MathPlotAI Logo MathPlotAI

Cutting a Cube into Several Tetrahedrons

Cutting a Cube into Several Tetrahedrons
Loading the math board and drawing, please wait…
2014-12-04 19:28
Solid GeometryTransformationGeometric Construction
This example demonstrates how to cut a cube into several tetrahedrons. Key mathematical concepts include solid geometry and the process of cutting and combining shapes. Using GeoGebra commands such as Point, Cube, Intersect, Polygon, and Tetrahedron, the cutting process is visually illustrated. Suitable for middle school and above students or teachers for teaching and learning.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE_1, edgeDH, edgeEH, edgeEF_1, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Intersect(edgeCG, xOyPlane) → I
  4. Polygon(F, I, A) → poly1, a_1, f, i
  5. Point(Circle[Midpoint[A, F], (Distance[A, F] * sqrt(3) / 2), Segment[A, F]]) → J
  6. Tetrahedron(A, F, poly1) → b, K, edgeAL, edgeKL, edgeFL, L, faceAFK, faceAKL, faceAFL, faceFKL, edgeAK, edgeAF, edgeFK
  7. Ray(C, E) → c
  8. Point(c) → M
  9. Vector(E, M) → u
  10. Pyramid(faceAFL, E) → d, faceAEF, faceAEL, faceEFL, edgeEF, edgeAE, edgeEL
  11. Translate(d, u) → d'
  12. Plane(F, H, D) → e
  13. Mirror(d', e) → d''
  14. Plane(A, F, G) → g
  15. Mirror(d', g) → d''_1
  16. Plane(H, A, G) → h
  17. Mirror(d', h) → d''_2