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Jack Puzzle Cube

Jack Puzzle Cube
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2017-05-03 23:46
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric construction of a cube. Key mathematical concepts include the geometric properties of a cube and solid geometry. Using GeoGebra commands such as Intersect and Point, the faces and edges of the cube can be constructed. Suitable for high school or university students and teachers for teaching geometric construction and solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xAxis) → A
  2. Point(yAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC_1, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(Circle[C, Distance[B, C], Segment[B, C]]) → I
  6. Point(zAxis) → J
  7. Point(zAxis) → K
  8. Point(Circle[K, Distance[J, K], Segment[J, K]]) → L
  9. Point(Circle[M, Distance[C, M], Segment[C, M]]) → N
  10. Cube(C, M, N) → b, O, faceNOSR, facePQRS, edgeCO, edgeCM, edgeMN, edgeNO, edgeCP, edgeOS, edgePS, edgePQ, P, edgeMQ, edgeQR, edgeNR_1, edgeRS, Q, R, S, faceCMNO, faceCOSP, faceCMQP, faceMNRQ
  11. Point(yAxis) → T
  12. Point(Circle[T, Distance[B, T], Segment[B, T]]) → U
  13. Cube(B, T, U) → c, V, face3, face4, edgeBV, edgeBT, edgeTU, edgeUV, edgeBW, edge2, edge3, edgeWZ, W, edgeTZ, edge4, edge1, edge5, Z, A_1, B_1, faceBTUV, face1, faceBTZW, face2
  14. Point(Circle[C_1, Distance[U, C_1], Segment[U, C_1]]) → D_1
  15. Cube(U, C_1, D_1) → d, E_1, face9, face10, edge7, edge6, edge9, edge11, edge8, edge13, edge15, edge14, F_1, edge10, edge16, edge12, edge17, G_1, H_1, I_1, face5, face7, face6, face8
  16. Point(Circle[R, Distance[N, R], Segment[N, R]]) → K_1
  17. Point(Circle[H, Distance[Q, H], Segment[Q, H]]) → L_1
  18. Point(Circle[R, Distance[H, R], Segment[H, R]]) → J_1
  19. Point(Circle[Q, Distance[G, Q], Segment[G, Q]]) → M_1
  20. Cube(G, Q, M_1) → e, N_1, face15, face16, edge18, edgeGQ, edge20, edge22, edge19, edge24, edge26, edge25, O_1, edge21, edge27, edge23, edge28, P_1, Q_1, R_1, face11, face13, face12, face14
  21. Point(Circle[P_1, Distance[O_1, P_1], Segment[O_1, P_1]]) → S_1
  22. Cube(O_1, P_1, S_1) → f, T_1, face21, face22, edge30, edge29, edge32, edge34, edge31, edge36, edge38, edge37, U_1, edge33, edge39, edge35, edge40, V_1, W_1, Z_1, face17, face19, face18, face20
  23. Point(Circle[V_1, Distance[U_1, V_1], Segment[U_1, V_1]]) → A_2
  24. Point(xAxis) → B_2
  25. Point(xAxis) → C_2
  26. Point(Circle[C_2, Distance[B_2, C_2], Segment[B_2, C_2]]) → D_2
  27. Point(Circle[F_2, Distance[E_2, F_2], Segment[E_2, F_2]]) → G_2
  28. Cube(E_2, F_2, G_2) → g, H_2, face27, face28, edge42, edge41, edge44, edge46, edge43, edge48, edge50, edge49, I_2, edge45, edge51, edge47, edge52, J_2, K_2, L_2, face23, face25, face24, face26
  29. Point(Circle[N_2, Distance[M_2, N_2], Segment[M_2, N_2]]) → O_2
  30. Cube(M_2, N_2, O_2) → h, P_2, face33, face34, edge54, edge53, edge56, edge58, edge55, edge60, edge62, edge61, Q_2, edge57, edge63, edge59, edge64, R_2, S_2, T_2, face29, face31, face30, face32
  31. Point(Circle[O_2, Distance[C_2, O_2], Segment[C_2, O_2]]) → U_2
  32. Cube(C_2, O_2, U_2) → i, V_2, face39, face40, edge66, edge65, edge68, edge70, edge67, edge72, edge74, edge73, W_2, edge69, edge75, edge71, edge76, Z_2, A_3, B_3, face35, face37, face36, face38
  33. Point(Circle[A_3, Distance[J_2, A_3], Segment[J_2, A_3]]) → C_3
  34. Cube(J_2, A_3, C_3) → j, D_3, face45, face46, edge78, edge77, edge80, edge82, edge79, edge84, edge86, edge85, E_3, edge81, edge87, edge83, edge88, F_3, G_3, H_3, face41, face43, face42, face44
  35. Point(Circle[F_3, Distance[E_3, F_3], Segment[E_3, F_3]]) → I_3
  36. Cube(E_3, F_3, I_3) → k, J_3, face51, face52, edge90, edge89, edge92, edge94, edge91, edge96, edge98, edge97, K_3, edge93, edge99, edge95, edge100, L_3, M_3, N_3, face47, face49, face48, face50
  37. Point(Circle[O_3, Distance[D_2, O_3], Segment[D_2, O_3]]) → P_3
  38. Point(Circle[R_3, Distance[Q_3, R_3], Segment[Q_3, R_3]]) → S_3
  39. Cube(Q_3, R_3, S_3) → l, T_3, face57, face58, edge102, edge101, edge104, edge106, edge103, edge108, edge110, edge109, U_3, edge105, edge111, edge107, edge112, V_3, W_3, Z_3, face53, face55, face54, face56
  40. Point(Circle[A_4, Distance[R_3, A_4], Segment[R_3, A_4]]) → B_4
  41. Cube(R_3, A_4, B_4) → m, C_4, face63, face64, edge114, edge113, edge116, edge118, edge115, edge120, edge122, edge121, D_4, edge117, edge123, edge119, edge124, E_4, F_4, G_4, face59, face61, face60, face62
  42. Point(Circle[H_4, Distance[A_4, H_4], Segment[A_4, H_4]]) → I_4
  43. Cube(A_4, H_4, I_4) → n, J_4, face69, face70, edge126, edge125, edge128, edge130, edge127, edge132, edge134, edge133, K_4, edge129, edge135, edge131, edge136, L_4, M_4, N_4, face65, face67, face66, face68
  44. Point(Circle[P_4, Distance[O_4, P_4], Segment[O_4, P_4]]) → Q_4
  45. Cube(O_4, P_4, Q_4) → o, R_4, face75, face76, edge138, edge137, edge140, edge142, edge139, edge144, edge146, edge145, S_4, edge141, edge147, edge143, edge148, T_4, U_4, V_4, face71, face73, face72, face74
  46. Point(Circle[E_4, Distance[V_3, E_4], Segment[V_3, E_4]]) → W_4
  47. Cube(V_3, E_4, W_4) → p, Z_4, face81, face82, edge150, edge149, edge152, edge154, edge151, edge156, edge158, edge157, A_5, edge153, edge159, edge155, edge160, B_5, C_5, D_5, face77, face79, face78, face80
  48. Point(Circle[F_5, Distance[E_5, F_5], Segment[E_5, F_5]]) → G_5
  49. Cube(E_5, F_5, G_5) → q, H_5, face87, face88, edge162, edge161, edge164, edge166, edge163, edge168, edge170, edge169, I_5, edge165, edge171, edge167, edge172, J_5, K_5, L_5, face83, face85, face84, face86
  50. Point(Circle[F_5, Distance[M_5, F_5], Segment[M_5, F_5]]) → N_5
  51. Point(Circle[M_5, Distance[F_5, M_5], Segment[F_5, M_5]]) → O_5
  52. Cube(F_5, M_5, O_5) → r, P_5, face93, face94, edge174, edge173, edge176, edge178, edge175, edge180, edge182, edge181, Q_5, edge177, edge183, edge179, edge184, R_5, S_5, T_5, face89, face91, face90, face92
  53. Point(Circle[U_5, Distance[M_5, U_5], Segment[M_5, U_5]]) → V_5
  54. Cube(M_5, U_5, V_5) → s, W_5, face99, face100, edge186, edge185, edge188, edge190, edge187, edge192, edge194, edge193, Z_5, edge189, edge195, edge191, edge196, A_6, B_6, C_6, face95, face97, face96, face98
  55. Point(Circle[D_6, Distance[M_5, D_6], Segment[M_5, D_6]]) → E_6
  56. Cube(M_5, D_6, E_6) → t, F_6, face105, face106, edge198, edge197, edge200, edge202, edge199, edge204, edge206, edge205, G_6, edge201, edge207, edge203, edge208, H_6, I_6, J_6, face101, face103, face102, face104
  57. Point(Circle[R_5, Distance[J_5, R_5], Segment[J_5, R_5]]) → K_6
  58. Cube(J_5, R_5, K_6) → u, L_6, face111, face112, edge210, edge209, edge212, edge214, edge211, edge216, edge218, edge217, M_6, edge213, edge219, edge215, edge220, N_6, O_6, P_6, face107, face109, face108, face110
  59. Point(Circle[S_6, Distance[R_6, S_6], Segment[R_6, S_6]]) → T_6
  60. Cube(R_6, S_6, T_6) → v, U_6, face117, face118, edge222, edge221, edge224, edge226, edge223, edge228, edge230, edge229, V_6, edge225, edge231, edge227, edge232, W_6, Z_6, A_7, face113, face115, face114, face116
  61. Point(Circle[B_7, Distance[S_6, B_7], Segment[S_6, B_7]]) → C_7
  62. Cube(S_6, B_7, C_7) → w, D_7, face123, face124, edge234, edge233, edge236, edge238, edge235, edge240, edge242, edge241, E_7, edge237, edge243, edge239, edge244, F_7, G_7, H_7, face119, face121, face120, face122
  63. Point(Circle[I_7, Distance[B_7, I_7], Segment[B_7, I_7]]) → J_7
  64. Cube(B_7, I_7, J_7) → a_1, K_7, face129, face130, edge246, edge245, edge248, edge250, edge247, edge252, edge254, edge253, L_7, edge249, edge255, edge251, edge256, M_7, N_7, O_7, face125, face127, face126, face128
  65. Point(Circle[Q_7, Distance[P_7, Q_7], Segment[P_7, Q_7]]) → R_7
  66. Cube(P_7, Q_7, R_7) → b_1, S_7, face135, face136, edge258, edge257, edge260, edge262, edge259, edge264, edge266, edge265, T_7, edge261, edge267, edge263, edge268, U_7, V_7, W_7, face131, face133, face132, face134
  67. Point(Circle[Z_7, Distance[Q_7, Z_7], Segment[Q_7, Z_7]]) → A_8
  68. Cube(Q_7, Z_7, A_8) → c_1, B_8, face141, face142, edge270, edge269, edge272, edge274, edge271, edge276, edge278, edge277, C_8, edge273, edge279, edge275, edge280, D_8, E_8, F_8, face137, face139, face138, face140
  69. Point(Circle[F_7, Distance[W_6, F_7], Segment[W_6, F_7]]) → G_8
  70. Cube(W_6, F_7, G_8) → d_1, H_8, face147, face148, edge282, edge281, edge284, edge286, edge283, edge288, edge290, edge289, I_8, edge285, edge291, edge287, edge292, J_8, K_8, L_8, face143, face145, face144, face146