MathPlotAI Logo MathPlotAI

Cube Dissection

Cube Dissection
Loading the math board and drawing, please wait…
2015-12-03 20:57
Solid GeometryTransformationGeometric Construction
In collections Dissecting a cube into equal parts
This example demonstrates the dissection of a cube. Key mathematical concepts include the intersection of planes and solids in solid geometry, rotation, and translation. Using GeoGebra commands such as Point, Pyramid, Rotate, and Mirror, the faces and edges of the cube are constructed. Suitable for students at the middle school level and above for learning solid geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → C
  2. Pyramid((0, 0, 0), (4, 0, 0), (4, 4, 0), (0, 4, 0), (0, 0, 4)) → a, face5, edge3, edge5, edge7, edge8, face1, face3, face4, face2, edge1, edge4, edge6, edge2
  3. Line((4, 0, 0), (4, 4, 0)) → b
  4. Rotate(A, 90*°, b) → A'
  5. CircleArc(C, A', A) → h
  6. Circle(b, (0, 0, 4)) → c
  7. Point(h) → B
  8. AngularBisector(A, C, B) → d
  9. Plane(b, d) → e
  10. Mirror(a, e) → a'
  11. Line((4, 4, 0), (0, 0, 4)) → f
  12. Plane(D, f) → g
  13. Mirror(a', g) → a''