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Pmg Frame

Pmg Frame
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2014-07-28 10:46
VectorSolid GeometryGeometric Construction
This example demonstrates the geometric construction of a cube frame. Key mathematical concepts include the symmetry and solid geometry of a cube. Using GeoGebra commands such as Point, Midpoint, Vector, Segment, LineBisector, Mirror, etc., the vertices and edges of the cube can be constructed. Suitable for middle school and above students to learn solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Midpoint(A, B) → E
  3. Midpoint(B, D) → F
  4. Midpoint(D, C) → G
  5. Midpoint(C, A) → H
  6. Midpoint(C, B) → I
  7. Vector(A, B) → u
  8. Vector(A, C) → v
  9. Vector(C, D) → w
  10. Vector(B, D) → a
  11. Segment(H, F) → b
  12. Segment(E, G) → c
  13. Segment(J, K) → e
  14. Segment(K, L) → f
  15. Segment(K, M) → g
  16. Segment(K, N) → h
  17. LineBisector(A, E) → j
  18. LineBisector(E, B) → k
  19. Mirror(cell1, j) → cell2
  20. Mirror(cell1, I) → cell3
  21. Mirror(cell2, I) → cell4
  22. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling
  23. Line(H, F) → m

AI Drawing Prompt Reference

Draw a cube frame with 8 vertices and 12 edges. Start by defining one vertex A of the cube, then find its adjacent vertices B, C, and D. Construct the midpoints E, F, G, and H of the edges AB, BC, CD, and DA. Use vectors u, v, w, and a to define the direction of the edges, and construct the edges through points and midpoints. Finally, use mirroring and rotation to generate the entire cube frame.
The prompt above was compiled from the original drawing commands and is for reference only.