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Octahedron and Dodecahedron

Octahedron and Dodecahedron
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2017-08-19 01:37
PolygonSolid Geometry
In collections Polyeder, whose coordinates are golden numbers
This example demonstrates the geometric construction and relationship between an octahedron and a dodecahedron. It involves core math concepts like polygons, solid geometry, and geometric transformations. GeoGebra commands and objects used include If, Circle, Point, Rotate, Distance, Dodecahedron, Midpoint, Polygon, Octahedron. Suitable for high school solid geometry teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. If(n ≟ 3, L / t, If[n ≟ 4, L / c, If[n ≟ 5, L / p]]) → ar
  2. If(RA ≟ 0, L, If[RA ≟ 1, ar]) → des
  3. Circle(O, des, xOyPlane) → ci
  4. Point(ci) → A
  5. Rotate(A, (360 * ° / n), O) → A'
  6. Rotate(A', (360 * ° / n), O) → A''
  7. Distance(A, A') → b
  8. Distance(A, A') → arista
  9. Distance(O, A'') → radio
  10. Dodecahedron(A, A', A'') → a, B, K, M, N, P, Q, R, S, T, caraAA'A''BC, caraACGNH, C, caraAA'DIH, caraA'A''EJD, caraA''BFKE, caraBCGMF, caraGMSTN, caraHIPTN, caraDIPQJ, caraEJQRK, caraFKRSM, caraPQRST, D, aristaAC, aristaAA', aristaA'A'', aristaA''B, aristaBC, aristaAH, aristaCG, aristaGN, aristaHN, aristaHI, E, aristaDI, aristaA'D, aristaDJ, aristaEJ, aristaA''E, aristaEK, aristaFK, aristaBF, aristaFM, aristaGM, F, aristaMS, aristaST, aristaNT, aristaPT, aristaIP, aristaPQ, aristaJQ, aristaQR, aristaKR, aristaRS, G, H, I, J
  11. Midpoint(aristaCG) → U
  12. Midpoint(aristaA'A'') → V
  13. Midpoint(aristaFK) → W
  14. Polygon(U, V, W) → polígono1, w, u, v_1
  15. Octahedron(V, W, U) → d, Z, cara3, cara6, aristaUV, aristaVW, aristaUW, arista3, arista2, aristaVZ, arista6, aristaWZ, A_1, arista4, arista5, arista1, arista7, B_1, caraUVW, cara1, cara4, caraVWZ, cara5, cara2
  16. Rotate(d, 72°, zAxis) → d1
  17. Rotate(d1, 72°, zAxis) → d2
  18. Rotate(d2, 72°, zAxis) → d3
  19. Rotate(d3, 72°, zAxis) → d4

AI Drawing Prompt Reference

Draw a dodecahedron and an octahedron. Start by creating a regular pentagon, then rotate it around the center to form a dodecahedron. Next, create a regular quadrilateral and rotate it to form an octahedron. Finally, rotate the faces of the dodecahedron to generate its symmetric faces, demonstrating the geometric relationship between the two polyhedra.
The prompt above was compiled from the original drawing commands and is for reference only.