正四面体的旋转对称性探究
2015-01-21 04:44
本 GeoGebra 数学范例动态演示了正四面体的旋转对称性。通过构造正四面体的顶点、边和面，并利用旋转命令和圆弧等几何对象，用户可以直观地观察正四面体绕特定轴旋转后与自身重合的过程。该范例有助于深入理解三维空间中的立体几何对称变换，是学习多面体对称群和空间几何性质的优秀可视化工具。
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<show object="true" label="false" ev="7"/>
<condition showObject="(α < 360°) ∧ i"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="1" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Circle">
<input a0="b" a1="A"/>
<output a0="p"/>
</command>
<element type="conic3d" label="p">
<show object="true" label="false" ev="4"/>
<condition showObject="α ≟ 360° ∧ i"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-0.7981540701523955" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<element type="boolean" label="i">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="322" y="23"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="追蹤橙色點"/>
</element>
</construction>
</geogebra>