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Kayley Pyramid

Kayley Pyramid
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2020-06-05 23:07
Coordinate GeometrySolid GeometryCalculusGeometric Construction
This example demonstrates the construction of a complex pyramid structure composed of multiple polygons. It involves core mathematical concepts such as polygon construction, midpoint calculation, coordinate geometry, calculus, ratios, and statistics. The construction utilizes GeoGebra commands/objects like Polygon and Midpoint. Suitable for high school students and educators.

GeoGebra Commands & Parameters

  1. Polygon(A_2, B_2, 4) → poly1, f, g, h, i, C_2, D_2
  2. Polygon(D_2, C_2, 4) → poly2, j, k, l, m, E, F
  3. Polygon(F, E, 4) → poly3, n, p, q, r, G, H
  4. Polygon(H, G, 4) → poly4, s, t, a_2, b_2, I_1, J
  5. Midpoint(F, H) → M
  6. Midpoint(H, J) → N
  7. Midpoint(A_2, D_2) → K
  8. Midpoint(D_2, F) → L
  9. Polygon(K, L, 4) → poly5, c, d, e, f_1, O, P
  10. Polygon(O, L, 4) → poly7, k_1, l_1, m_1, n_1, S, T
  11. Polygon(T, M, 4) → poly8, p_1, q_1, r_1, s_1, U, V
  12. Midpoint(P, O) → Q
  13. Midpoint(O, T) → R
  14. Midpoint(T, V) → W
  15. Polygon(Q, R, 4) → poly6, g_1, h_1, i_1, j_1, Z, A_1
  16. Polygon(Z, R, 4) → poly9, t_1, a_1, b_1, c_1, B_1, C_1
  17. Midpoint(A_1, Z) → D_1
  18. Midpoint(Z, C_1) → E_1
  19. Polygon(D_1, E_1, 4) → poly10, d_1, e_1, f_2, g_2, F_1, G_1

AI Drawing Prompt Reference

Draw a complex pyramid structure composed of multiple squares. The base is a square, and the sides are also squares. Start by drawing the base square, then sequentially draw four adjacent squares as the sides. Find the midpoints of the intersections between the base and the sides, connect these midpoints to form new squares, and finally create a multi-layered complex pyramid structure.
The prompt above was compiled from the original drawing commands and is for reference only.