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Cube Construction and Surface Demo

Cube Construction and Surface Demo
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2017-10-31 05:45
PolygonSolid GeometryGeometric Construction
This example dynamically demonstrates the construction process and surface layout of a cube, visually showcasing the generation and decomposition of three-dimensional geometric figures. Core math concepts include solid geometry, polygonal surfaces, vector operations, and spatial coordinates. Key construction elements from the summary involve GeoGebra commands/objects like Point, Cube, face, and edge, achieving precise cube and surface modeling with interactivity. Suitable for high school students and math enthusiasts studying solid geometry construction, spatial visualization, and geometric drawing techniques.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD_1, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Point(Circle[C, Distance[D, C], Segment[D, C]]) → I
  4. Cube(D, C, I) → b, J, faceIJNM, faceKLMN, edgeDJ, edgeCD, edgeCI, edgeIJ_1, edgeDK, edgeJN, edgeKN, edgeKL, K, edgeCL, edgeLM, edgeIM, edgeMN, L, M, N, faceCDJI, faceDJNK, faceCDKL, faceCIML
  5. Point(Circle[I, Distance[J, I], Segment[J, I]]) → O
  6. Cube(J, I, O) → c, P, faceOPTS, faceQRST, edgeJP, edgeIJ, edgeIO, edgeOP_1, edgeJQ, edgePT, edgeQT, edgeQR, Q, edgeIR, edgeRS, edgeOS, edgeST, R, S, T, faceIJPO, faceJPTQ, faceIJQR, faceIOSR
  7. Point(Circle[O, Distance[P, O], Segment[P, O]]) → U
  8. Cube(P, O, U) → d, V, face3, face4, edgePV, edgeOP, edgeOU, edgeUV, edgePW, edge2, edge3, edgeWZ, W, edgeOZ, edge4, edge1, edge5, Z, A_1, B_1, faceOPVU, face2, faceOPWZ, face1
  9. Point(Circle[D_1, Distance[C_1, D_1], Segment[C_1, D_1]]) → E_1
  10. Cube(C_1, D_1, E_1) → e, F_1, face9, face10, edge7, edge6, edge9, edge11, edge8, edge13, edge15, edge14, G_1, edge10, edge16, edge12, edge17, H_1, I_1, J_1, face5, face7, face6, face8
  11. Point(Circle[E_1, Distance[K_1, E_1], Segment[K_1, E_1]]) → L_1
  12. Cube(K_1, E_1, L_1) → f, M_1, face15, face16, edge21, edge18, edge19, edge23, edge22, edge25, edge27, edge26, N_1, edge20, edge28, edge24, edge29, O_1, P_1, Q_1, face11, face14, face12, face13
  13. Point(Circle[G_1, Distance[P_1, G_1], Segment[P_1, G_1]]) → R_1
  14. Cube(P_1, G_1, R_1) → g, S_1, face21, face22, edge33, edge30, edge31, edge35, edge34, edge37, edge39, edge38, T_1, edge32, edge40, edge36, edge41, U_1, V_1, W_1, face17, face20, face18, face19
  15. Point(Circle[J_1, Distance[O_1, J_1], Segment[O_1, J_1]]) → Z_1
  16. Cube(O_1, J_1, Z_1) → h, A_2, face27, face28, edge45, edge42, edge43, edge47, edge46, edge49, edge51, edge50, B_2, edge44, edge52, edge48, edge53, C_2, D_2, E_2, face23, face26, face24, face25
  17. Point(Circle[Z, Distance[R, Z], Segment[R, Z]]) → F_2
  18. Cube(R, Z, F_2) → i, G_2, face33, face34, edge54, edgeRZ, edge56, edge58, edge55, edge60, edge62, edge61, H_2, edge57, edge63, edge59, edge64, I_2, J_2, K_2, face29, face31, face30, face32
  19. Point(Circle[C_2, Distance[B_2, C_2], Segment[B_2, C_2]]) → L_2
  20. Cube(B_2, C_2, L_2) → j, M_2, face39, face40, edge66, edge65, edge68, edge70, edge67, edge72, edge74, edge73, N_2, edge69, edge75, edge71, edge76, O_2, P_2, Q_2, face35, face37, face36, face38