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Nets and Skins of Cuboids

Nets and Skins of Cuboids
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2016-05-08 16:45
PolygonVectorSolid GeometryTransformationGeometric Construction
This GeoGebra example demonstrates the relationship between a cuboid and its planar nets/skins, showing how a three-dimensional prism can be unfolded along selected edges into flat polygons. It highlights solid geometry concepts such as cuboids, prisms, faces, edges, vertices, rotations, and 3D vectors, with possible connections to linear equations and parametric or random-variable settings. The construction uses Point to define vertices A through H, Segment to draw edges such as AE, BF, CG, and DH, Polygon and PolyLine to form faces like ABCD, BIJC, and IKLJ, and If statements to switch between unfolding states or display branches. It is suitable for middle school to high school solid geometry lessons, geometric construction practice, and introductory 3D modeling in GeoGebra.

GeoGebra Commands & Parameters

  1. If(t < 4, 1, If[(t ≥ 4) ∧ (t < 5), 5 - t, 0]) → t5
  2. If(t < 1, t, 1) → t1
  3. Point(O, u) → U2
  4. Point(O, v) → V2
  5. Point(O, w) → W2
  6. Polygon({A, B, C, D}) → ABCD
  7. Segment(A, E) → AE
  8. Segment(B, F) → BF
  9. Segment(C, G) → CG
  10. Segment(D, H) → DH
  11. PolyLine({E, F, G, H, E}) → EFGHE
  12. If(t < 1, 1, If[(t ≥ 1) ∧ (t < 2), 2 - t, 0]) → t2
  13. If(t < 1, I + ((a * cos((t1 * π / 2))) * v) + ((a * sin((t1 * π / 2))) * w), I - ((a * cos((t2 * π / 2))) * v) + ((a * sin((t2 * π / 2))) * w)) → K
  14. Polygon({I, K, L, J}) → IKLJ
  15. Polygon({B, I, J, C}) → BIJC
  16. If(t < 2, 1, If[(t ≥ 2) ∧ (t < 3), 3 - t, 0]) → t3
  17. Polygon({A, M, N, B}) → AMNB
  18. If(t < 3, 1, If[(t ≥ 3) ∧ (t < 4), 4 - t, 0]) → t4
  19. Polygon({A, D, Q, P}) → ADQP
  20. Polygon({C, R, S, D}) → CRSD
  21. Polygon({A, T, U, P}) → ATUP
  22. Polygon({D, V, W, Q}) → DVWQ

AI Drawing Prompt Reference

Draw a cube with six square faces and its planar net. The cube has six faces, each a square. The net shows how the cube unfolds along certain edges into flat polygons, such as a hexagon or multiple squares. First, draw the six vertices of the cube, then connect them to form the faces. Next, unfold the cube along specific edges to display its planar shape. Ensure the drawing is clear to show the relationship between three-dimensional and flat forms.
The prompt above was compiled from the original drawing commands and is for reference only.