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Hollow Pyramid Construction

Hollow Pyramid Construction
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2016-07-09 01:08
Solid GeometryGeometric Construction
In collections surface 3D surface 3D
This example demonstrates the geometric construction and surface representation of a hollow pyramid. It involves core mathematical concepts such as solid geometry, surface construction, quadrilaterals, area calculation, translation transformations, and coordinate systems. The construction uses GeoGebra commands and objects like Point, Spline, Surface, Segment, and Mirror as outlined in the summary. It is suitable for high school students learning about solid geometry, spatial visualization, and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(x = y) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → H
  4. Spline({D, E, F, G, H}, 3) → a
  5. Surface(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), (y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → c
  6. Surface(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), (-((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → e
  7. Surface((-(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))))), (y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → f
  8. Surface((-(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))))), (-((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → g
  9. Surface((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))), x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → h
  10. Surface((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))), (-(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → i
  11. Surface((-((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))))), x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → j
  12. Surface((-((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))))), (-(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → k
  13. Surface((x(A) * u), (x(A) * v), 0, u, -1, 1, v, -1, 1) → b
  14. Segment(A, B) → l
  15. Surface(((x(A) + (cos(d) * (x(a(u)) - x(A)))) * (1 - v)) + (v * ((-x(A)) + (cos(π - d) * (x(a(u)) - x(A))))), y(a(u)), (sin(d) * (x(a(u)) - x(A))), u, 0, 1, v, 0, 1) → m
  16. Surface(((x(A) + (cos(d) * (x(a(u)) - x(A)))) * (1 - v)) + (v * ((-x(A)) + (cos(π - d) * (x(a(u)) - x(A))))), (-y(a(u))), (sin(d) * (x(a(u)) - x(A))), u, 0, 1, v, 0, 1) → n
  17. Surface(y(a(u)), ((x(A) + (cos(d) * (x(a(u)) - x(A)))) * (1 - v)) + (v * ((-x(A)) + (cos(π - d) * (x(a(u)) - x(A))))), (sin(d) * (x(a(u)) - x(A))), u, 0, 1, v, 0, 1) → o
  18. Surface((-y(a(u))), ((x(A) + (cos(d) * (x(a(u)) - x(A)))) * (1 - v)) + (v * ((-x(A)) + (cos(π - d) * (x(a(u)) - x(A))))), (sin(d) * (x(a(u)) - x(A))), u, 0, 1, v, 0, 1) → r
  19. Mirror(a, xAxis) → a'
  20. Mirror(A, xAxis) → A'
  21. Mirror(B, xAxis) → B'
  22. Segment(A', B') → l'
  23. Segment(A, A') → q

AI Drawing Prompt Reference

Draw a hollow pyramid with a pentagonal base and a point at the top. The sides of the pyramid are made up of multiple triangles, each connecting the base to the top through quadrilaterals. Use different colors and materials to distinguish the base and sides of the pyramid. Decorate both the base and sides with grid lines to better showcase their geometric structure.
The prompt above was compiled from the original drawing commands and is for reference only.