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Net of a Dodecahedron

Net of a Dodecahedron
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2019-05-23 16:17
PolygonSolid GeometryGeometric Construction
In collections Learn GeoGebra Classic
① This example demonstrates the net of a regular dodecahedron, unfolding its twelve regular pentagonal faces into a planar arrangement. ② Core mathematical concepts include solid geometry, polyhedron nets, the structure of a dodecahedron (12 pentagonal faces, 30 edges, 20 vertices), and the correspondence between 3D folding and 2D unfolding. ③ Construction highlights: using GeoGebra commands such as Dodecahedron to create the solid, Intersect and Point to define vertices and edges, and Net to generate the unfolded pattern; objects include vertices A through T, faces like faceABCDE and faceAEIOJ, and edges such as edgeAE and edgeAB, illustrating the transformation from 3D to 2D. ④ Suitable for upper secondary or early university students to explore properties of regular polyhedra, enhance spatial reasoning, and see dynamic geometric construction in action.

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 the net of a regular dodecahedron, showing its twelve regular pentagonal faces arranged in a plane. First construct the dodecahedron, labeling its vertices, edges, and faces, then unfold it into a flat pattern to clearly demonstrate the correspondence between 3D folding and 2D unfolding, including the relationships and transformations among vertices, edges, and faces.
The prompt above was compiled from the original drawing commands and is for reference only.