MathPlotAI Logo MathPlotAI

Four Square Flexagon

Four Square Flexagon
Loading the math board and drawing, please wait…
2020-07-17 00:27
PolygonVectorGeometric Construction
In collections Action Modular Origami
This example demonstrates the animation of a model folded from paper into a four-square flexagon. Key mathematical concepts include geometric transformations and polygons. Using GeoGebra commands such as Point, Intersect, Plane, Line, etc., the folding process of the flexagon is shown. Suitable for middle school and above students to learn about geometric transformations and polygon properties.

GeoGebra Commands & Parameters

  1. Point(zAxis) → E
  2. Intersect(xAxis, yAxis) → A
  3. Plane(B, E, A) → a
  4. Line(A, B) → f
  5. Point(f) → D
  6. OrthogonalLine(D, a) → i
  7. OrthogonalLine(A, f) → g
  8. OrthogonalLine(A, xOyPlane) → h
  9. Point(f) → C
  10. Rotate(C, (-α), i) → C'
  11. If(x(C') < x(D), x(C'), x(D)) → shift
  12. Vector(((-shift), 0, 0)) → vShift
  13. Point(i) → F
  14. Translate(Plane[C', D, F], vShift) → b
  15. Translate(C', vShift) → C''
  16. Translate(D, vShift) → D'
  17. Polygon(C'', D', 4, b) → poly1, j, k, l, m, G, H
  18. Point(g) → I
  19. Plane(E, A, I) → c
  20. Mirror(poly1, a) → poly1'
  21. Mirror(poly1, c) → poly1'_1
  22. Mirror(poly1', c) → poly1''
  23. Translate({poly1, poly1', poly1'', poly1'_1}, Vector[(0, 0, 0)]) → pos1
  24. Rotate(pos1, 90°, h) → pos2
  25. Vector((0, 0, If[fractionalPart(clock) < 0.5, (-offset), offset])) → vOffset
  26. Translate(pos1, vOffset) → pos1'
  27. Rotate(pos1', 90°, h) → pos2'

AI Drawing Prompt Reference

Draw an animated four-square flexagon made from folded paper, showing the transformation process. Start by plotting the axes and determining intersection points and a reference plane, then create lines and orthogonal lines. Rotate and translate points to form multiple vertices, and finally assemble these into several quadrilaterals to display the flipping animation.
The prompt above was compiled from the original drawing commands and is for reference only.