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Hexagonal Pyramid Design

Hexagonal Pyramid Design
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2019-05-01 23:41
PolygonSolid GeometryGeometric Construction
This example demonstrates how to construct a hexagonal pyramid using GeoGebra, involving core mathematical concepts like polygon construction, solid geometry, functions, and transformations. Key GeoGebra commands and objects used include Polygon, Point, Tetrahedron, and Pyramid, making it suitable for high school students and educators for practicing solid geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6, xOyPlane) → poly1, f, F, g, h, i, j, k, C, D, E
  2. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → G
  3. Tetrahedron(A, B, G) → a, H, edgeGH, edgeBH, faceABG, faceAGH, faceABH, faceBGH, edgeAG, edgeAB, edgeBG, edgeAH
  4. Point(Circle[Midpoint[B, C], (Distance[B, C] * sqrt(3) / 2), Segment[B, C]]) → I
  5. Tetrahedron(B, C, I) → b, J, edgeIJ, edgeCJ, faceBCI, faceBIJ, faceBCJ, faceCIJ, edgeBI, edgeBC, edgeCI, edgeBJ
  6. Point(Circle[Midpoint[C, D], (Distance[C, D] * sqrt(3) / 2), Segment[C, D]]) → K
  7. Tetrahedron(C, D, K) → c, L, edgeKL, edgeDL, faceCDK, faceCKL, faceCDL, faceDKL, edgeCK, edgeCD, edgeDK, edgeCL
  8. Point(Circle[Midpoint[D, E], (Distance[D, E] * sqrt(3) / 2), Segment[D, E]]) → M
  9. Tetrahedron(D, E, M) → d, N, edgeMN, edgeEN, faceDEM, faceDMN, faceDEN, faceEMN, edgeDM, edgeDE, edgeEM, edgeDN
  10. Point(Circle[Midpoint[E, F], (Distance[E, F] * sqrt(3) / 2), Segment[E, F]]) → O
  11. Tetrahedron(E, F, O) → e, P, edgeOP, edgeFP, faceEFO, faceEOP, faceEFP, faceFOP, edgeEO, edgeEF, edgeFO, edgeEP
  12. Point(Circle[Midpoint[F, A], (Distance[F, A] * sqrt(3) / 2), Segment[F, A]]) → Q
  13. Tetrahedron(F, A, Q) → l, R, edgeQR, edgeAR, faceAFQ, faceFQR, faceAFR, faceAQR, edgeFQ, edgeAF, edgeAQ, edgeFR
  14. Point(Circle[Midpoint[P, R], (Distance[P, R] * sqrt(3) / 2), Segment[P, R]]) → S
  15. Tetrahedron(P, R, S) → m, T, edgeST, edgeRT, facePRS, facePST, facePRT, faceRST, edgePS, edgePR, edgeRS, edgePT
  16. Point(Circle[Midpoint[R, H], (Distance[R, H] * sqrt(3) / 2), Segment[R, H]]) → U
  17. Tetrahedron(R, H, U) → n, V, edgeUV, edgeHV, faceHRU, faceRUV, faceHRV, faceHUV, edgeRU, edgeHR, edgeHU, edgeRV
  18. Point(Circle[Midpoint[H, J], (Distance[H, J] * sqrt(3) / 2), Segment[H, J]]) → W
  19. Tetrahedron(H, J, W) → o, Z, edgeWZ, edgeJZ, faceHJW, faceHWZ, faceHJZ, faceJWZ, edgeHW, edgeHJ, edgeJW, edgeHZ
  20. Point(Circle[Midpoint[J, L], (Distance[J, L] * sqrt(3) / 2), Segment[J, L]]) → A_1
  21. Tetrahedron(J, L, A_1) → p, B_1, edge5, edge4, face1, face3, face2, face4, edge1, edgeJL, edge3, edge2
  22. Point(Circle[Midpoint[L, N], (Distance[L, N] * sqrt(3) / 2), Segment[L, N]]) → C_1
  23. Tetrahedron(L, N, C_1) → q, D_1, edge10, edge9, face5, face7, face6, face8, edge6, edgeLN, edge8, edge7
  24. Point(Circle[Midpoint[N, P], (Distance[N, P] * sqrt(3) / 2), Segment[N, P]]) → E_1
  25. Tetrahedron(N, P, E_1) → r, F_1, edge15, edge14, face9, face11, face10, face12, edge11, edgeNP, edge13, edge12
  26. Polygon(B_1, D_1, F_1, T, V, Z) → poly2, b_1, d_1, f_1, t, v, z_1
  27. Pyramid(poly2, Q) → s, face15, edgeQT, edgeQV, edgeQZ, face16, face13, faceQTV, faceQVZ, face14, edge16, edge17, edge18