四面体的旋转对称性 by Dragon Lee

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2019-12-06 09:42

解析几何立体几何变换

本范例演示了四面体的旋转对称性。涉及的核心数学概念包括旋转对称性和立体几何。通过使用GeoGebra命令如Tetrahedron, Point, PointIn, Circle, Center, Line, Rotate, Midpoint等，构建了四面体的各个面和边，并展示了其旋转对称性。适合高中或大学的立体几何课程。

GeoGebra 命令及参数

Tetrahedron(A, B, xOyPlane) → a, C, edge4, edge5, edge6, D, face1, face2, face3, face4, edge1, edge2, edge3
Point({edge4, edge5, edge6}) → E
PointIn(face1) → F
Circle(A, B, D) → e
Circle(B, C, D) → f
Circle(C, A, D) → g
Circle(A, B, C) → h
Center(h) → J
Line(E, F) → b
Rotate(face1, (-α), b) → face1'
Rotate(face2, (-α), b) → face2'
Rotate(face3, (-α), b) → face3'
Rotate(face4, (-α), b) → face4'
Midpoint(edge6) → K
Midpoint(edge5) → L
Midpoint(edge4) → M
Midpoint(edge2) → N
Midpoint(edge1) → O
Midpoint(edge3) → P