Prism, Midpoint, and Polygon in GeoGebra. Suitable for high school and above students learning solid geometry, spatial visualization, and geometric construction.

GeoGebra Commands & Parameters

  1. Rotate(D, α, C) → D'
  2. Angle(D, C, D') → β
  3. Circle(C, n - s) → c
  4. Circle(D', n - s) → d
  5. Line(C, D') → f
  6. OrthogonalLine(C, f) → g
  7. OrthogonalLine(D', f) → i
  8. Intersect(c, g) → E, F
  9. Intersect(d, i) → G, H
  10. Prism(Polygon[A, B, C, D], n) → a, I, edgeAI, edgeBJ, edgeCK, edgeDL, edgeIJ, edgeJK, edgeKL, edgeIL, J, K, L, faceABJI, faceBCKJ, faceCDLK, faceADLI, faceIJKL
  11. Prism(Polygon[C, D', H, F], n) → b, M, edgeCM, edgeD'N, edgeHO, edgeFP, edgeMN, edgeNO, edgeOP, edgeMP, N, O, P, faceCD'NM, faceD'HON, faceFHOP, faceCFPM, faceMNOP
  12. Midpoint(edgeKL) → Q
  13. Midpoint(edgeMN) → S
  14. Line(M, U) → j
  15. Line(N, U) → k
  16. Line(T, edgeMN) → l
  17. Intersect(l, k) → V
  18. Intersect(j, l) → W
  19. Midpoint((n / 2, 0, n), (n / 2, n, n)) → R
  20. Line(A_1, Z) → m
  21. Line(B_1, Z) → p
  22. Line(C_1, edgeKL) → q
  23. Intersect(p, q) → D_1
  24. Intersect(m, q) → E_1
  25. Polygon(J, G_1, Z) → t1, z_1, j_1, g_1
  26. Polygon(J, I, Z) → t2, z_2, j_2, i_1
  27. Polygon(I, F_1, Z) → t3, z_3, i_2, f_1
  28. Polygon(G_1, M, D_1, Z) → q1, g_2, m_1, d_1, z_4
  29. Polygon(Z, D_1, E_1) → t4, e_1, z_5, d_2
  30. Polygon(F_1, L, E_1, Z) → q2, f_2, l_1, e_2, z_6
  31. Polygon(L, M, D_1, E_1) → q3, l_2, m_2, d_3, e_3
  32. Polygon(P, M, W) → t5, w, p_1, m_3
  33. Polygon(P, O, V, W) → q4, p_2, o, v, w_1
  34. Polygon(O, V, N) → t6, n_1, o_1, v_1
  35. Polygon(M, W, V, N) → q5, m_4, w_2, v_2, n_2
  36. Polygon(C, D, L, E_1, D_1, M) → poly1, c_1, d_4, l_3, e_4, d_5, m_5
  37. Polygon(C, D', N, V, W, M) → poly2, c_2, d', n_3, v_3, w_3, m_6

AI Drawing Prompt Reference

Draw a cube and a tetrahedron slice to demonstrate their geometric relationship and spatial distribution. The cube and tetrahedron slice partially overlap, with intersections formed by rotating and constructing orthogonal lines. Use these intersection points to generate multiple polygonal faces. First, create the basic shapes of the cube and tetrahedron slice, then find their intersections, and finally fill the intersection area with polygonal faces to create a clear 3D effect.
The prompt above was compiled from the original drawing commands and is for reference only.