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Spherical Cuboctahedron

Spherical Cuboctahedron
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2014-07-04 02:42
TrigonometrySolid GeometryGeometric Construction
In collections Spherical Geometry Ideas
This example demonstrates the construction and properties of a spherical cuboctahedron, a semiregular tessellation. Dragging the blue and red points allows exploration of its geometry. Key mathematical concepts include spherical geometry, symmetry, and semiregular tessellations. The construction utilizes commands like Sphere, PointIn, Mirror, Line, OrthogonalPlane, IntersectPath, Point, Circle, Plane, OrthogonalLine, Rotate, and Angle. Suitable for high school students and math enthusiasts studying solid geometry.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → a
  2. PointIn(a) → A
  3. Mirror(A, O) → A'
  4. Line(A, A') → b
  5. OrthogonalPlane(O, b) → c
  6. IntersectPath(c, a) → d
  7. Point(d) → B
  8. Circle(A, B, A') → e
  9. Plane(A, O, B) → f
  10. OrthogonalLine(O, f) → g
  11. Rotate(B, -36*°, g) → B'
  12. Plane(B', g) → i
  13. IntersectPath(i, a) → p
  14. Line(O, B) → j
  15. Rotate(p, 90*°, j) → p'
  16. Rotate(p, -90*°, j) → p'_1
  17. Rotate(B', 180*°, j) → B''
  18. Plane(B'', g) → h
  19. IntersectPath(h, a) → k
  20. Angle(B'', O, B') → α

AI Drawing Prompt Reference

Draw a spherical cuboctahedron on a sphere, showing its semiregular tessellation properties. Include draggable blue and red points for geometric exploration. Key elements are spheres, points, lines, planes, and rotations, constructed via mirroring, intersections, and rotations. Start with a sphere, create points and mirror them, find intersections and draw circles, then use rotations and plane intersections to complete the construction, highlighting spherical geometry, symmetry, and semiregular tessellations.
The prompt above was compiled from the original drawing commands and is for reference only.