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Johnson Solid J26 - Gyrobifastigium

Johnson Solid J26 - Gyrobifastigium
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2019-04-01 03:13
VectorSolid GeometryTransformationOptimizationGeometric Construction
In collections ₉Extreme Verteilung der 8 Punkten auf der Kugel
This example demonstrates the geometric construction and properties of Johnson Solid J26 (Gyrobifastigium). Key mathematical concepts include solid geometry, vector operations, rotational transformations, and calculations of volume and surface area. Construction highlights involve commands like Sphere, Polygon, Translate, Segment, Circle, Sort, Sum, Max, Min, and Vector in GeoGebra. Suitable for high school students and math enthusiasts to develop spatial reasoning and understanding of 3D shapes.

GeoGebra Commands & Parameters

  1. Sphere(O, R) → a
  2. Polygon(l0) → q0
  3. Translate(q0, Vector[O1]) → q01
  4. Translate(l0, Vector[O1]) → l01
  5. Translate(l0, Vector[(-Vector[O1])]) → l02
  6. Translate(q0, Vector[(-Vector[O1])]) → q02
  7. Segment(B01, B02) → g02
  8. Segment(C01, C02) → g01
  9. Translate(C01, Vector[O1]) → C1
  10. Translate(C02, Vector[O1]) → C2
  11. Segment(C1, C2) → g1
  12. Translate(B01, Vector[(-Vector[O1])]) → B1
  13. Translate(B02, Vector[(-Vector[O1])]) → B2
  14. Segment(B1, B2) → g2
  15. Circle((0, 0), r) → c
  16. Segment(A6, A1) → r1
  17. Segment(A6, A4) → r2
  18. Segment(A5, A2) → r3
  19. Segment(A5, A3) → r4
  20. Segment(A8, A1) → m1
  21. Segment(A8, A2) → m2
  22. Segment(A7, A4) → m3
  23. Segment(A7, A3) → m4
  24. Segment(A6, A5) → a1
  25. Segment(A7, A8) → a2
  26. Sort(Join[Sequence[Sequence[Segment[lA(i), lA(j)], j, i + 1, 8], i, 1, 8]]) → lseg
  27. Sum(lseg) → rom00
  28. Max(ff, 0, 5) → max
  29. Min(ff, 0, 5) → min
  30. Segment((0, 4), (R, 4)) → g
  31. Vector(A, AA) → u
  32. Segment(l01(1), l02(1)) → h

AI Drawing Prompt Reference

Draw Johnson Solid J26 (Gyrobifastigium), consisting of two square bases and a circular side, constructed through rotation and translation. Start by sketching two squares and a connecting circle, then translate the squares along a vector and join them to form the 3D shape. Finally, connect key points with lines to highlight the geometric features and spatial relationships, emphasizing the effects of rotation and translation transformations.
The prompt above was compiled from the original drawing commands and is for reference only.