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Geometry Prisms: Constructing a Prism via Vector Translation

Geometry Prisms: Constructing a Prism via Vector Translation
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2025-03-12 00:39
PolygonVectorSolid GeometryTransformationGeometric Construction
In collections Geometry - Area & Volume
This example demonstrates how to build a prism by starting from a base polygon in the plane, translating it with a vector to obtain the top face, and then connecting corresponding vertices to form the lateral edges and faces. It highlights core ideas of solid geometry (the prism structure), geometric transformation by vector translation, and constructive geometry: creating points, polygons, and intersections to ensure consistent connectivity. In GeoGebra it uses commands such as Sequence (to generate point sets), Polygon (to form the base/top faces), Vector and Translate (to define and apply the displacement that maps A..B..l1 to A’..B’..l2), Prism (to create the prism body), Point (to define key vertices), and Intersect (to obtain intersection-based construction points). Suitable for middle/high school geometry lessons, especially for spatial reasoning, geometry construction skills, and interactive visualization of 3D solids from 2D components.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[B, ((2 * pi / b) * i), A], i, 0, b) → l1
  2. Polygon(l1) → poly1
  3. Vector(A, C) → u
  4. Translate(poly1, u) → poly1'
  5. Sequence(Rotate[D, ((2 * pi / b) * i), C], i, 0, b) → l2
  6. Prism(poly1, D) → c, E, N, edge10, edge12, edge14, edge16, edge18, edge20, edge22, edge24, edge26, edge28, O, edge32, edge33, edge34, edge39, edge40, edge41, edge42, edge47, edge48, edge49, P, edge50, edge54, edge55, edge56, edge58, Q, R, S, T, U, V, W, F, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, G, J_1, face1, face3, face4, face2, face5, face6, face7, face8, face9, H, face10, face11, face12, face13, face14, face15, face16, face17, face18, face19, I, face20, face21, face22, face23, face24, face25, face26, face27, face28, face29, J, face30, face31, faceDEFG, edge1, edge2, edge3, edge4, edge5, edge7, edge9, K, edge11, edge13, edge15, edge17, edge19, edge21, edge23, edge25, edge27, edge29, L, edge30, edge31, edge35, edge36, edge37, edge38, edge43, edge44, edge45, edge46, M, edge51, edge52, edge53, edge57, edgeDE, edgeEF, edgeFG, edgeDG, edge6, edge8
  7. Sequence(Rotate[B, ((2 * pi / 3) * i), A], i, 0, 3) → l3
  8. Sequence(Rotate[B, ((2 * pi / 3) * i) + pi / 3, A], i, 0, 3) → l4
  9. Point(l3) → K_1
  10. Point(l3) → L_1
  11. Point(l3) → M_1
  12. Polygon(K_1, L_1, M_1) → t1, m_1, k_1, l_1
  13. Point(l4) → N_1
  14. Point(l4) → O_1
  15. Point(l4) → P_1
  16. Polygon(N_1, O_1, P_1) → t2, p_1, n_1, o_1
  17. Intersect(m_1, o_1) → Q_1
  18. Intersect(m_1, p_1) → R_1
  19. Intersect(k_1, p_1) → S_1
  20. Intersect(k_1, n_1) → T_1
  21. Intersect(l_1, n_1) → U_1
  22. Intersect(l_1, o_1) → V_1
  23. Polygon(M_1, T_1, P_1, U_1, O_1, S_1, L_1, R_1, N_1, Q_1, K_1, V_1) → poly2, f, v_1, k, u_1, t_1, g, s_1, h, r_1, i, q_1, j
  24. Prism(poly2, D) → e, W_1, H_2, I_2, face32, face41, face40, face37, face36, face39, face38, face34, Z_1, face35, face43, face42, face33, face44, edge59, edge70, edge65, edge69, edge63, A_2, edge68, edge64, edge67, edge62, edge72, edge66, edge71, edge60, edge73, edge74, B_2, edge75, edge76, edge77, edge78, edge79, edge80, edge81, edge82, edge61, C_2, D_2, E_2, F_2, G_2
  25. Polygon(J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2) → poly3, j_2, k_2, l_2, m_2, n_2, o_2, p_2, q_2, r_2
  26. Prism(poly3, S_2) → m, T_2, face47, face48, face49, face50, face51, face52, face53, face46, face54, edge83, U_2, edge84, edge85, edge86, edge87, edge88, edge89, edge90, edge91, edge92, edge94, V_2, edge95, edge96, edge97, edge98, edge99, edge100, edge93, W_2, Z_2, A_3, B_3, C_3, face45

AI Drawing Prompt Reference

Construct a 3D prism by starting from a planar base polygon (a regular-like multi-vertex shape) and translating the entire polygon by a defined vector to obtain a corresponding top face polygon. Ensure the vertices of the translated top face match the original base vertices one-to-one, then connect each corresponding pair to form the lateral edges and side faces, producing the prism solid. To mirror the more intricate example, also generate additional polygon sets from rotated point triples around the central position and integrate them so the final figure shows a prism body composed of multiple faces and edges.
The prompt above was compiled from the original drawing commands and is for reference only.