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Christopher's Conjecture - Spoiler & Net

Christopher's Conjecture - Spoiler & Net
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2017-11-20 04:50
PolygonSolid GeometryGeometric Construction
This example demonstrates the geometric figures and nets related to Christopher's Conjecture. It involves core mathematical concepts such as geometric construction, polygonal unfolding, and spatial geometry. Key GeoGebra commands/objects used include Cube, Line, Point, Polygon, OrthogonalPlane, Plane, IntersectPath, Perimeter, Net, Distance, and Segment. Suitable for high school students and math enthusiasts studying solid geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Cube(C_2, B, A) → r, U, faceUEZF, faceVFZW, arêteCU, arêteBC, arêteBE, arêteEU, arêteCV, arête1, arête2, arêteVW, V, arêteBW, arêteWZ, arêteEZ, arête3, W, Z, G, faceBCUE, faceVCUF, faceBCVW, faceBEZW
  2. Line(C_2, Z) → g
  3. Point(g) → N
  4. Polygon(B, C_2, D_2, A) → faceBCDE, b, c, d, e
  5. OrthogonalPlane(N, g) → h
  6. Plane(N, h) → i
  7. IntersectPath(i, r) → poly3, D, m_1, n_1, p_1, C, D_1, K_1, F, E, s, t, f_1
  8. Perimeter(poly3) → o
  9. Net(r, net, faceBCVW, Segment[B, C_2], Segment[V, C_2], Segment[Z, A], Segment[Z, G]) → a, G_1, Q, U', S, T, G'_1, faceJPRS, faceHKOM, faceGHIJ, faceIJPQ, face1, H_1, faceHILK, arêteJP, arêtePR, arêteRS, arêteJS, arêteHK, arêteHM, arêteMO, arêteKO, arêteGJ, I, arêteGH, arêteHI, arêteIJ, arêteIQ, arêtePQ, arêtePT, arête5, arête4, arêteKL, arêteIL, J, G', L, M, U2, A'
  10. Distance(B, C) → BC
  11. Distance(B, A) → BA
  12. Distance(A, D) → AD
  13. Distance(A, U) → AU
  14. Distance(U, E) → UE
  15. Distance(U, G) → UG
  16. Distance(V, F) → VF
  17. Distance(V, G) → VG
  18. Distance(G, E) → GE
  19. Distance(G, U) → GU
  20. Segment(D_1, C') → f
  21. Segment(C', D') → k
  22. Segment(D', E') → l
  23. Segment(K_1, F') → m
  24. Segment(F', E2) → n

AI Drawing Prompt Reference

Draw a cube and its net. Start by creating a cube, then draw a line through one of its vertices. Pick a point on this line as a reference for the net. Construct the faces and edges of the cube, as well as the edges and diagonals of the net. Finally, label the lengths of the edges in the net.
The prompt above was compiled from the original drawing commands and is for reference only.