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Fold a Box

Fold a Box
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2017-12-15 02:55
Solid GeometryGeometric Construction
This example demonstrates how to construct a 3D box using folding techniques. It involves core math concepts like solid geometry, volume calculation, and polygon construction. GeoGebra commands and objects used include Point, Polygon, Segment, Join, and Prism. Suitable for high school students learning about 3D shapes and volume computation.

GeoGebra Commands & Parameters

  1. Point({((-length)) / 2, ((-width)) / 2, 0}) → homeCorner
  2. Polygon((0, 0) + homeCorner, (length, 0) + homeCorner, (length, width) + homeCorner, (0, width) + homeCorner) → poly1, f, g, h, i
  3. Polygon(A, B, C, D) → q1, a, b, c, d
  4. Polygon(D, E, F, G) → q2, d_1, e, f_1, g_1
  5. Polygon(G, H, I, J) → q3, g_2, h_1, i_1, j
  6. Polygon(J, K, L, C) → q4, j_1, k, l_1, c_1
  7. Polygon(P, Q, G, R) → q5, p, q, g_3, r
  8. Polygon(Z, O, W, J) → q6, z_1, o, w_1, j_2
  9. Polygon(T, D, S, homeCorner) → q7, t, d_2, s, homecorner
  10. Polygon(C, U, N, V) → q8, c_2, u, n, v
  11. Segment(D, D + (0, ((width - (2 * cut)) * creases))) → m
  12. Segment(G, G + (((length - (2 * cut)) * creases), 0)) → k_1
  13. Segment(J, J + (0, ((-(width - (2 * cut))) * creases))) → m_1
  14. Segment(C, C + (((-(length - (2 * cut))) * creases), 0)) → n_1
  15. Polygon(G, J, C, D) → q9, g_4, j_3, c_3, d_3
  16. Polygon(P, H, G, F) → q10, p_1, h_2, g_5, f_2
  17. Polygon(I, O, K, J) → q11, i_2, o_1, k_2, j_4
  18. Polygon(E, homeCorner, A, D) → q12, e_1, homecorner_1, a_1, d_4
  19. Polygon(C, L, N, B) → q13, c_4, l_2, n_2, b_1
  20. Join({Sequence[Segment[homeCorner + (i, 0), homeCorner + (i, width)], i, 0, length], Sequence[Segment[homeCorner + (0, i), homeCorner + (length, i)], i, 0, width]}) → L_1
  21. Prism(q9, (-cut)) → q_1, M, edgeGM, edge3, edge1, edge2, edge4, edge6, edge7, edge5, A_1, B_1, C_1, face4, face2, face1, face3, face5