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Cubic 3D Visualization

Cubic 3D Visualization
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2015-11-09 12:06
PolygonSolid GeometryGeometric Construction
In collections Algebra II|CH7: Polynomial Functions
This GeoGebra example demonstrates the construction and visualization of a three-dimensional cube, illustrating key concepts in solid geometry such as spatial coordinates, polygon formation, and prism generation. The construction utilizes commands like Intersect, Point, Polygon, Cube, and Prism to define points and polygons, creating a detailed 3D model. It is suitable for high school or introductory college geometry courses to teach spatial reasoning and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → C
  4. Point(yAxis) → F
  5. Point(yAxis) → G
  6. Polygon(B, C, D, E) → poly1, b, c, d, e
  7. Polygon(B, A, F, E) → poly2, b_1, a, f, e_1
  8. Polygon(F, G, H, E) → poly3, f_1, g, h, e_2
  9. Polygon(D, E, H, I) → poly4, d_1, e_3, h_1, i
  10. Point(Circle[J, Distance[C, J], Segment[C, J]]) → S
  11. Cube(C, J, S) → j, T, faceSTZW, faceUVWZ, edgeCT, edgeCJ, edgeJS, edgeST, edgeCU, edgeTZ, edgeUZ, edgeUV, U, edgeJV, edgeVW, edgeSW, edgeWZ, V, W, Z, faceCJST, faceCTZU, faceCJVU, faceJSWV
  12. Prism(poly2, -4) → k, A_1, edge2, edge1, edge4, edge3, edge5, edge7, edge8, edge6, B_1, C_1, D_1, face1, face2, face4, face3, face5
  13. Prism(poly4, -4) → l, E_1, edge9, edge10, edge11, edge12, edge13, edge15, edge16, edge14, F_1, G_1, H_1, face6, face8, face9, face7, face10
  14. Prism(poly3, -4) → m, I_1, edge18, edge19, edge20, edge17, edge21, edge23, edge24, edge22, J_1, K_1, L_1, face13, face14, face12, face11, face15
  15. Polygon(J, K, N, M) → poly5, j_1, k_1, n, m_1
  16. Prism(poly5, 2) → o, V_1, edge25, edge26, edge28, edge27, edge29, edge31, edge32, edge30, W_1, Z_1, A_2, face16, face18, face19, face17, face20
  17. Polygon(O, N, K, L) → poly6, o_1, n_1, k_2, l_1
  18. Prism(poly6, 2) → p, B_2, edge36, edge35, edge33, edge34, edge37, edge39, edge40, edge38, C_2, D_2, E_2, face24, face22, face21, face23, face25
  19. Polygon(N, Q, P, M) → poly7, n_2, q, p_1, m_2
  20. Prism(poly7, 2) → r, F_2, edge42, edge44, edge43, edge41, edge45, edge47, edge48, edge46, G_2, H_2, I_2, face28, face29, face27, face26, face30
  21. Polygon(N, O, R, Q) → poly8, n_3, o_2, r_1, q_1
  22. Prism(poly8, 2) → s, J_2, edge49, edge50, edge52, edge51, edge53, edge55, edge56, edge54, K_2, L_2, M_2, face31, face33, face34, face32, face35