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3-D Solids: Prisms, Pyramids, Cylinders, Cones, and Spheres

3-D Solids: Prisms, Pyramids, Cylinders, Cones, and Spheres
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2017-08-10 09:30
PolygonVectorSolid GeometryTransformationGeometric Construction
In collections Elementary Geometry
This GeoGebra example demonstrates a comprehensive collection of three-dimensional solids, including prisms, pyramids, cylinders, cones, and spheres, along with their combinations and rotations. It covers core mathematical concepts in solid geometry such as polyhedra, surfaces of revolution, volume and surface area, three-dimensional vectors, and quadratic equations (e.g., sphere equations). The construction uses GeoGebra commands like Point, Polygon, Prism, Pyramid, Cylinder, Cone, Sphere, Rotate, Line, and PointIn to build the solids, with multiple faces (face1) forming the complete shapes. Suitable for high school or early college students learning spatial reasoning and 3D modeling, and for teachers demonstrating geometric properties in class.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0, 0), (1, 0, 0)]) → A
  2. Polygon(A, Rotate[A, (360 * ° / N), Ray[(0, 0, 0), (0, 0, 1)]], N, xOyPlane) → poly1, e, l_1, m_1, n_1, E_2, C_2, D_2, E_3, F_2, G_2, H_2, l_2, I_1, J_1, K_1, m_2, f_1, g_1, h_1, i_1, j_1, k_1
  3. Point(Ray[A + (0, 0, 0.5), A + (0, 0, 1)]) → B
  4. Prism(poly1, B) → a, C_1, L, M, face1, face3, face2, face4, face5, face6, face7, face8, D, face9, face10, face11, face12, faceBCD, edge1, edge2, edge3, edge4, edge6, E, edge8, edge10, edge12, edge14, edge16, edge17, edge20, edgeBC, edgeCD, edgeBD, F, edge5, edge7, edge9, edge11, edge13, edge15, edge18, edge19, edge21, G, H, I, J, K
  5. Point(Ray[(0, 0, 0), (0, 1, 0)]) → C
  6. Polygon((x(A), y(C), 0), ((-x(A)), y(C), 0), ((-x(A)), (-y(C)), 0), (x(A), (-y(C)), 0)) → poly2, g, h, i, j
  7. Prism(poly2, (x(A), y(C), z(B))) → c, Q, edge23, edge24, edge25, edge26, edgeQR, edgeRS, edge27, R, S, face13, face15, face16, face14, face17, edge22
  8. Polygon((b, 0, 0), (0, b, 0), ((-b), 0, 0), (0, (-b), 0)) → poly3, k, l, m, n
  9. Prism(poly3, (b, 0, (sqrt(2) * b))) → d, O, edge29, edge30, edge31, edge32, edge33, edge34, edge35, T, U, face18, face19, face20, face21, face22, edge28
  10. PointIn(z = 0) → V
  11. Line(V, V + (0, 0, 1)) → f
  12. Cylinder(Circle[(0, 0, 0), A, xOyPlane], z(B)) → q, r, s
  13. Sphere((0, 0, b), b) → t
  14. Prism(poly2, B) → u, W, edge62, edge63, edge64, edgeBW, edgeWZ, edge65, edge61, Z, A_1, face47, face50, face51, face48, face49, edge60
  15. Prism(Polygon[Sequence[Rotate[A, ((i * 90))°], i, 0, 3]], B) → v, B_1, edge69, edge70, edge71, edge67, edge72, edge73, edge68, D_1, E_1, face52, face55, face56, face53, face54, edge66
  16. Pyramid(Polygon[Sequence[Rotate[A, ((i * 90))°], i, 0, 3]], z(B)) → w, F_1, face57, face59, face60, face58, edge74, edge75, edge76, edge77
  17. Pyramid(Polygon[A, Rotate[A, 120°, Ray[(0, 0, 0), (0, 0, 1)]], 3, xOyPlane], (sqrt(2) * b)) → a_1, G_1, face23, face24, face25, edge36, edge37, edge38
  18. Rotate(A, (360 * ° / N), Ray[(0, 0, 0), (0, 0, 1)]) → A'
  19. Pyramid(poly1, z(B)) → o, H_1, face34, face35, face36, face37, edge39, edge40, edge41, edge42, edge43, edge44, face26, edge45, edge46, edge47, edge48, edge49, edge50, face27, face28, face29, face30, face31, face32, face33
  20. Cone(Circle[(0, 0, 0), A, xOyPlane], z(B)) → o_1, c_2, u_1