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Cube Division Demonstration by Diego Lieban (2)

Cube Division Demonstration by Diego Lieban (2)
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2018-12-18 23:14
VectorSolid GeometryGeometric Construction
In collections Developing games and puzzles with 3D printing for STEAM
This example demonstrates how to divide a cube into four parts through geometric construction. It involves core mathematical concepts such as solid geometry, symmetry, volume calculation, fractions, and integer operations. The construction uses GeoGebra commands and objects like Intersect, Point, Cube, Pyramid, OrthogonalLine, Midpoint, Plane, Line, and Vector as outlined in the construction summary. It is suitable for high school and above students to learn spatial geometric division, volume calculation, and symmetry principles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC_1, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF_1, edgeFG, edgeCG_1, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Pyramid(faceABCD, -1) → b, I, faceADI, faceABI, faceBCI, faceCDI, edgeDI, edgeAI, edgeBI, edgeCI
  6. Pyramid(faceCDHG, -1) → c, J, faceCDJ, faceCGJ, faceGHJ, faceDHJ, edgeDJ, edgeCJ, edgeGJ, edgeHJ
  7. OrthogonalLine(I, xOyPlane) → f
  8. Pyramid(faceABFE, -1) → d, K, faceABK, faceAEK, faceEFK, faceBFK_1, edgeBK_1, edgeAK, edgeEK, edgeFK_1
  9. Midpoint(edgeEF) → L
  10. Plane(L, faceBCGF) → e
  11. Intersect(edgeAB, e) → M
  12. Intersect(edgeCD, e) → N
  13. Intersect(edgeGH, e) → O
  14. Pyramid(L, M, B, F, K) → g, faceBFLM, edgeKL, edgeKM_1, edgeBK_2, edgeFK, faceKLM, faceBKM_1, faceBFK, faceFKL, edgeLM, edgeBM_1, edgeBF, edgeFL
  15. Pyramid(C, N, O, G, K) → h, faceCGON, edgeCK_1, edgeKN_1, edgeKO, edgeGK, faceCKN_1, faceKNO, faceGKO, faceCGK, edgeCN_1, edgeNO, edgeGO, edgeCG
  16. Pyramid(B, M, N, C, K) → i, faceBCNM, edgeBK, edgeKM, edgeKN, edgeCK, faceBKM, faceKMN, faceCKN, faceBCK, edgeBM, edgeMN, edgeCN, edgeBC
  17. Line(K, edgeAB) → j
  18. Vector(M, L) → u

AI Drawing Prompt Reference

Draw a cube. Construct an inverted pyramid with its apex at the center of the bottom face, another inverted pyramid with apex at the center of the top face, and a third inverted pyramid with apex at the center of the left face. Then take the midpoint of an edge on the top face, and through this midpoint draw a plane parallel to the right face. This plane intersects three edges of the cube, giving three intersection points. Using these points, the midpoint, and cube vertices, construct three new pyramids that divide the cube into four parts. Finally, draw a line from the internal apex to an edge on the bottom face, and draw a vector from an intersection point to the midpoint.
The prompt above was compiled from the original drawing commands and is for reference only.