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Regular Tetrahedron Inside a Cube

Regular Tetrahedron Inside a Cube
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2019-02-19 17:42
Solid GeometryTransformationGeometric Construction
In collections Cuboids & their Nets
This example demonstrates the construction of a regular tetrahedron inside a cube. It involves core mathematical concepts such as solid geometry, spatial geometric relationships, and geometric construction. Key GeoGebra commands/objects used include Point, OrthogonalPlane, OrthogonalLine, PointIn, Circle, Rotate, Mirror, Polygon, Prism, and Pyramid. Suitable for high school and above students studying solid geometry, spatial visualization, and geometric construction.

GeoGebra Commands & Parameters

  1. Point(zAxis) → A
  2. OrthogonalPlane(A, zAxis) → a
  3. OrthogonalLine(A, a) → f
  4. PointIn(a) → B
  5. Circle(f, B) → c
  6. Rotate(B, 90°) → B'
  7. Mirror(B, A) → B'_1
  8. Mirror(B', A) → B''
  9. Polygon(B, B', B'_1, B'') → q1, b, b', b'_1, b''
  10. Prism(q1, b) → d, C, edgeBC, edgeB'D, edge1, edgeB''F, edgeCD, edgeDE, edgeEF, edgeCF, D, E, F, faceBB'DC, face1, face2, faceBB''FC, faceCDEF
  11. Polygon(E, B'', B') → t1, b'_2, e, b''_1
  12. Pyramid(t1, C) → g, faceB''CE, faceB'B''C, faceB'CE, edgeCE, edgeB''C, edgeB'C