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Hexagonal Prism Cross Sections

Hexagonal Prism Cross Sections
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2015-05-01 22:32
PolygonSolid GeometryGeometric ConstructionGraphing
In collections Cross Sections of Prisms
This example demonstrates the various cross-sections formed by intersecting a hexagonal prism with different planes. It involves core mathematical concepts such as solid geometry, polygonal cross-sections, and spatial geometric transformations. The construction utilizes GeoGebra commands like Intersect, Point, Polygon, Prism, OrthogonalLine, Plane, and IntersectPath. Suitable for high school geometry teaching or for beginners in geometric modeling.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 6) → poly1, a, F, b, c, d, e, f, C, D, E
  4. Prism(poly1, 4.881975827544018) → g, G, faceDEKJ, faceEFLK, faceAFLG, faceGHIJKL, edgeAG, edgeBH, edgeCI, edgeDJ, edgeEK, edgeFL, H, edgeGH, edgeHI, edgeIJ, edgeJK, edgeKL, edgeGL, I, J, K, L, faceABHG, faceBCIH, faceCDJI
  5. Point(edgeDJ) → M
  6. OrthogonalLine(M, edgeCI, space) → h
  7. OrthogonalLine(M, edgeEK, space) → i
  8. Intersect(edgeCI, h) → N
  9. Intersect(i, edgeEK) → O
  10. Plane(N, M, O) → j
  11. IntersectPath(j, g) → poly2, P, n, p, q, Q, R, S, T, U, k, l, m
  12. Point(edgeHI) → V
  13. Point(edgeKL) → W
  14. OrthogonalLine(V, b, space) → r
  15. Intersect(b, r) → Z
  16. Plane(W, V, Z) → s
  17. IntersectPath(s, g) → poly3, A_1, B_1, C_1, D_1, t, a_1, b_1, c_1
  18. Point(edgeKL) → E_1
  19. Point(edgeGH) → F_1
  20. Point(edgeCI) → G_1
  21. Plane(F_1, E_1, G_1) → v
  22. IntersectPath(v, g) → poly4, H_1, f_1, g_1, h_1, i_1, j_1, I_1, J_1, K_1, L_1, M_1, N_1, d_1, e_1
  23. Point(edgeHI) → O_1
  24. Point(edgeIJ) → P_1
  25. Point(edgeCI) → Q_1
  26. Plane(O_1, P_1, Q_1) → k_1
  27. IntersectPath(k_1, g) → poly5, R_1, p_1, q_1, r_1, S_1, T_1, U_1, V_1, W_1, l_1, m_1, n_1

AI Drawing Prompt Reference

Draw a hexagonal prism and show various cross-sections formed by intersecting it with different planes. Start by constructing a regular hexagon and extrude it to form a prism. Then, find points on the edges of the prism and draw lines perpendicular to the base. Use these lines and their intersections with the prism edges to create planes. Finally, calculate the intersections of these planes with the prism to display different cross-sectional shapes.
The prompt above was compiled from the original drawing commands and is for reference only.