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Joining Regular Tetrahedron & Right Square Pyramid

Joining Regular Tetrahedron & Right Square Pyramid
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2016-06-30 12:36
PolygonVectorSolid GeometryGeometric Construction
This example demonstrates the construction of joining a regular tetrahedron with a right square pyramid. It involves core mathematical concepts such as polygons, solid geometry, vectors, and three-dimensional space. The construction utilizes GeoGebra commands and objects like Polygon, Pyramid, Point, Tetrahedron, Circle, OrthogonalPlane, Intersect, OrthogonalLine, and PolyLine as outlined in the construction summary. It is suitable for high school and above students studying solid geometry, vectors, and spatial geometry, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Polygon((0, 0, 0), (2, 0, 0), 4, xOyPlane) → poly1
  2. Pyramid(poly1, E) → b, face1, face3, face4, face2, edge1, edge2, edge3, edge4
  3. Point(Circle[Midpoint[(2, 0, 0), (0, 0, 0)], (Distance[(2, 0, 0), (0, 0, 0)] * sqrt(3) / 2), Segment[(2, 0, 0), (0, 0, 0)]]) → A
  4. Tetrahedron((2, 0, 0), (0, 0, 0), A) → a, B, edgeAB, edge9, face5, face7, face6, face8, edge6, edge5, edge8, edge7
  5. Circle(xAxis, E) → c
  6. Point(c) → C
  7. OrthogonalPlane(A, xAxis) → d
  8. Intersect(xAxis, d) → D
  9. OrthogonalLine(C, d) → e
  10. Circle(C, 2, e) → f
  11. Intersect(c, f, 1) → F
  12. Tetrahedron((2, 0, 0), (0, 0, 0), F) → g, G, edge14, edge15, face9, face10, face11, face12, edge10, edge11, edge12, edge13
  13. PolyLine((0, 0, 0), (2, 0, 0), (2, 2, 0), (0, 2, 0)) → h