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Basic Solids

Basic Solids
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2018-01-16 16:21
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates basic solid shapes such as cubes, pyramids, prisms, and tetrahedrons. Key mathematical concepts include the properties and construction of these solid shapes. Using GeoGebra commands like Point, Cube, Polygon, Pyramid, etc., the construction process of these solid shapes is visually illustrated. Suitable for middle school and above students or teachers for teaching or self-study.

GeoGebra Commands & Parameters

  1. Point(Circle[B_2, Distance[A_2, B_2], Segment[A_2, B_2]]) → C
  2. Cube(A_2, B_2, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB_1, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Polygon(I, J, 4) → poly1, f, g, h, i, K, L
  4. Polygon(M, N, 5) → poly2, j, k, l, m, n, O, P, Q
  5. Polygon(R, S, 6) → poly3, p, W, q, r, s, t, b, T, U, V
  6. Pyramid(poly1, 1) → c, Z, faceIJZ, faceJKZ, faceKLZ, faceILZ, edgeIZ, edgeJZ, edgeKZ, edgeLZ
  7. Pyramid(poly2, 1) → d, A_1, edge4, edge5, face1, face3, face4, face5, face2, edge1, edge2, edge3
  8. Pyramid(poly3, 1) → e, B_1, edge8, edge9, edge10, edge11, face6, face8, face9, face10, face11, face7, edge6, edge7
  9. Point(Circle[Midpoint[C_1, D_1], (Distance[C_1, D_1] * sqrt(3) / 2), Segment[C_1, D_1]]) → E_1
  10. Tetrahedron(C_1, D_1, E_1) → o, F_1, edge17, edge16, face12, face14, face13, face15, edge13, edge12, edge15, edge14
  11. Circle(G_1, 0.5) → c_1
  12. Circle(H_1, 0.5) → d_1
  13. Cone(d_1, 1) → u, e_1, v
  14. Cylinder(c_1, 1) → w, f_1, a_1
  15. Polygon(A_3, J_1, B_3, I_1) → poly4, a_2, j_1, b_1, i_1
  16. Prism(poly4, 1) → g_1, K_1, edge18, edge21, edge19, edge20, edge22, edge24, edge25, edge23, L_1, M_1, N_1, face17, face19, face18, face16, face20
  17. Sphere(A_4 + (0, 0, 0.5), 0.5) → h_1
  18. Point(Circle[Midpoint[A_5, B_4], (Distance[A_5, B_4] * sqrt(3) / 2), Segment[A_5, B_4]]) → O_1
  19. Octahedron(A_5, B_4, O_1) → k_1, P_1, face27, face28, edge26, edgeAB_2, edge29, edge28, edge33, edge27, edge35, edge30, Q_1, edge31, edge34, edge32, edge36, R_1, face21, face23, face24, face22, face26, face25
  20. Point(Circle[Midpoint[A_6, B_5], (Distance[A_6, B_5] * sqrt(3) / 2), Segment[A_6, B_5]]) → S_1
  21. Icosahedron(A_6, B_5, S_1) → l_1, T_1, face29, face31, face33, face32, face30, face35, face36, face34, face37, face38, U_1, face41, face42, face47, face44, face46, face48, face45, face43, face40, face39, V_1, edge37, edgeAB_3, edge41, edge39, edge46, edge40, edge54, edge38, edge48, edge42, W_1, edge44, edge49, edge43, edge51, edge45, edge47, edge52, edge55, edge53, edge60, Z_1, edge61, edge62, edge65, edge56, edge63, edge59, edge64, edge58, edge57, edge50, C_2, D_2, E_2, F_2
  22. Point(Circle[((A * (1 - sqrt(5))) + (B * (3 + sqrt(5)))) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → G_2
  23. Dodecahedron(A, B, G_2) → m_1, H_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, face49, face51, I_2, face50, face52, face53, face54, face58, face59, face55, face56, face57, face60, J_2, edge66, edgeAB, edge68, edge70, edge72, edge67, edge74, edge82, edge84, edge83, K_2, edge75, edge69, edge76, edge77, edge71, edge78, edge79, edge73, edge80, edge81, L_2, edge88, edge94, edge89, edge91, edge85, edge90, edge86, edge92, edge87, edge93, M_2, N_2, O_2, P_2
  24. Polygon(C_3, D_3, 4, xOyPlane) → poly5, n_1, p_1, q_1, r_1, E_3, F_3
  25. Polygon(G_3, H_3, 3, xOyPlane) → poly6, s_1, t_1, f_2, I_3
  26. Polygon(J_3, K_3, 5, xOyPlane) → poly7, g_2, h_2, i_2, j_2, k_2, L_3, M_3, N_3
  27. Polygon(O_3, P_3, 6, xOyPlane) → poly8, l_2, T_3, m_2, n_2, p_2, q_2, r_2, Q_3, R_3, S_3
  28. Prism(poly5, 2) → o_1, U_3, edge95, edge96, edge97, edge98, edge99, edge101, edge102, edge100, V_3, W_3, Z_3, face61, face63, face64, face62, face65
  29. Prism(poly6, 1) → u_1, C_4, edge105, edge106, edge108, edge107, D_4, E_4, face67, face69, face68, face66, edge103, edge104
  30. Prism(poly7, 1) → v_1, F_4, face71, face75, edge109, edge110, edge111, edge112, edge113, edge114, edge116, edge117, G_4, edge118, edge115, H_4, I_4, J_4, face70, face72, face73, face74
  31. Prism(poly8, 1) → w_1, K_4, face80, face81, face77, face82, edge119, edge120, edge121, edge122, edge123, edge124, L_4, edge125, edge127, edge128, edge129, edge130, edge126, M_4, N_4, O_4, P_4, face76, face78, face79

AI Drawing Prompt Reference

Draw a scene containing basic solid shapes such as a cube, tetrahedron, pentagonal pyramid, hexagonal pyramid, cone, cylinder, prism, octahedron, icosahedron, and dodecahedron. Start by drawing a cube, then a tetrahedron, followed by a pentagonal pyramid and a hexagonal pyramid. Next, draw a cone and a cylinder, then a prism. After that, draw an octahedron, followed by an icosahedron and a dodecahedron. Finally, draw some planar polygons including a quadrilateral, a triangle, a pentagon, and a hexagon, all located on the xOy plane.
The prompt above was compiled from the original drawing commands and is for reference only.