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Rotation of Cubes

Rotation of Cubes
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2019-10-10 19:13
Solid GeometryTransformationGeometric Construction
This example demonstrates the rotation of cubes. Key mathematical concepts include rotation and symmetry in solid geometry. Using GeoGebra commands such as Cube and Sequence, various faces and edges of the cube are constructed. Suitable for middle school and above students to learn solid geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Cube((-1, -1, -1), (1, -1, -1), (1, 1, -1)) → c, A, face5, faceBCDE, arête2, arête1, arête4, arête6, arête3, arêteAE, arêteBE, arêteBC, B, arête5, arêteCD, arête7, arêteDE, C, D, E, face1, face3, face2, face4
  2. Sequence(Rotate[c, i, Line[(0, 0, 0), (1, 1, 1)]], i, (2 * π / ((3 * (n + 1)))), (2 * π / 3) - (2 * π / ((3 * (n + 1)))), (2 * π / ((3 * (n + 1))))) → liste1
  3. Sequence(Rotate[c, i, Line[(0, 0, 0), (1, -1, 1)]], i, (2 * π / ((3 * (n + 1)))), (2 * π / 3) - (2 * π / ((3 * (n + 1)))), (2 * π / ((3 * (n + 1))))) → liste2
  4. Sequence(Rotate[c, i, Line[(0, 0, 0), (-1, -1, 1)]], i, (2 * π / ((3 * (n + 1)))), (2 * π / 3) - (2 * π / ((3 * (n + 1)))), (2 * π / ((3 * (n + 1))))) → liste3
  5. Sequence(Rotate[c, i, Line[(0, 0, 0), (-1, 1, 1)]], i, (2 * π / ((3 * (n + 1)))), (2 * π / 3) - (2 * π / ((3 * (n + 1)))), (2 * π / ((3 * (n + 1))))) → liste4

AI Drawing Prompt Reference

Draw a cube and then rotate it around the center point, with specific angles relative to the main diagonal, to generate a series of rotated cubes. First, draw a cube centered at the origin, then sequentially rotate the cube around different axes to generate four rotation sequences.
The prompt above was compiled from the original drawing commands and is for reference only.