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3D Correspondence of Symmetry Spheres-B

3D Correspondence of Symmetry Spheres-B
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2019-05-24 04:24
Solid GeometryMatrixGeometric Construction
This example demonstrates the 3D correspondence of symmetry spheres in space. It involves core mathematical concepts such as centroid, circle, circumcircle, general quadrilateral, geometric distribution, geometric mean, geometry, matrices, polygons, prism, quadrilaterals, solids or 3D shapes, symmetry, and geometric transformations. The construction uses commands and objects like Polygon, Prism, Barycenter, Sphere, PointIn, and Segment in GeoGebra. Suitable for high school and above learning solid geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  2. Prism(poly1, h) → g, F, faceAEJF, faceFGHIJ, edgeAF, edgeBG, edgeCH, edgeDI, edgeEJ, edgeFG, edgeGH, edgeHI, G, edgeIJ, edgeFJ, H, I, J, faceABGF, faceBCHG, faceCDIH, faceDEJI
  3. Barycenter({A, B, C, D, E, G, H, F, J, I}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}) → NN
  4. Sphere(NN, r) → f
  5. PointIn(f) → K
  6. Segment(G, K) → i
  7. Segment(B, K) → j
  8. Segment(F, K) → k
  9. Segment(H, K) → l
  10. Segment(C, K) → m
  11. Segment(D, K) → n
  12. Segment(E, K) → p
  13. Segment(J, K) → q
  14. Segment(I, K) → s
  15. Segment(K, A) → t

AI Drawing Prompt Reference

Construct a 3D geometric solid consisting of a pentagonal prism with height h. Place a sphere centered at the centroid of all the prism's vertices with radius r. Draw line segments from the sphere's center to each vertex of the prism and mark their intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.