Exploring the Rotational Symmetry of a Regular Tetrahedron
2015-01-21 04:44
This GeoGebra applet dynamically demonstrates the rotational symmetry of a regular tetrahedron. By constructing its vertices, edges, and faces, and using rotation commands, users can observe the tetrahedron coinciding with itself around specific axes. It is an excellent visualization tool for understanding 3D solid geometry symmetry transformations and polyhedral properties.
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<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>