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Dodecahedron Net by Anthony OR 柯志明

Dodecahedron Net by Anthony OR 柯志明
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2014-11-12 23:30
PolygonVectorSolid GeometryTransformationGeometric Construction
In collections 3D Geometry & Cross Sections Surface Area and Volume Nets of 3D Figures 立體圖形的摺紙圖樣
This example demonstrates the net of a dodecahedron and its construction process. Key math concepts include polygons, solid geometry, vectors, and transformations. Construction highlights involve using GeoGebra commands like Point, Dodecahedron, Segment, Rotate, Circle, Center, OrthogonalLine, Polygon, and TableText to draw points, lines, and faces, with operations like rotation and orthogonal lines. Suitable for high school students and math enthusiasts learning solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Point(Circle[(((1 - sqrt(5)) * A) + ((3 + sqrt(5)) * B)) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → C
  2. Dodecahedron(A, B, C) → a, D, M, N, O, P, Q, R, S, T, faceABCDE, faceAEIOJ, E, faceABFKJ, faceBCGLF, faceCDHMG, faceDEINH, faceINSTO, faceJKPTO, faceFKPQL, faceGLQRM, faceHMRSN, facePQRST, F, edgeAE, edgeAB, edgeBC, edgeCD, edgeDE, edgeAJ, edgeEI, edgeIO, edgeJO, edgeJK, G, edgeFK, edgeBF, edgeFL, edgeGL, edgeCG, edgeGM, edgeHM, edgeDH, edgeHN, edgeIN, H, edgeNS, edgeST, edgeOT, edgePT, edgeKP, edgePQ, edgeLQ, edgeQR, edgeMR, edgeRS, I, J, K, L
  3. Segment(U, U + (0, 0, 2)) → b
  4. Point(b) → V
  5. Rotate(Polygon[A, B, F, K, J], (α * t), Segment[A, B]) → poly1
  6. Rotate(Polygon[F, K, P, Q, L], (α * t), Segment[K, F]) → poly2
  7. Rotate(Polygon[P, Q, R, S, T], (α * t), Segment[P, Q]) → poly3
  8. Rotate(poly2, (α * t), Segment[A, B]) → poly2'
  9. Rotate(poly3, (α * t), Segment[K, F]) → poly3'
  10. Rotate(poly3', (α * t), Segment[A, B]) → poly3''
  11. Circle(A, B, D) → c
  12. Center(c) → W
  13. OrthogonalLine(W, Plane[A, B, D]) → d
  14. Rotate(poly1, 72°, d) → poly1'
  15. Rotate(poly1', 72°, d) → poly1''
  16. Rotate(poly1'', 72°, d) → poly1'''
  17. Rotate(poly1''', 72°, d) → poly4
  18. Rotate(poly2', 72°, d) → poly2''
  19. Rotate(poly2'', 72°, d) → poly2'''
  20. Rotate(poly2''', 72°, d) → poly5
  21. Rotate(poly5, 72°, d) → poly5'
  22. Polygon(A, B, C, D, E) → poly6, a_1, b_1, c_1, d_1, e
  23. TableText({{LaTeX[A, true, true]}, {LaTeX[B, true, true]}, {LaTeX[C, true, true]}, {LaTeX[D, true, true]}, {LaTeX[E, true, true]}, {LaTeX[F, true, true]}, {LaTeX[G, true, true]}, {LaTeX[H, true, true]}, {LaTeX[I, true, true]}, {LaTeX[J, true, true]}, {LaTeX[K, true, true]}, {LaTeX[L, true, true]}, {LaTeX[M, true, true]}, {LaTeX[N, true, true]}, {LaTeX[O, true, true]}, {LaTeX[P, true, true]}, {LaTeX[Q, true, true]}, {LaTeX[R, true, true]}, {LaTeX[S, true, true]}, {LaTeX[T, true, true]}, {LaTeX[U, true, true]}, {LaTeX[V, true, true]}, {LaTeX[W, true, true]}}) → text1
  24. Rotate(poly2''', 72°, d) → poly7
  25. Rotate(poly1'', 72°, d) → poly1'''_1
  26. Polygon(A, B, C, D, E) → poly8, a_2, b_2, c_2, d_2, e_1
  27. Rotate(poly1''', 72°, d) → poly9
  28. Rotate(poly5, 72°, d) → poly5'_1
  29. Rotate(Polygon[A, B, F, K, J], (α * t), Segment[A, B]) → poly10
  30. Rotate(poly2, (α * t), Segment[A, B]) → poly2'_1
  31. Rotate(poly3', (α * t), Segment[A, B]) → poly3''_1
  32. Rotate(poly1, 72°, d) → poly1'_1
  33. Rotate(poly2', 72°, d) → poly2''_1
  34. Rotate(poly1', 72°, d) → poly1''_1
  35. Rotate(poly2'', 72°, d) → poly2'''_1

AI Drawing Prompt Reference

Draw the net of a dodecahedron to demonstrate its construction process. Start by sketching twelve regular pentagons, then rotate and connect them to form the 3D shape of a dodecahedron. Use rotations and orthogonal lines to ensure accuracy in the shape, and label key points and edges, resulting in a clear and understandable net of a dodecahedron.
The prompt above was compiled from the original drawing commands and is for reference only.