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Geogebra Construction of Dodecahedral Pentagonal Prisms

Geogebra Construction of Dodecahedral Pentagonal Prisms
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2018-06-01 08:03
PolygonSolid GeometryMatrixTransformation
This example demonstrates how to construct a dodecahedral pentagonal prism using GeoGebra, involving core mathematical concepts like solid geometry, polygons, matrix operations, and rotational transformations. Key GeoGebra commands and objects used include Point, Rotate, Dodecahedron, Prism, and a series of vertices and edges like A, A', B, a_1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, c, e, d, b, f, g, k, l, h, i, j, a, edgeAD, edgeAA', edgeA'B, edgeBC, edgeCD, edgeAI, edgeDH. Suitable for high school geometry teaching and modeling practice.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Rotate(A, (2 * π / 5)) → A'
  3. Point(Circle[((A * (1 - sqrt(5))) + (A' * (3 + sqrt(5)))) / 4, (Distance[A, A'] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, A']]) → B
  4. Dodecahedron(A, A', B) → a_1, C, L, M, N, O, P, Q, R, S, c, e, D, d, b, f, g, k, l, h, i, j, a, E, edgeAD, edgeAA', edgeA'B, edgeBC, edgeCD, edgeAI, edgeDH, edgeHN, edgeIN, edgeIJ, F, edgeEJ, edgeA'E, edgeEK, edgeFK, edgeBF, edgeFL, edgeGL, edgeCG, edgeGM, edgeHM, G, edgeMR, edgeRS, edgeNS, edgeOS, edgeJO, edgeOP, edgeKP, edgePQ, edgeLQ, edgeQR, H, I, J, K
  5. Prism(a, w) → m, T, faceOSTZ, faceTUVWZ, edgeST, edgeRU, edgeQV, edgePW, edgeOZ, edgeTU, edgeUV, edgeVW, U, edgeWZ, edgeTZ, V, W, Z, faceRSTU, faceQRUV, facePQVW, faceOPWZ
  6. Prism(b, w) → n, A_1, face3, face6, edge2, edge1, edge3, edge5, edge4, edge6, edge8, edge9, B_1, edge10, edge7, C_1, D_1, E_1, face1, face2, face4, face5
  7. Prism(c, w) → o, F_1, face11, face12, edge15, edge11, edge12, edge13, edge14, edge16, edge18, edge19, G_1, edge20, edge17, H_1, I_1, J_1, face8, face7, face9, face10
  8. Prism(d, w) → p, K_1, face15, face18, edge22, edge21, edge24, edge25, edge23, edge26, edge28, edge29, L_1, edge30, edge27, M_1, N_1, O_1, face13, face14, face17, face16
  9. Prism(e, w) → q, P_1, face23, face24, edge34, edge31, edge32, edge33, edge35, edge36, edge38, edge39, Q_1, edge40, edge37, R_1, S_1, T_1, face20, face19, face21, face22
  10. Prism(f, w) → r, U_1, face27, face30, edge42, edge41, edge43, edge45, edge44, edge46, edge48, edge49, V_1, edge50, edge47, W_1, Z_1, A_2, face25, face26, face28, face29
  11. Prism(g, w) → s, B_2, face33, face36, edge52, edge51, edge53, edge55, edge54, edge56, edge58, edge59, C_2, edge60, edge57, D_2, E_2, F_2, face31, face32, face34, face35
  12. Prism(h, w) → t, G_2, face38, face42, edge61, edge62, edge64, edge65, edge63, edge66, edge68, edge69, H_2, edge70, edge67, I_2, J_2, K_2, face37, face39, face41, face40
  13. Prism(i, w) → u, L_2, face44, face48, edge71, edge72, edge74, edge75, edge73, edge76, edge78, edge79, M_2, edge80, edge77, N_2, O_2, P_2, face43, face45, face47, face46
  14. Prism(j, w) → v, Q_2, face50, face54, edge81, edge82, edge84, edge85, edge83, edge86, edge88, edge89, R_2, edge90, edge87, S_2, T_2, U_2, face49, face51, face53, face52
  15. Prism(k, w) → b_1, V_2, face58, face60, edge93, edge91, edge92, edge94, edge95, edge96, edge98, edge99, W_2, edge100, edge97, Z_2, A_3, B_3, face56, face55, face57, face59
  16. Prism(l, w) → c_1, C_3, face61, face66, edge101, edge103, edge105, edge104, edge102, edge106, edge108, edge109, D_3, edge110, edge107, E_3, F_3, G_3, face62, face64, face65, face63