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Collapsoid Model Animation

Collapsoid Model Animation
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2020-07-17 00:40
Solid GeometryGeometric Construction
In collections Action Modular Origami
This example demonstrates the dynamic folding process of a paper model from the book 'Action Modular Origami' (ISBN 9781911093947). It involves core mathematical concepts such as special points, addition, quadratic equations, similar triangles, and functions. The construction utilizes GeoGebra commands like Point, Dodecahedron, Midpoint, Sphere, PointIn, Line, OrthogonalPlane, Plane, Circle, Center, Intersect, OrthogonalLine, Rotate, Polygon, LineBisector, AngularBisector, Sequence, Vector, Translate, and Mirror. It is suitable for high school and above, focusing on solid geometry, geometric construction, and animation creation.

GeoGebra Commands & Parameters

  1. Point(Circle[((A * (1 - sqrt(5))) + (B * (3 + sqrt(5)))) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → C
  2. Dodecahedron(A, B, C) → a, D, M, N, O, P, Q, R, S, T, faceABCDE, faceAEIOJ, E, faceABFKJ, faceBCGLF, faceCDHMG, faceDEINH, faceINSTO, faceJKPTO, faceFKPQL, faceGLQRM, faceHMRSN, facePQRST, F, edgeAE, edgeAB, edgeBC, edgeCD, edgeDE, edgeAJ, edgeEI, edgeIO, edgeJO, edgeJK, G, edgeFK, edgeBF, edgeFL, edgeGL, edgeCG, edgeGM, edgeHM, edgeDH, edgeHN, edgeIN, H, edgeNS, edgeST, edgeOT, edgePT, edgeKP, edgePQ, edgeLQ, edgeQR, edgeMR, edgeRS, I, J, K, L
  3. Midpoint(A, R) → OOO
  4. Sphere(OOO, Distance[OOO, A]) → b
  5. PointIn(b) → B_3
  6. PointIn(b) → N_2
  7. Line(P, D) → p
  8. OrthogonalPlane(OOO, p) → b_1
  9. PointIn(b_1) → L_1
  10. Plane(L_1, P, OOO) → e_1
  11. Circle(A, B, C) → c
  12. Center(c) → OO
  13. Line(OOO, OO) → f
  14. Intersect(f, b) → U, V
  15. Plane(P, U, D) → q
  16. OrthogonalLine(U, p, q) → h_1
  17. Intersect(p, h_1) → F_1
  18. OrthogonalPlane(F_1, p) → w
  19. Rotate(U, (-2 * β), F_1, w) → U'_1
  20. Polygon(P, OOO, U'_1) → poly7, j_1, k_1, l_1
  21. Rotate(U, (-β), F_1, w) → U'_3
  22. Polygon(U'_3, P, OOO) → poly3, ooo, u'_3, p_1
  23. LineBisector(P, H, q) → t
  24. Circle(OOO, P, q) → s
  25. Intersect(t, s) → C_1, D_1
  26. Polygon(OOO, C_1, U'_3) → poly4, u'_1, ooo_1, c_2
  27. OrthogonalLine(C_1, p, q) → i_1
  28. Intersect(p, i_1) → G_1
  29. OrthogonalPlane(G_1, p) → a_1
  30. Rotate(C_1, ((-3 * fac^(3)) * β), G_1, a_1) → J_1
  31. Polygon(OOO, U'_1, J_1) → poly12, j_2, ooo_8, u'_6
  32. Rotate(C_1, ((-2 * fac^(2)) * β), G_1, a_1) → H_1
  33. Polygon(OOO, H_1, U'_1) → poly10, u'_5, ooo_6, h_2
  34. Rotate(C_1, ((-fac) * β), G_1, a_1) → I_1
  35. Polygon(OOO, U'_1, I_1) → poly6, i_3, ooo_3, u'_4
  36. Polygon(OOO, I_1, U'_3) → poly5, u'_2, ooo_2, i_2
  37. AngularBisector(H, OOO, C_1) → f_1
  38. Intersect(f_1, s) → B_1, E_1
  39. Polygon(OOO, I_1, B_1) → poly9, b_3, ooo_5, i_4
  40. Polygon(OOO, C_1, B_1) → poly8, b_2, ooo_4, c_3
  41. Line(OOO, M_1) → m_1
  42. Rotate(Mirror[I_1, e_1], 180°, m_1) → O_1
  43. Polygon(OOO, H_1, O_1) → poly11, o_1, ooo_7, h_3
  44. Circle(E, I, N) → d
  45. Center(d) → OO'
  46. Plane(N, OO', OOO) → o
  47. Plane(U, Q, L) → n
  48. Point(f) → Z
  49. Polygon(Z, E, OOO) → poly1, h, i, j
  50. Rotate(V, α, OOO, o) → E'
  51. Polygon(E, E', OOO) → poly2, k, l, m
  52. Sequence(Rotate[poly1, ((n * 360) * ° / 5), f], n, 0, 4, 1) → list1
  53. Point(list1) → W
  54. Line(OOO, B) → g
  55. Rotate(list1, 120°, g) → list1'
  56. Sequence(Rotate[list1', ((n * 360) * ° / 5), f], n, 0, 5, 1) → list2
  57. Vector(OO, OOO) → u
  58. Translate(xOyPlane, u) → xOyPlane'
  59. Rotate(Mirror[{list1, list2}, xOyPlane'], 36°, f) → list2'
  60. Sequence(Rotate[poly2, ((n * 360) * ° / 5), f], n, 0, 4, 1) → list01
  61. Plane(O, T, U) → e
  62. Rotate(Z, (-α), OOO, e) → Z'
  63. Rotate(Z, α, OOO, n) → Z'_1
  64. Intersect(l, f) → A_1
  65. Mirror(list01, o) → list01'
  66. OrthogonalLine(R, q) → r
  67. Translate({list01, list01', list1', list2, list2'}, Vector[(0, 0, 0)]) → pos02
  68. Sphere(OOO, P) → v
  69. OrthogonalLine(OOO, p, q) → g_1
  70. Mirror(U, g_1) → U'
  71. Circle(F_1, U, w) → c_1
  72. Circle(G_1, C_1, a_1) → d_1
  73. Rotate(U, (-3 * β), F_1, w) → U'_2
  74. Intersect(t, p) → K_1
  75. Translate({listCollapse, Mirror[listCollapse, e_1]}, Vector[(0, 0, 0)]) → pos04
  76. Rotate(Mirror[H_1, e_1], 180°, m_1) → N_1
  77. Polygon(H_1, OOO, N_1) → poly13, n_1, h_4, ooo_9
  78. Mirror(O_1, e_1) → P_1
  79. Mirror(N_1, e_1) → Q_1
  80. Mirror(I_1, e_1) → R_1
  81. Mirror(H_1, e_1) → S_1
  82. Rotate(Mirror[J_1, e_1], 180°, m_1) → T_1
  83. Rotate(Mirror[C_1, e_1], 180°, m_1) → U_1
  84. Mirror(U_1, e_1) → V_1
  85. Polygon(OOO, P_1, R_1) → poly14, r_1, ooo_{10}, p_2
  86. Rotate(Mirror[U, e_1], 180°, m_1) → W_1
  87. Rotate(Mirror[U'_1, e_1], 180°, m_1) → Z_1
  88. Rotate(Mirror[U'_2, e_1], 180°, m_1) → A_2
  89. Mirror(A_2, e_1) → B_2
  90. Mirror(Z_1, e_1) → C_2
  91. Mirror(W_1, e_1) → D_2
  92. Point(pos04) → E_2
  93. Polygon(V_1, D_2, E_2) → poly15, e_2, v_1, d_2
  94. Polygon(P_1, E_2, D_2) → poly16, d_3, p_3, e_3
  95. Translate(listCollapseFix, Vector[(0, 0, 0)]) → pos04Fix
  96. Translate({list1, list2, list2'}, Vector[(0, 0, 0)]) → pos01
  97. Point(pos01) → F_2
  98. PointIn(b) → G_2
  99. PointIn(b) → H_2
  100. PointIn(b) → I_2
  101. PointIn(b) → J_2
  102. PointIn(b) → K_2
  103. PointIn(b) → L_2
  104. PointIn(b) → M_2
  105. OrthogonalPlane(OOO, p) → q_1
  106. Intersect(g_1, b) → O_2, P_2
  107. Circle(OOO, P_2, q_1) → s_1
  108. PointIn(b) → Q_2
  109. PointIn(b) → R_2
  110. Polygon(OOO, H_2, J_2) → poly17, j_3, ooo_{11}, h_5
  111. Polygon(OOO, K_2, J_2) → poly18, k_2, s_2, t_2
  112. Polygon(G_2, K_2, OOO) → poly19, ooo_{13}, g_2, k_3
  113. Polygon(OOO, L_2, G_2) → poly20, g_3, ooo_{14}, l_2
  114. Polygon(L_2, M_2, OOO) → poly21, ooo_{15}, l_3, m_2
  115. Polygon(B_3, N_2, OOO) → poly23, n_2, p_4, q_4
  116. Polygon(M_2, K_2, OOO) → poly22, ooo_{16}, m_3, k_4
  117. Polygon(N_2, OOO, Q_2) → poly24, a_2, f_3, n_3
  118. OrthogonalLine(OOO, g_1, q_1) → t_1
  119. Intersect(t_1, s_1) → U_2, V_2
  120. Plane(L_2, V_2, OOO) → u_1
  121. Circle(OOO, L_2, u_1) → f_2
  122. Circle(OOO, O_2, e_1) → q_2
  123. Polygon(OOO, G_2, H_2) → poly25, h_7, ooo_{19}, g_4
  124. PointIn(b) → W_2
  125. Polygon(M_2, W_2, OOO) → poly26, ooo_{20}, m_4, w_2
  126. Polygon(W_2, N_2, OOO) → poly27, ooo_{21}, w_1, n_4
  127. Polygon(N_2, R_2, OOO) → poly28, ooo_{22}, n_5, r_2
  128. PointIn(b) → C_3
  129. PointIn(b) → D_3
  130. PointIn(b) → E_3
  131. PointIn(b) → F_3
  132. PointIn(b) → G_3
  133. PointIn(b) → H_3
  134. Intersect(h_5, p) → I_3
  135. Polygon(G_3, OOO, G_2) → poly29, g_5, g_6, ooo_{12}
  136. Intersect(h_5, f_3) → J_3
  137. Polygon(G_3, H_3, OOO) → poly30, ooo_{18}, g_7, h_6
  138. Intersect(f_3, p) → K_3
  139. Polygon(H_3, OOO, L_2) → poly31, l_4, h_8, ooo_{23}
  140. Intersect(h_5, p) → L_3
  141. Polygon(D_3, M_2, OOO) → poly32, q_3, r_3, s_3
  142. Intersect(h_5, p) → M_3
  143. Polygon(D_3, M_2, OOO) → poly33, ooo_{25}, d_5, m_5
  144. Intersect(h_5, f_3) → N_3
  145. Polygon(D_3, E_3, OOO) → poly34, ooo_{26}, d_6, e_4
  146. Intersect(f_3, n_5) → O_3
  147. Polygon(E_3, W_2, OOO) → poly35, ooo_{27}, e_5, w_3
  148. Intersect(h_5, p) → P_3
  149. Polygon(N_2, OOO, I_2) → poly36, t_3, a_3, f_4
  150. Intersect(f_3, p) → Q_3
  151. Intersect(a_3, p) → R_3
  152. Polygon(OOO, I_2, J_2) → poly37, j_4, ooo_{24}, i_5
  153. Intersect(a_3, h_5) → S_3
  154. Polygon(OOO, G_2, C_3) → poly38, c_4, ooo_{28}, g_8
  155. Intersect(h_5, a_3) → T_2
  156. Polygon(OOO, J_2, B_3) → poly39, b_4, ooo_{17}, j_5
  157. Intersect(f_3, p) → Z_2
  158. Intersect(a_3, p) → A_3
  159. Polygon(OOO, B_3, M_2) → poly40, m_6, ooo_{29}, b_5
  160. Polygon(E_3, OOO, R_2) → poly41, r_4, e_6, ooo_{30}
  161. Intersect(q_4, p) → T_3
  162. Polygon(OOO, H_3, D_3) → poly42, s_4, t_4, a_4
  163. PointIn(b) → V_3
  164. PointIn(b) → W_3
  165. PointIn(b) → Z_3
  166. PointIn(b) → A_4
  167. PointIn(b) → B_4
  168. PointIn(b) → C_4
  169. PointIn(b) → D_4
  170. Intersect(m_4, w_3) → E_4
  171. Polygon(V_3, U_3, H_3) → poly43, p_5, q_5, r_5
  172. Polygon(E_3, V_3, U_3) → poly44, d_4, k_5, l_5
  173. Polygon(H_3, F_3, OOO) → poly45, ooo_{31}, h_9, f_5
  174. Polygon(V_3, Z_3, OOO) → poly46, ooo_{32}, v_3, z_3
  175. Polygon(Z_3, W_3, OOO) → poly47, ooo_{33}, z_1, w_4
  176. Polygon(W_3, E_3, OOO) → poly48, ooo_{34}, w_5, e_7
  177. Polygon(J_2, D_4, OOO) → poly49, ooo_{35}, j_6, d_7
  178. Mirror(c_1, q_1) → c_5
  179. Mirror(d_1, q_1) → s_5
  180. OrthogonalPlane(OOO, g_1) → o_2
  181. PointIn(b) → F_4
  182. PointIn(b) → G_4
  183. PointIn(b) → H_4
  184. PointIn(b) → I_4
  185. PointIn(b) → J_4
  186. PointIn(b) → K_4
  187. PointIn(b) → L_4
  188. PointIn(b) → M_4
  189. Intersect(a_3, j_6) → N_4
  190. Polygon(OOO, K_4, D_4) → poly51, d_8, ooo_{37}, k_6
  191. Intersect(a_3, d_8) → O_4
  192. Polygon(OOO, I_2, K_4) → poly52, i_6, a_6, c_6
  193. Intersect(d_8, p) → P_4
  194. Polygon(K_4, Q_2, OOO) → poly54, q_6, f_7, k_7
  195. Intersect(d_8, p) → Q_4
  196. Intersect(d_8, p) → R_4
  197. Polygon(OOO, R_2, M_4) → poly57, m_7, ooo_{43}, r_6
  198. Circle(OOO, V_2, o_2) → t_5
  199. Polygon(OOO, Q_2, M_4) → poly58, m_8, ooo_{44}, q_7
  200. Polygon(OOO, M_4, I_4) → poly59, i_8, ooo_{45}, m_9
  201. Polygon(OOO, I_4, K_4) → poly53, k_8, ooo_{39}, i_7
  202. Polygon(OOO, W_3, M_4) → poly55, m_{10}, ooo_{38}, w_6
  203. Polygon(OOO, F_4, F_3) → poly56, f_6, ooo_{40}, f_8
  204. Polygon(OOO, F_4, V_3) → poly50, v_2, ooo_{36}, f_9
  205. Polygon(OOO, I_4, J_4) → poly60, j_7, ooo_{41}, i_9
  206. Polygon(OOO, G_4, J_4) → poly61, j_8, ooo_{42}, g_9
  207. Polygon(OOO, M_4, G_4) → poly62, g_{10}, ooo_{46}, m_{11}
  208. Polygon(W_3, OOO, H_4) → poly63, h_{10}, w_7, ooo_{47}
  209. Polygon(H_4, G_4, OOO) → poly64, ooo_{48}, h_{11}, g_{11}
  210. Polygon(OOO, J_4, A_4) → poly65, a_5, ooo_{49}, j_9
  211. Polygon(OOO, L_4, G_4) → poly66, g_{12}, ooo_{50}, l_6
  212. Polygon(OOO, L_4, A_4) → poly67, a_7, ooo_{51}, l_7
  213. Rotate(listMiddle, 180°, g_1) → listMiddle'
  214. Translate({listMiddle, listMiddle'}, Vector[(0, 0, 0)]) → pos03
  215. Rotate(pos04, 180°, m_1) → pos04'

AI Drawing Prompt Reference

Create an animation showing the dynamic folding process of a paper model from a book, featuring a dodecahedron with core points, midpoints, spheres, lines, planes, and circles. Use rotations and reflections to build complex folded structures, highlighting special points, similar triangles, and function applications, suitable for high school solid geometry and geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.