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Hexagonal Pyramid by Norm Prokup

Hexagonal Pyramid by Norm Prokup
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2017-08-27 09:55
PolygonAngleSolid Geometry
This example demonstrates the construction of a hexagonal pyramid. It involves key concepts in polygons, angles, and solid geometry. Using GeoGebra commands such as Sequence, Point, Polygon, and Pyramid, various faces and edges of the hexagonal pyramid are constructed. Suitable for middle and high school students studying solid geometry.

GeoGebra Commands & Parameters

  1. Sequence((cos(((2 * π) * n / 6)), sin(((2 * π) * n / 6)), 0), n, 0, 5) → list1
  2. Point(list1) → A
  3. Point(list1) → B
  4. Point(list1) → C
  5. Point(list1) → D_1
  6. Point(list1) → E
  7. Point(zAxis) → M
  8. Point(list1) → D
  9. Point(list1) → F
  10. Polygon(C, D, E, F, A, B) → poly1, c, g, e, h_1, a_1, b
  11. Pyramid(poly1, M) → d, faceCFG, edgeFH, l, edgeBF, faceEFG, faceEFH, faceAFH, faceABF, faceBCF, edgeCF, edgeFG, edgeEF
  12. Segment(A, D) → f
  13. Segment(B, E) → i
  14. Segment(F, C) → j
  15. Intersect(j, i) → O
  16. Segment(O, M) → h
  17. Segment(K, M) → k
  18. Segment(K, O) → a
  19. Angle(B, K, O) → α
  20. Angle(A, K, M) → β
  21. Angle(K, O, M) → γ

AI Drawing Prompt Reference

Draw a regular hexagonal pyramid. Start with a regular hexagon on a horizontal plane, with six vertices evenly spaced on a circle. Place a point directly above the center of the hexagon as the apex, and connect it to each vertex to form six lateral edges and six triangular faces. Then draw three diagonals inside the hexagon that intersect at its center. From this center, draw a vertical segment to the apex, and mark several key angles formed between this vertical, the base, and the lateral edges to illustrate the geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.