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Octahedron Net Animation

Octahedron Net Animation
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2012-05-03 19:58
Solid GeometryGeometric Construction
In collections Area, Surface Area, Volume--Nets
This GeoGebra example demonstrates the net of an octahedron and animates its construction process. Key mathematical concepts include solid geometry and geometric construction. It uses commands such as point, line segment, circle, rotation, and mirror. Suitable for middle school and above students learning solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Point(Circle[A, s]) → B
  2. Segment(A, B) → a
  3. Line(A, B) → b
  4. Circle(B, 3.0 * s / 4.5) → c
  5. Intersect(c, b, 2.0) → C
  6. Rotate(C, 30.0*°, B) → C'
  7. Line(C', b) → d
  8. Segment(B, C') → e
  9. Line(A, e) → f
  10. Intersect(d, f) → D
  11. Segment(A, C') → g
  12. Segment(D, B) → h
  13. Intersect(g, h) → E
  14. OrthogonalLine(E, a) → i
  15. Rotate(i, 5.0*°, E) → i'
  16. Circle(E, s * sqrt(3.0) / 2.0) → k
  17. Intersect(k, i', 1.0) → F
  18. Intersect(k, i', 2.0) → G
  19. Polygon(D, C', 3.0) → poly1, j, d_1, c', H
  20. Polygon(D, H, 3.0) → poly2, l, d_2, h_1, I
  21. Polygon(I, H, 3.0) → poly3, m, i_1, h_2, J
  22. Polygon(H, C', 3.0) → poly4, n, h_3, c'_1, K
  23. Polygon(C', D, 3.0) → poly5, p, c'_2, d_3, L
  24. Polygon(C', L, 3.0) → poly6, q, c'_3, l_1, M
  25. Polygon(L, D, 3.0) → poly7, r, l_2, d_4, N
  26. Polygon(M, L, 3.0) → poly8, t, m_1, l_3, O
  27. Polygon(G, A, D) → poly9, d_5, g_1, a_1
  28. Mirror(D, d_5) → D'
  29. Vector(B, D') → u
  30. Vector(A, I) → v
  31. Vector(D', J) → w
  32. Circle(J, D', B) → c_1
  33. Translate(B, Vector[u * o]) → B'_1
  34. Center(c_1) → P
  35. Ray(P, B'_1) → b_1
  36. Intersect(c_1, b_1, 1.0) → Q
  37. Translate(D', Vector[w * (o - 1.0)]) → D''
  38. Ray(P, D'') → e_1
  39. Intersect(c_1, e_1, 1.0) → R
  40. If(o < 1.0, Q, If[o < 2.0, R, J]) → S
  41. Segment(I, A) → f_1
  42. LineBisector(f_1) → j_1
  43. Intersect(f, j_1) → T
  44. CircleArc(T, I, A) → k_1
  45. Translate(A, Vector[v * (o - 1.0)]) → A'_1
  46. Ray(T, A'_1) → n_1
  47. Intersect(k_1, n_1, 1.0) → U
  48. If(o < 1.0, A, If[o < 2.0, U, I]) → V
  49. Segment(B, K) → p_1
  50. LineBisector(p_1) → q_1
  51. Intersect(q_1, c') → Z
  52. Vector(G, H) → z
  53. Vector(B, K) → u_1
  54. Translate(G, Vector[z * (o - 1.0)]) → G'
  55. LineBisector(G, H) → r_1
  56. Intersect(b, r_1) → W
  57. CircleArc(W, H, G) → s_1
  58. Ray(W, G') → t_1
  59. Intersect(s_1, t_1) → A_1,
  60. If(o < 1.0, G, If[o < 2.0, A_1, H]) → B_1
  61. Polygon(B_1, D, C') → poly10, c'_4, b_2, d_6
  62. Polygon(V, B_1, S) → poly11, s_2, v_1, b_3
  63. Polygon(V, D, B_1) → poly12, b_4, v_2, d_7
  64. LineBisector(K, B) → a_2
  65. LineBisector(A, B) → c_2
  66. OrthogonalLine(H, b) → e_2
  67. Intersect(b, c_2) → C_1
  68. Intersect(e_2, b) → D_1
  69. Vector(C_1, D_1) → w_1
  70. Translate(c_2, Vector[w_1 * (o - 1.0)]) → f_2
  71. Mirror(V, f_2) → V'
  72. If(o < 1.0, B, If[o < 2.0, V', K]) → E_1
  73. Polygon(B_1, E_1, C') → poly13, c'_5, b_5, e_3
  74. Polygon(B_1, D, C') → poly14, c'_6, b_6, d_8
  75. Midpoint(A, B) → F_1
  76. Vector(B, M) → z_1
  77. Vector(F, L) → u_2
  78. Polygon(C', B, F) → poly15, f_3, c'_7, b_7
  79. Mirror(C', B) → C''
  80. Vector(A, C'') → w_2
  81. Vector(A, N) → g_2
  82. Circle(C'', s / 5.0) → k_2
  83. Line(C', B) → i_2
  84. Intersect(k_2, i_2, 2.0) → G_1
  85. CircumcircleArc(A, G_1, O) → p_2
  86. Center(p_2) → H_1
  87. Translate(A, Vector[w_2 * (o - 2.0)]) → A'
  88. Ray(H_1, A') → j_2
  89. Intersect(p_2, j_2, 1.0) → I_1
  90. Vector(G_1, O) → z_2
  91. Translate(G_1, Vector[z_2 * (o - 3.0)]) → J_1
  92. Ray(H_1, J_1) → m_2
  93. Intersect(p_2, m_2, 1.0) → K_1
  94. If(o < 2.0, A, If[o < 3.0, I_1, If[o < 4.0, K_1, O]]) → L_1
  95. LineBisector(B, M) → n_2
  96. Translate(B, Vector[z_1 * (o - 3.0)]) → B'
  97. Segment(A, H_1) → q_2
  98. Segment(B, M) → r_2
  99. Intersect(n_2, r_2) → M_1
  100. Intersect(n_2, q_2) → N_1
  101. CircleArc(N_1, B, M) → t_2
  102. Ray(N_1, B') → a_3
  103. Intersect(t_2, a_3, 1.0) → O_1
  104. If(o < 3.0, B, If[o < 4.0, O_1, M]) → P_1
  105. LineBisector(F, L) → c_3
  106. Intersect(l_2, c_3) → Q_1
  107. CircleArc(Q_1, F, L) → g_3
  108. Translate(F, Vector[u_2 * (o - 3.0)]) → F'
  109. Ray(Q_1, F') → i_3
  110. Intersect(g_3, i_3, 1.0) → R_1
  111. If(o < 3.0, F, If[o < 4.0, R_1, L]) → S_1
  112. Polygon(S_1, P_1, L_1) → poly16, l_4, s_3, p_3
  113. Polygon(S_1, C', P_1) → poly17, p_4, s_4, c'_8
  114. Polygon(S_1, C', D) → poly18, d_9, s_5, c'_9
  115. Midpoint(A, B) → T_1
  116. OrthogonalLine(T_1, b) → j_3
  117. Intersect(b, e_2) → U_1
  118. Vector(T_1, U_1) → u_3
  119. Translate(j_3, Vector[u_3 * (o - 3.0)]) → k_3
  120. Mirror(P_1, k_3) → V_1
  121. If(o < 3.0, A, If[o < 4.0, V_1, N]) → W_1
  122. Polygon(W_1, S_1, D) → poly19, d_{10}, w_3, s_6
  123. Intersect(b_6, s_5) → Z_1
  124. Intersect(c'_5, s_5) → A_2
  125. Intersect(b_4, s_6) → B_2
  126. Intersect(v_1, s_6) → C_2
  127. Segment(C_2, A) → m_3
  128. Segment(C_2, D) → n_3
  129. Segment(V, D) → q_3
  130. Segment(C', A_2) → r_3
  131. Segment(D, A_2) → t_3
  132. Intersect(v_1, t_3) → D_2
  133. Segment(D_2, A_2) → a_4
  134. Segment(D_2, D) → c_4
  135. Intersect(s_3, c'_9) → E_2
  136. Segment(E_2, S_1) → e_4
  137. Intersect(v_1, c'_9) → F_2
  138. Segment(F_2, E_2) → f_4
  139. Segment(F_2, D) → g_4
  140. Segment(E_2, D) → h_4
  141. Intersect(b_3, c'_9) → G_2
  142. Segment(G_2, D) → i_4
  143. Segment(G_2, E_2) → j_4
  144. Point(Circle[H_2, s]) → I_2
  145. Segment(H_2, I_2) → k_4
  146. Line(H_2, I_2) → m_4
  147. Circle(I_2, 3.0 * s / 4.5) → q_4
  148. Intersect(q_4, m_4, 2.0) → J_2
  149. Rotate(J_2, 30.0*°, I_2) → K_2
  150. Line(K_2, m_4) → n_4
  151. Segment(I_2, K_2) → r_4
  152. Line(H_2, r_4) → t_4
  153. Intersect(n_4, t_4) → L_2
  154. Segment(H_2, K_2) → a_5
  155. Segment(I_2, L_2) → c_5
  156. Intersect(a_5, c_5) → M_2
  157. Circle(M_2, s * sqrt(3.0) / 2.0) → e_5
  158. OrthogonalLine(M_2, m_4) → f_5
  159. Rotate(f_5, 5.0*°, M_2) → g_5
  160. Intersect(e_5, g_5, 2.0) → N_2
  161. Intersect(e_5, g_5, 1.0) → O_2
  162. Polygon(H_2, I_2, N_2) → poly20, n_5, h_5, i_5
  163. Polygon(N_2, K_2, I_2) → poly21, i_6, n_6, k_5
  164. Polygon(I_2, K_2, O_2) → poly22, o_2, i_7, k_6
  165. Polygon(O_2, H_2, I_2) → poly23, i_8, o_1, h_6
  166. Segment(H_2, L_2) → j_5
  167. Segment(L_2, N_2) → l_5
  168. Segment(L_2, K_2) → m_5
  169. Segment(L_2, O_2) → p_5

AI Drawing Prompt Reference

Draw the net of an octahedron and show its construction process step by step. Start by creating a circle with center A, select a point B on the circle, and draw a line segment AB. Then draw a line b parallel to AB. Next, draw a circle with center B and radius 3/4.5 times the circle's radius, intersecting line b at point C. Rotate C 30 degrees around B to get C', draw a line d parallel to BC', and draw a line f parallel to AB, intersecting d at point D. Draw a line g from A to D, and a line h from B to D, intersecting g and h at point E. Draw a perpendicular line i from E, rotate i to get i', and draw a circle k with center E and radius sqrt(3)/2 times the circle's radius, intersecting i' at points F and G. Connect these points to form the net of the octahedron.
The prompt above was compiled from the original drawing commands and is for reference only.