Rotational Symmetry of a Regular Tetrahedron
2017-04-11 03:41
This GeoGebra applet dynamically demonstrates the rotational symmetry of a regular tetrahedron. Using commands like Tetrahedron and Rotate, it constructs the solid along with its faces and edges, illustrating how it maps onto itself when rotated around specific axes. The model visually presents the symmetry group characteristics of regular polyhedra in solid geometry, helping learners deeply under
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</element>
<command name="Rotate">
<input a0="A" a1="((-α)) / 2" a2="b"/>
<output a0="A'_1"/>
</command>
<element type="point3d" label="A'_1">
<show object="false" label="true" ev="7"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="0.5829530330079244" y="0.20656720495525224" z="-0.2689783813448745" w="1"/>
<pointSize val="3"/>
</element>
<command name="CircumcircleArc">
<input a0="A" a1="A'_1" a2="A'"/>
<output a0="k"/>
</command>
<element type="conicpart" label="k">
<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"/>
<isShape val="false"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<eigenvectors x0="-1" y0="-6.213508085624229e-17" z0="1.0" x1="6.213508085624229e-17" y1="-1" z1="1.0"/>
<matrix A0="0" A1="0" A2="0" A3="0" A4="3.1067540428121147e-17" A5="-0.5"/>
<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"/>
<isShape val="false"/>
<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>