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Rhombic Dodecahedron from Cube Animation

Rhombic Dodecahedron from Cube Animation
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2018-11-26 13:41
PolygonVectorSolid GeometryGeometric Construction
This example demonstrates the dynamic generation of a rhombic dodecahedron from a cube. Key math concepts include polygon construction, solid geometry, and vector operations. The construction leverages GeoGebra commands like Polygon, Pyramid, and If, along with objects such as buttons and sliders. Ideal for high school students and math enthusiasts exploring spatial geometry and dynamic constructions.

GeoGebra Commands & Parameters

  1. Polygon(A3, A7, A1, A5) → poly1, a3, a7, a1, a5
  2. Polygon(A7, A6, A4, A1) → poly2, f, a6, a4, g
  3. Polygon(A6, A2, A8, A4) → poly3, h, a2, a8, i
  4. Polygon(A2, A3, A5, A8) → poly4, j, k, l, m
  5. Polygon(A8, A5, A1, A4) → poly5, n, p, q, r
  6. Pyramid(poly1, C) → P1, faceA3A7C_1, faceA1A7C_1, faceA1A5C_1, faceA3A5C_1, edgeA3C_1, edgeA7C_1, edgeA1C_1, edgeA5C_1
  7. Pyramid(poly2, C) → P2, faceA6A7C_1, faceA4A6C_1, faceA1A4C_1, faceA1A7C, edgeA7C_2, edgeA6C_1, edgeA4C_1, edgeA1C_2
  8. Pyramid(poly3, C) → P3, faceA2A6C_1, faceA2A8C_1, faceA4A8C_1, faceA4A6C, edgeA6C_2, edgeA2C_1, edgeA8C_1, edgeA4C_2
  9. Pyramid(poly4, C) → P4, faceA2A3C_1, faceA3A5C, faceA5A8C_1, faceA2A8C, edgeA2C_2, edgeA3C_2, edgeA5C_2, edgeA8C_2
  10. Pyramid(poly5, C) → P5, faceA5A8C, faceA1A5C, faceA1A4C, faceA4A8C, edgeA8C, edgeA5C, edgeA1C, edgeA4C
  11. If(0 ≤ t ≤ 1, Translate[P1, Vector[(0, 0, 0), (t, 0, 0)]], If[1 < t ≤ 2, Rotate[Translate[P1, Vector[(0, 0, 0), (1, 0, 0)]], (π * (t - 1)), Line[(2, 0, 0), (2, 0, 1)]], Translate[Rotate[Translate[P1, Vector[(0, 0, 0), (1, 0, 0)]], π, Line[(2, 0, 0), (2, 0, 1)]], Vector[(0, 0, 0), ((-t) + 2, 0, 0)]]]) → P1A
  12. Polygon(A2, A3, A7, A6) → poly6, s, a, b, c
  13. Pyramid(poly6, C) → P6, faceA2A3C, faceA3A7C, faceA6A7C, faceA2A6C, edgeA2C, edgeA3C, edgeA7C, edgeA6C
  14. If(0 ≤ t ≤ 1, Translate[P2, Vector[(0, 0, 0), (0, t, 0)]], If[1 < t ≤ 2, Rotate[Translate[P2, Vector[(0, 0, 0), (0, 1, 0)]], (π * (t - 1)), Line[(0, 2, 0), (0, 2, 1)]], Translate[Rotate[Translate[P2, Vector[(0, 0, 0), (0, 1, 0)]], π, Line[(0, 2, 0), (0, 2, 1)]], Vector[(0, 0, 0), (0, (-t) + 2, 0)]]]) → P2A
  15. If(0 ≤ t ≤ 1, Translate[P3, Vector[(0, 0, 0), ((-t), 0, 0)]], If[1 < t ≤ 2, Rotate[Translate[P3, Vector[(0, 0, 0), (-1, 0, 0)]], (π * (t - 1)), Line[(-2, 0, 0), (-2, 0, 1)]], Translate[Rotate[Translate[P3, Vector[(0, 0, 0), (-1, 0, 0)]], π, Line[(-2, 0, 0), (-2, 0, 1)]], Vector[(0, 0, 0), (t - 2, 0, 0)]]]) → P3A
  16. If(0 ≤ t ≤ 1, Translate[P4, Vector[(0, 0, 0), (0, (-t), 0)]], If[1 < t ≤ 2, Rotate[Translate[P4, Vector[(0, 0, 0), (0, -1, 0)]], (π * (t - 1)), Line[(0, -2, 0), (0, -2, 1)]], Translate[Rotate[Translate[P4, Vector[(0, 0, 0), (0, -1, 0)]], π, Line[(0, -2, 0), (0, -2, 1)]], Vector[(0, 0, 0), (0, t - 2, 0)]]]) → P4A
  17. If(0 ≤ t ≤ 1, Translate[P5, Vector[(0, 0, 0), (0, 0, t)]], If[1 < t ≤ 2, Rotate[Translate[P5, Vector[(0, 0, 0), (0, 0, 1)]], (π * (t - 1)), Line[(0, 0, 2), (0, -1, 2)]], Translate[Rotate[Translate[P5, Vector[(0, 0, 0), (0, 0, 1)]], π, Line[(0, 0, 2), (0, -1, 2)]], Vector[(0, 0, 0), (0, 0, (-t) + 2)]]]) → P5A
  18. If(0 ≤ t ≤ 1, Translate[P6, Vector[(0, 0, 0), (0, 0, (-t))]], If[1 < t ≤ 2, Rotate[Translate[P6, Vector[(0, 0, 0), (0, 0, -1)]], (π * (t - 1)), Line[(0, 0, -2), (0, -1, -2)]], Translate[Rotate[Translate[P6, Vector[(0, 0, 0), (0, 0, -1)]], π, Line[(0, 0, -2), (0, -1, -2)]], Vector[(0, 0, 0), (0, 0, t - 2)]]]) → P6A

AI Drawing Prompt Reference

Draw a dynamically generated rhombic dodecahedron showing its evolution from a cube. Start by constructing multiple rhombuses as base faces, then stack them into pyramid shapes using vector operations to form each face of the cube. Finally, use controls to animate the rotation around different axes, dynamically revealing the complete form of the rhombic dodecahedron.
The prompt above was compiled from the original drawing commands and is for reference only.