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Skeletal Cube Animation

Skeletal Cube Animation
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2020-07-17 00:31
Solid GeometryTransformationGeometric Construction
In collections Action Modular Origami
This example demonstrates an animation of a paper model folded from the book 'Action Modular Origami' (ISBN 9781911093947). It involves core mathematical concepts like cube construction, difference and slope, real numbers, dilation, quadrilaterals, and means. The construction uses GeoGebra commands such as Point, Intersect, Cube, Midpoint, OrthogonalLine, Plane, Segment, Rotate, Polygon, Mirror, and Angle. Suitable for high school students and math enthusiasts studying solid geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Intersect(zAxis, xOyPlane) → A
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Midpoint(A, G) → OO
  6. OrthogonalLine(OO, faceABCD) → k
  7. Plane(F, C, OO) → c
  8. Segment(OO, G) → h
  9. Point(h) → I
  10. Segment(OO, F) → i
  11. Point(i) → J
  12. Plane(OO, B, G) → b
  13. Rotate(I, (-rot), J, b) → I'
  14. Polygon(F, J, I') → poly1, j, l, m
  15. Mirror(poly1, c) → poly1'_1
  16. Mirror(poly1, b) → poly1'
  17. Mirror(poly1', c) → poly1''
  18. Segment(OO, B) → f
  19. Segment(OO, C) → g
  20. Rotate(Translate[{poly1, poly1', poly1'', poly1'_1}, Vector[OO, OO]], β, k) → listPoly1
  21. Rotate(listPoly1, 90°, k) → listPoly1'
  22. Rotate(listPoly1, 180°, k) → listPoly1'_1
  23. Rotate(listPoly1, 270°, k) → listPoly1'_2
  24. Angle(J, F, I, poly1) → α

AI Drawing Prompt Reference

Create an animation of a paper model folded from a book, showing the process of folding a cube. Start by plotting points on the coordinate axes and where the axes intersect the plane. Construct a cube using these points. Then find midpoints and perpendicular lines, creating planes that include these points. Use rotations and reflections to generate multiple polygons, and finally rotate these polygons around a line to form the animation.
The prompt above was compiled from the original drawing commands and is for reference only.