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Dodecahedron Coordinates

Dodecahedron Coordinates
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2015-01-10 12:26
PolygonVectorCoordinate GeometrySolid Geometry
This example demonstrates how to construct the vertices of a regular dodecahedron using coordinates. It involves core mathematical concepts such as 3D coordinates, vectors, and polygon construction. Key GeoGebra commands and objects used include Polygon, Textfield, and various geometric entities like u, a, A, B, C, E, D, poly1, a_1, b, c, d, e, button1, F, G, H, poly2, c_1, b_1, f, g, h, I, J, poly3, a_2, b_2, f_1, i, j, K, L, poly4, e_1, a_3, j_1, k, l, M. This is suitable for high school and above students learning about polyhedra in solid geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E) → poly1, a_1, b, c, d, e
  2. Polygon(C, B, F, G, H) → poly2, c_1, b_1, f, g, h
  3. Polygon(A, B, F, I, J) → poly3, a_2, b_2, f_1, i, j
  4. Polygon(E, A, J, K, L) → poly4, e_1, a_3, j_1, k, l
  5. Polygon(D, E, L, M, N) → poly5, d_1, e_2, l_1, m, n
  6. Polygon(D, C, H, O, N) → poly6, d_2, c_2, h_1, o, n_1
  7. Polygon(K, J, I, P, Q) → poly7, k_1, j_2, i_1, p, q
  8. Polygon(G, F, I, P, R) → poly8, g_1, f_2, i_2, p_1, r
  9. Polygon(S, M, L, K, Q) → poly10, s_1, m_2, l_2, k_2, q_1
  10. Polygon(S, M, N, O, T) → poly9, s, m_1, n_2, o_1, t
  11. Polygon(T, O, H, G, R) → poly11, t_1, o_2, h_2, g_2, r_1
  12. Polygon(S, T, R, P, Q) → poly12, s_2, t_2, r_2, p_2, q_2
  13. Textfield(u) → inputBox1

AI Drawing Prompt Reference

Draw a regular dodecahedron using 3D coordinates and vectors, first defining the positions of its twelve vertices, then connecting them to form twelve faces each consisting of five equilateral triangles, and finally label the key vertices and faces for clarity.
The prompt above was compiled from the original drawing commands and is for reference only.