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Icosahedral Triangular Prisms

Icosahedral Triangular Prisms
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2018-06-02 01:37
Solid GeometryTransformationGeometric Construction
This example demonstrates the construction of icosahedral triangular prisms. Key mathematical concepts include polyhedra and prisms in solid geometry. Using GeoGebra commands such as Point, Rotate, Icosahedron, Prism, etc., the rotation and construction process of polyhedra can be visually understood. Suitable for high school students and educators for teaching and learning solid geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Rotate(A, (2 * π / 3)) → A'
  3. Point(Circle[Midpoint[A, A'], (Distance[A, A'] * sqrt(3) / 2), Segment[A, A']]) → B
  4. Icosahedron(A, A', B) → a_1, C, d, f, h, g, e, b, c, a, i, j, D, m, n, s, p, r, t, q, o, l, k, E, edgeAB, edgeAA', edgeA'B, edgeAE, edgeBE, edgeAF, edgeEF, edgeAC, edgeCF, edgeA'C, F, edgeA'G, edgeCG, edgeA'D, edgeDG, edgeBD, edgeBH, edgeDH, edgeEH, edgeDJ, edgeGJ, G, edgeHJ, edgeHK, edgeJK, edgeEK, edgeIJ, edgeGI, edgeIK, edgeFK, edgeFI, edgeCI, H, I, J, K
  5. Prism(a, u) → v, L, edgeDN, edgeLM, edgeMN, edgeLN, M, N, faceA'BLM, faceA'DNM, faceBDNL, faceLMN, edgeBL, edgeA'M
  6. Prism(b, u) → w, O, edgeCQ, edgeOP, edgePQ, edgeOQ, P, Q, faceA'GOP, faceA'CQP, faceCGOQ, faceOPQ, edgeGO, edgeA'P
  7. Prism(c, u) → b_1, R, edgeGT, edgeRS, edgeST, edgeRT, S, T, faceA'DRS, faceA'GTS, faceDGTR, faceRST, edgeDR, edgeA'S
  8. Prism(d, u) → c_1, U, edgeA'W, edgeUV, edgeVW, edgeUW, V, W, faceABUV, faceAA'WV, faceA'BUW, faceUVW, edgeBU, edgeAV
  9. Prism(e, u) → d_1, Z, edge2, edge3, edge5, edge4, A_1, B_1, face2, face3, face4, face1, edgeA'Z, edge1
  10. Prism(f, u) → e_1, C_1, edge7, edge9, edge11, edge10, D_1, E_1, face7, face6, face8, face5, edge8, edge6
  11. Prism(g, u) → f_1, F_1, edge14, edge15, edge17, edge16, G_1, H_1, face10, face11, face12, face9, edge13, edge12
  12. Prism(h, u) → g_1, I_1, edge19, edge21, edge23, edge22, J_1, K_1, face15, face14, face16, face13, edge20, edge18
  13. Prism(i, u) → h_1, M_1, edge25, edge27, edge29, edge28, N_1, O_1, face19, face18, face20, face17, edge26, edge24
  14. Prism(j, u) → i_1, P_1, edge32, edge33, edge35, edge34, Q_1, R_1, face22, face23, face24, face21, edge31, edge30
  15. Prism(k, u) → j_1, S_1, edge36, edge39, edge41, edge40, T_1, U_1, face28, face27, face26, face25, edge37, edge38
  16. Prism(l, u) → k_1, V_1, edge43, edge45, edge47, edge46, W_1, Z_1, face31, face32, face30, face29, edge42, edge44
  17. Prism(m, u) → l_1, A_2, edge49, edge51, edge53, edge52, B_2, C_2, face35, face34, face36, face33, edge50, edge48
  18. Prism(n, u) → m_1, D_2, edge56, edge57, edge59, edge58, E_2, F_2, face38, face39, face40, face37, edge55, edge54
  19. Prism(o, u) → n_1, G_2, edge61, edge63, edge65, edge64, H_2, I_2, face43, face44, face42, face41, edge60, edge62
  20. Prism(p, u) → o_1, J_2, edge68, edge69, edge71, edge70, K_2, L_2, face46, face48, face47, face45, edge66, edge67
  21. Prism(q, u) → p_1, M_2, edge73, edge75, edge77, edge76, N_2, O_2, face51, face52, face50, face49, edge72, edge74
  22. Prism(r, u) → q_1, P_2, edge78, edge81, edge83, edge82, Q_2, R_2, face56, face55, face54, face53, edge79, edge80
  23. Prism(s, u) → r_1, S_2, edge85, edge87, edge89, edge88, T_2, U_2, face59, face58, face60, face57, edge86, edge84
  24. Prism(t, u) → s_1, V_2, edge90, edge93, edge95, edge94, W_2, Z_2, face64, face62, face63, face61, edge92, edge91