MathPlotAI Logo MathPlotAI

From Cube to Dodecahedron

From Cube to Dodecahedron
Loading the math board and drawing, please wait…
2017-12-09 03:43
Solid GeometryTransformationGeometric Construction
In collections Polyeder, whose coordinates are golden numbers
This example demonstrates the transformation from a cube to a dodecahedron. Key mathematical concepts include solid geometry transformations and properties of polyhedra. Using commands like Vector, Mirror, Translate, and Rotate, students can understand the process of transforming one polyhedron into another. Suitable for middle and high school students studying solid geometry and transformations.

GeoGebra Commands & Parameters

  1. Vector((0, 0, 0), (0, 1, 0)) → u
  2. Cube((-1, -1, -1), (1, -1, -1), (1, 1, -1)) → a, B, face5, face6, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, C, edge9, edge10, edge11, edge12, D, E, F, face1, face2, face3, face4
  3. Polygon(E, F, F1, F2, E) → poly1, e, f, f1_1, f2_1, e_1
  4. Mirror(poly1, xOyPlane) → poly1'
  5. Polygon(E, F2, (1, 1, -1)) → tre, c, e_2, f2_2
  6. Mirror(tre, yAxis) → tre'
  7. Translate(list1, Vector[(b * u)]) → list1'_2
  8. Rotate(list1'_2, π / 2, xAxis) → list1'
  9. Rotate(list1', π / 2, zAxis) → list1''
  10. Rotate(list1', π / 2, yAxis) → list1''_1
  11. Mirror(list1, xAxis) → list1'_1
  12. Mirror(list1'', xAxis) → list1'''
  13. Mirror(list1''_1, zAxis) → list2
  14. Mirror(list1'_2, xAxis) → list3
  15. Rotate(list10, d, zAxis) → list10'