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Pyramid Inscribed in a Cube

Pyramid Inscribed in a Cube
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2017-05-02 15:17
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction of a pyramid inscribed in a cube. The core mathematical concepts involved are solid geometry, specifically pyramids and cubes. Using GeoGebra commands such as Intersect, Point, Cube, Segment, etc., the faces and edges of the pyramid can be constructed. Suitable for high school students and teachers for teaching geometric construction and solid geometry.

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, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Segment(E, C) → f
  6. Segment(B, H) → g
  7. Segment(D, F) → h
  8. Segment(G, A) → i
  9. Intersect(g, i) → I
  10. Pyramid(faceABFE, I) → b, faceABI, faceAEI, faceEFI, faceBFI, edgeBI, edgeAI, edgeEI, edgeFI
  11. Plane(I, faceABFE) → c