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Stellated Icosahedron

Stellated Icosahedron
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2014-12-28 22:57
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction of a stellated icosahedron. It involves the concept of polyhedra in solid geometry. Using GeoGebra commands such as Point, Line, and Intersect, various faces and edges of the stellated icosahedron are constructed. Suitable for high school or university-level solid geometry studies.

GeoGebra Commands & Parameters

  1. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → C
  2. Icosahedron(A, B, C) → a, D, faceABC, faceACF, faceAFG, faceADG, faceABD, faceBDH, faceBEH, faceBCE, faceCEI, faceCFI, E, faceEHK, faceEIK, faceIKL, faceFIL, faceHJK, faceJKL, faceGJL, faceFGL, faceDHJ, faceDGJ, F, edgeAC, edgeAB, edgeBC, edgeAF, edgeCF, edgeAG, edgeFG, edgeAD, edgeDG, edgeBD, G, edgeBH, edgeDH, edgeBE, edgeEH, edgeCE, edgeCI, edgeEI, edgeFI, edgeEK, edgeHK, H, edgeIK, edgeIL, edgeKL, edgeFL, edgeJK, edgeHJ, edgeJL, edgeGL, edgeGJ, edgeDJ, I, J, K, L
  3. Line(G, J) → b
  4. Line(B, H) → c
  5. Intersect(c, b) → M
  6. Pyramid(faceHJK, M) → d, faceJKM, faceHKM, faceHJM, edgeJM, edgeKM, edgeHM
  7. Midpoint(D, I) → N
  8. Mirror(d, N) → d'
  9. Line(I, F) → e
  10. Intersect(b, e) → O
  11. Line(F, G) → f
  12. Line(J, K) → g
  13. Line(K, I) → h
  14. Intersect(g, e) → P
  15. Intersect(h, f) → Q
  16. Intersect(f, g) → R
  17. Pyramid(faceAFG, O) → i, faceAGO, faceAFO, faceFGO, edgeGO, edgeAO, edgeFO
  18. Pyramid(faceCFI, Q) → j, faceCFQ, faceCIQ, faceFIQ, edgeFQ, edgeCQ, edgeIQ
  19. Pyramid(faceEIK, P) → k, faceEIP, faceEKP, faceIKP, edgeIP, edgeEP, edgeKP
  20. Pyramid(faceDGJ, R) → l, faceGJR, faceDJR, faceDGR, edgeGR, edgeJR, edgeDR
  21. Mirror(i, N) → i'
  22. Mirror(j, N) → j'
  23. Mirror(k, N) → k'
  24. Mirror(l, N) → l'
  25. Line(I, E) → m
  26. Line(J, H) → n
  27. Line(J, D) → p
  28. Line(F, A) → q
  29. Line(G, A) → r
  30. Intersect(q, p) → S
  31. Pyramid(faceABD, S) → o, faceABS, faceADS, faceBDS, edgeBS, edgeAS, edgeDS
  32. Intersect(m, n) → T
  33. Pyramid(faceBEH, T) → s, faceBET, faceBHT, faceEHT, edgeET, edgeBT, edgeHT
  34. Mirror(o, N) → o'
  35. Mirror(s, N) → s'
  36. Intersect(m, q) → U
  37. Pyramid(faceFIL, U) → t, faceFIU, faceILU, faceFLU, edgeFU, edgeIU, edgeLU
  38. Mirror(t, N) → t'
  39. Intersect(n, r) → V
  40. Pyramid(faceGJL, V) → u, faceGLV, faceJLV, faceGJV, edgeGV, edgeLV, edgeJV
  41. Mirror(u, N) → u'
  42. Line(H, B) → a_1
  43. Intersect(a_1, r) → W
  44. Pyramid(faceABC, W) → v, faceACW, faceABW, faceBCW, edgeCW, edgeAW, edgeBW
  45. Mirror(v, N) → v'

AI Drawing Prompt Reference

Draw a stellated icosahedron by first constructing the basic points and edges of the icosahedron, then determining key positions through intersections of points and lines, followed by constructing multiple pyramids using these points as vertices, and finally generating symmetric star-like structures through mirror operations to present a complex geometric shape.
The prompt above was compiled from the original drawing commands and is for reference only.