Reflection Symmetry of a Regular Tetrahedron
2015-01-20 08:33
This example demonstrates the reflection symmetry of a regular tetrahedron. By constructing the tetrahedron with its faces, edges, and vertices, and using tools like Mirror and OrthogonalPlane, it visually illustrates reflection across its symmetry planes. This model aids in understanding the symmetry groups of regular polyhedra and 3D geometric transformations.
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.214.0" id="19b96ec1-3772-4c97-bc9a-a9a1e080af98" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="875" height="580" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.17758620689655172" orientation="0" />
<pane location="1" divider="0.11428571428571428" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="255,237,876,684" />
<view id="1" visible="false" inframe="false" stylebar="false" location="1,3" size="254" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 22 , 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="true" inframe="false" stylebar="false" location="2,1" size="873" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="205" window="100,100,250,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="0" size="103" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="872" height="577"/>
<coordSystem xZero="214.99999999999997" yZero="314.9999999999999" scale="49.999999999999986" yscale="49.999999999999986"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="872" height="102"/>
<coordSystem xZero="214.99999999999997" yZero="315.0000000000003" scale="49.999999999999986" yscale="50.000000000000064"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="-0.245140183687659" yZero="0.407821269204633" zZero="-0.6037183863463419" scale="110.87986812315764" xAngle="18" zAngle="-57"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" rightAngleStyle="1" gridType="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="false" tickDistance="0.5"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="false" tickDistance="0.2886751345948129"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="1" showNumbers="false" tickDistance="0.816496580927726"/>
<plate show="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="2"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<element type="point3d" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-21" y="26"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="-1" y="-0.5773502691896258" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="2"/>
</element>
<element type="point3d" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-6" y="28"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="1" y="-0.5773502691896258" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="2"/>
</element>
<command name="Point">
<input a0="Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]"/>
<output a0="C"/>
</command>
<element type="point3d" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="0" y="30"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="1.1547005383792515" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="2"/>
</element>
<command name="Tetrahedron">
<input a0="A" a1="B" a2="C"/>
<output a0="a" a1="D" a2="faceABC" a3="faceACD" a4="faceABD" a5="faceBCD" a6="edgeAC" a7="edgeAB" a8="edgeBC" a9="edgeAD" a10="edgeCD" a11="edgeBD"/>
</command>
<element type="polyhedron" label="a">
<lineStyle thickness="4" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="point3d" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="-5.88418203051333e-15" z="1.6329931618554399" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="2"/>
</element>
<element type="polygon3d" label="faceABC">
<lineStyle thickness="4" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceACD">
<lineStyle thickness="4" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceABD">
<lineStyle thickness="4" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceBCD">
<lineStyle thickness="4" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="edgeAC">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAB">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBC">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAD">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeCD">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBD">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="edgeAB"/>
<output a0="E"/>
</command>
<element type="point3d" label="E">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-0.39653788619418506" y="-0.5773502691896258" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="4"/>
</element>
<command name="Plane">
<input a0="E" a1="edgeCD"/>
<output a0="b"/>
</command>
<element type="plane3d" label="b">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.828427124746169" y="-0.6475436565717149" z="-0.45788251067619806" w="0.7477190088674283"/>
<fading val="0.1"/>
</element>
<command name="IntersectPath">
<input a0="b" a1="a"/>
<outputSizes val="1,3,3"/>
<output a0="poly1" a1="F" a2="G" a3="H" a4="c" a5="d" a6="e"/>
</command>
<element type="polygon3d" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="2"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="point3d" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0" y="1.1547005383792512" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="G">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.39653788619418506" y="-0.577350269189626" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="H">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0" y="-6.050715484207103e-15" z="1.6329931618554396" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<element type="segment3d" label="c">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="true"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="d">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="true"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="e">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="true"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="Pyramid[poly1, B]" a1="0" a2="zAxis"/>
<output a0="f"/>
</command>
<element type="polyhedron" label="f">
<lineStyle thickness="1" type="0" typeHidden="2"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Mirror">
<input a0="f" a1="b"/>
<output a0="f'"/>
</command>
<element type="polyhedron" label="f'">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="215" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="OrthogonalLine">
<input a0="A" a1="faceBCD"/>
<output a0="g"/>
</command>
<element type="line3d" label="g">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="-1" oy="-0.5773502691896258" oz="0" ow="1" vx="-2.828427124746169" vy="-1.6329931618554399" vz="-1.1547005383792572" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="OrthogonalLine">
<input a0="D" a1="faceABC"/>
<output a0="h"/>
</command>
<element type="line3d" label="h">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="0" oy="-5.88418203051333e-15" oz="1.6329931618554399" ow="1" vx="0" vy="0" vz="3.4641016151377544" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="g" a1="h"/>
<output a0="I"/>
</command>
<element type="point3d" label="I">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.55351295663786e-15" y="-1.4432899320127035e-15" z="0.40824829046386707" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="Sphere">
<input a0="I" a1="2.7"/>
<output a0="i"/>
</command>
<element type="quadric" label="i">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="-7.123333333333331" A4="0" A5="0" A6="0" A7="2.55351295663786e-15" A8="1.4432899320127035e-15" A9="-0.40824829046386707"/>
</element>
<command name="IntersectPath">
<input a0="b" a1="i"/>
<output a0="k"/>
</command>
<element type="conic3d" label="k">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="0.9999999999999999" A1="1" A2="-7.090937591471781" A3="0" A4="1.970229075580888e-15" A5="-0.40325822860045335"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalPlane">
<input a0="I" a1="zAxis"/>
<output a0="j"/>
</command>
<element type="plane3d" label="j">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="0" z="1" w="-0.40824829046386707"/>
<fading val="0.1"/>
</element>
<command name="Intersect">
<input a0="j" a1="k"/>
<output a0="J" a1="K"/>
</command>
<element type="point3d" label="J">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.4126118581169064" y="2.668286239244453" z="0.4082482904638671" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="K">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.7894006970336727" y="-2.582023729465468" z="0.4082482904638671" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<command name="OrthogonalLine">
<input a0="I" a1="b"/>
<output a0="l"/>
</command>
<element type="line3d" label="l">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="-2.55351295663786e-15" oy="-1.4432899320127035e-15" oz="0.40824829046386707" ow="1" vx="2.828427124746169" vy="-0.6475436565717149" vz="-0.45788251067619806" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Polygon">
<input a0="Rotate[K, 45°, l]" a1="Rotate[K, 135°, l]" a2="Rotate[K, 225°, l]" a3="Rotate[K, 315°, l]"/>
<output a0="poly2" a1="m" a2="n" a3="p" a4="q"/>
</command>
<element type="polygon3d" label="poly2">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="192" g="192" b="192" alpha="0.05"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="segment3d" label="m">
<show object="true" label="false" ev="4"/>
<objColor r="192" g="192" b="192" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="n">
<show object="true" label="false" ev="4"/>
<objColor r="192" g="192" b="192" alpha="0"/>
<layer val="0"/>
<labelOffset x="23" y="-77"/>
<labelMode val="3"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="鏡面"/>
</element>
<element type="segment3d" label="p">
<show object="true" label="false" ev="4"/>
<objColor r="192" g="192" b="192" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="q">
<show object="true" label="false" ev="4"/>
<objColor r="192" g="192" b="192" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="n"/>
<output a0="L"/>
</command>
<element type="point3d" label="L">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0.2898614774489925" y="1.8837068236686139" z="0.7595587546728553" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="3"/>
</element>
<expression label="text1" exp=""鏡面""/>
<element type="text" label="text1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint exp="L"/>
<labelOffset x="18" y="-78"/>
</element>
<command name="Midpoint">
<input a0="edgeAB"/>
<output a0="M"/>
</command>
<element type="point3d" label="M">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-13" y="29"/>
<labelMode val="0"/>
<coords x="0" y="-0.5773502691896258" z="0" w="1"/>
<coordStyle style="cartesian"/>
<pointSize val="2"/>
</element>
<expression label="text2" exp=""ABCD為一正四面體,M是稜AB的中點。 拖拉紅點,觀察正四面體橙色部份的鏡像何時和正四面體的另一部份重合。 正四面體的反射對稱平面的名稱是甚麼?""/>
<element type="text" label="text2">
<show object="true" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="22" y="25"/>
</element>
</construction>
</geogebra>