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3D Cube Puzzle Demonstration

3D Cube Puzzle Demonstration
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2018-06-15 06:34
PolygonSolid GeometryGeometric Construction
This example demonstrates the dynamic changes and combinations of a 3D cube puzzle as the green points are dragged. It involves core mathematical concepts such as solid geometry, polygon construction, and spatial transformation. The construction highlights GeoGebra commands like Point, Polygon, and Prism. Suitable for high school and above, it aids in teaching solid geometry and spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Point(Segment[(0, -1, 0), (0, -4, 0)]) → A
  2. Point(Segment[(-4, 4, 0), (0, 1, 0)]) → M
  3. Polygon(A, B, C, F, E, D_2) → poly1, a, b, c, f, e, d
  4. Prism(poly1, 1) → g, G_3, faceEFJK, faceDEKL, faceADLG, faceGHIJKL, edgeAG, edgeBH, edgeCI, edgeFJ, edgeEK, edgeDL, H, edgeGH, edgeHI, edgeIJ, edgeJK, edgeKL, edgeGL, I, J_4, K, L, faceABHG, faceBCIH, faceCFJI
  5. Prism(M, N, O, P, Q, R, S_2, T, M + (0, 0, 1)) → h, U, faceNOVU, faceOPWV, facePQZW, face3, face4, face5, face2, face6, edgeMN, edgeNO, V_3, edgeOP, edgePQ, edgeQR, edgeRS, edgeST, edgeMT, edge1, edgeNU, edgeOV, edgePW, W, edgeQZ, edge2, edge3, edge4, edge5, edgeUV, edgeVW, edgeWZ, edge7, edge8, Z, edge9, edge6, A_1, B_1, C_1, faceMNOPQRST, face1
  6. Point(Segment[(0, 0, 4), (0, 0, 0)]) → D
  7. Prism(D, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1) → i, L_1, face9, face10, face11, face12, face13, face14, face8, face16, edge10, edge13, M_1, edge15, edge17, edge19, edge21, edge23, edge11, edge12, edge14, edge16, edge18, N_1, edge20, edge22, edge24, edge25, edge26, edge28, edge29, edge30, edge31, edge32, O_1, edge33, edge27, P_1, Q_1, R_1, face15, face7
  8. Point(Segment[(0, 4, 1), (0, 0, 1)]) → S
  9. Prism(S, S_1, T_1, U_1, V_1, W_1, Z_1) → j, A_2, face21, face22, face18, face24, edge34, edge37, edge39, edge41, edge43, edge35, B_2, edge36, edge38, edge40, edge42, edge44, edge45, edge46, edge48, edge49, edge50, C_2, edge51, edge47, E_2, F_2, face23, face17, face19, face20
  10. Point(Segment[(6, -1, 1), (3, -1, 1)]) → G
  11. Prism(G, G_2, H_2, I_2, J_2) → k, K_2, edge52, edge55, edge57, edge53, edge54, edge56, edge58, edge59, edge60, edge62, L_2, edge63, edge61, M_2, face25, face26, face28, face29, face27, face30
  12. Prism(N_2, P_2, Q_2, M_2, O_2) → l, R_2, edge68, edge71, edge65, edge64, edge67, edge72, edge73, edge66, edge69, edge74, T_2, edge75, edge70, U_2, face32, face34, face36, face33, face31, face35
  13. Point(Segment[(2, -6, 1), (2, -2, 1)]) → V
  14. Prism(V, Z_2, W_2, V_2, A_3) → m, B_3, edge77, edge81, edge79, edge76, edge78, edge83, edge82, edge80, edge84, edge86, C_3, edge87, edge85, D_3, face37, face39, face41, face40, face38, face42
  15. Prism(H_3, B_3, E_3, F_3, I_3) → n, K_3, edge89, edge88, edge91, edge93, edge95, edge90, edge92, edge94, edge96, edge98, L_3, edge99, edge97, M_3, face43, face45, face44, face46, face47, face48
  16. Point(Segment[(3, -2, 1), (5, -5, 3)]) → J
  17. Prism(J, J_3, N_3, O_3, P_3, Q_3, R_3) → o, S_3, face53, face54, face50, face56, edge100, edge103, edge105, edge107, edge109, edge101, T_3, edge102, edge104, edge106, edge108, edge110, edge111, edge112, edge114, edge115, edge116, U_3, edge117, edge113, W_3, Z_3, face55, face49, face51, face52
  18. Prism(S_3, B_4, W_3, A_4, C_4) → p, D_4, edge119, edge122, edge121, edge118, edge120, edge125, edge123, edge124, edge126, edge128, E_4, edge129, edge127, F_4, face57, face59, face61, face60, face58, face62