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Dodecahedron Net

Dodecahedron Net
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2020-01-16 17:44
PolygonSolid GeometryGeometric Construction
In collections 学习 GeoGebra 经典应用
This example demonstrates the net of a regular dodecahedron. Key mathematical concepts include the unfolding and reassembly of polyhedra. Using GeoGebra commands such as Intersect, Point, Dodecahedron, and Net, the net of a regular dodecahedron can be constructed. Suitable for middle school and above students or teachers for geometry education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[(((1 - sqrt(5)) * A) + ((3 + sqrt(5)) * B)) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → C
  4. 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
  5. Net(a, b) → c, U, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, V, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, W, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, face1, Z, face3, face2, face4, face5, face6, face8, face7, face10, face11, face12, A_1, face9, edge1, edgeUV, edgeVW, edgeWZ, edge8, edge11, edge15, edge13, edge2, B_1, edge3, edge27, edge28, edge4, edge5, edge33, edge34, edge6, edge7, edge39, C_1, edge40, edge9, edge10, edge45, edge46, edge12, edge16, edge19, edge20, edge17, D_1, edge18, edge25, edge26, edge14, edge29, edge31, edge32, edge30, edge35, edge37, E_1, edge38, edge36, edge41, edge43, edge44, edge42, edge21, edge23, edge24, edge22

AI Drawing Prompt Reference

Draw an unfolded net of a regular dodecahedron. The net consists of regular pentagons and hexagons connected by edges. The construction order starts from a central point, adding faces sequentially to ensure correct connections and proportions. The net should clearly show the structure of the dodecahedron, suitable for geometry education.
The prompt above was compiled from the original drawing commands and is for reference only.