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Pyramid and Cube

Pyramid and Cube
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2019-05-29 02:21
Solid GeometryOptimizationGeometric Construction
This example demonstrates the geometric construction and relationship between a pyramid and a cube. It involves core mathematical concepts such as solid geometry, polygons, and optimization problems. The construction uses commands like Point, Cube, and Pyramid to create points, cubes, and pyramids. It is suitable for high school mathematics teaching to understand the construction and properties of spatial geometric solids.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG_1, faceEFGH_1, edgeAD_1, edgeAB_1, edgeBC_1, edgeCD_1, edgeAE_1, edgeDH_1, edgeEH_1, edgeEF_1, E, edgeBF_1, edgeFG_1, edgeCG_1, edgeGH_1, F, G, H, faceABCD_1, faceADHE_1, faceABFE_1, faceBCGF_1
  3. Point(zAxis) → I
  4. Pyramid(H, E, F, G, I) → b, faceEFGH, edgeHI_1, edgeEI_1, edgeFI_1, edgeGI_1, faceEHI_1, faceEFI_1, faceFGI_1, faceGHI_1, edgeEH_2, edgeEF_2, edgeFG_2, edgeGH_2
  5. Pyramid(G, F, B, C, I) → c, faceBCGF, edgeGI_2, edgeFI_2, edgeBI_1, edgeCI_1, faceFGI, faceBFI_1, faceBCI_1, faceCGI_1, edgeFG, edgeBF_2, edgeBC_2, edgeCG_2
  6. Pyramid(A, E, F, B, I) → d, faceABFE, edgeAI_1, edgeEI_2, edgeFI, edgeBI_2, faceAEI_1, faceEFI, faceBFI, faceABI_1, edgeAE_2, edgeEF, edgeBF, edgeAB_2
  7. Pyramid(H, E, A, D, I) → e, faceADHE, edgeHI_2, edgeEI, edgeAI_2, edgeDI_1, faceEHI, faceAEI, faceADI_1, faceDHI_1, edgeEH, edgeAE, edgeAD_2, edgeDH_2
  8. Pyramid(C, D, A, B, I) → f, faceABCD, edgeCI_2, edgeDI_2, edgeAI, edgeBI, faceCDI_1, faceADI, faceABI, faceBCI, edgeCD_2, edgeAD, edgeAB, edgeBC
  9. Pyramid(G, H, D, C, I) → g, faceCDHG, edgeGI, edgeHI, edgeDI, edgeCI, faceGHI, faceDHI, faceCDI, faceCGI, edgeGH, edgeDH, edgeCD, edgeCG