Exploring the Rotational Symmetry of a Cube
2015-01-21 04:51
This GeoGebra applet visually demonstrates and explores the rotational symmetry of a cube through 3D geometric constructions. Using rotation commands along with auxiliary elements like midpoints and circular arcs, it illustrates the spatial transformations and symmetric properties of a cube rotating around specific axes. This interactive 3D model is an excellent educational tool for understanding
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<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="2" y="0" z="4" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="Midpoint">
<input a0="edgeGH"/>
<output a0="R"/>
</command>
<element type="point3d" label="R">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="2" z="4" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="Midpoint">
<input a0="edgeEH"/>
<output a0="S"/>
</command>
<element type="point3d" label="S">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-2" y="0" z="4" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="Midpoint">
<input a0="edgeEF"/>
<output a0="T"/>
</command>
<element type="point3d" label="T">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="-2" z="4" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="Midpoint">
<input a0="edgeBC"/>
<output a0="W"/>
</command>
<element type="point3d" label="W">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="2" y="0" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="Midpoint">
<input a0="edgeAD"/>
<output a0="B_1"/>
</command>
<element type="point3d" label="B_1">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-2" y="0" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="Midpoint">
<input a0="edgeAB"/>
<output a0="C_1"/>
</command>
<element type="point3d" label="C_1">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0" y="-2" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="Midpoint">
<input a0="edgeCD"/>
<output a0="D_1"/>
</command>
<element type="point3d" label="D_1">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0" y="2" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="Rotate">
<input a0="A" a1="(-α)" a2="b"/>
<output a0="A'"/>
</command>
<element type="point3d" label="A'">
<show object="true" label="false" ev="7"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="2" y="1.9999999999999996" z="4" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="4"/>
</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="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-0.9676674556963709" y="1.1169123940336518" z="5.236545366756493" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="4"/>
</element>
<command name="CircumcircleArc">
<input a0="A" a1="A'_1" a2="A'"/>
<output a0="e"/>
</command>
<element type="conicpart" label="e">
<show object="true" label="false" ev="4"/>
<condition showObject="(α < 360°) ∧ f"/>
<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="6.659891622435486e-17" z0="1.0" x1="-6.659891622435486e-17" y1="-1" z1="1.0"/>
<matrix A0="0" A1="0" A2="0" A3="0" A4="-3.329945811217743e-17" A5="-0.5"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="boolean" label="f">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="321" y="24"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="追蹤橙色點"/>
</element>
<command name="Circle">
<input a0="b" a1="A"/>
<output a0="g"/>
</command>
<element type="conic3d" label="g">
<show object="true" label="false" ev="4"/>
<condition showObject="α ≟ 360° ∧ f"/>
<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="-2.7789845728644242" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
</construction>
</geogebra>