正方体与正四面体的外接球构造与演示
2020-12-10 02:05
本GeoGebra范例动态演示了正方体与正四面体的外接球的几何构造过程。通过构建正方体和正四面体，并利用球面命令生成其外接球，直观展示了多面体顶点与外接球球心及半径之间的空间几何关系。该课件有助于学生深入理解立体几何中特殊多面体的外接球性质，是学习三维空间图形与球面位置关系的优质可视化教具。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.620.0" app="classic" platform="w" id="29de11aa-7df5-452f-a945-9276c50a663a" xsi:noNamespaceSchemaLocation="https://ggb123.cn/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1329" height="508" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.09104589917231001" orientation="1" />
<pane location="1" divider="0.19187358916478556" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1,1,1" size="400" window="11,151,700,550" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1,3" size="255" 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="false" location="1,1" 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 51 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 , 538 | 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="true" location="1,1" size="935" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="121" tab="ALGEBRA" window="100,100,250,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="712" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 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 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="12"/>
<consProtColumns col0="true" col1="true" col2="false" col3="false" col4="true" col5="true" col6="true" col7="false"/>
<consProtocol useColors="false" addIcons="false" showOnlyBreakpoints="false"/>
<consProtNavigationBar id="32" playButton="true" playDelay="2" protButton="true" consStep="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="255" height="506"/>
<coordSystem xZero="575.7892210801879" yZero="432.03656925689484" scale="88.69725338869273" yscale="88.69723770485164"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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="0"/>
<labelStyle axes="0" serif="true"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="1"/>
<auxiliary show="true"/>
<collapsed val="7"/>
</algebraView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="0" yZero="0" zZero="0" scale="110.44307042156987" xAngle="21" zAngle="-1445.848643417555"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<element type="numeric" label="r">
<value val="1.44"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="2" absoluteScreenLocation="true" width="200" x="35" y="62" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="true"/>
</element>
<command name="Cube">
<input a0="(-1, -1, -1)" a1="(1, -1, -1)" a2="(1, 1, -1)"/>
<output a0="a" a1="A" a2="B" a3="C" a4="D" a5="E" a6="face1" a7="face3" a8="face2" a9="face4" a10="face5" a11="faceBCDE" a12="edge2" a13="edge1" a14="edge4" a15="edge6" a16="edge3" a17="edgeAE" a18="edgeBE" a19="edgeBC" a20="edge5" a21="edgeCD" a22="edge7" a23="edgeDE"/>
</command>
<element type="polyhedron" label="a">
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.4099999964237213"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="point3d" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1" y="1" z="-1" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="B">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1" y="-1" z="1" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="C">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="-1" z="1" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="D">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="1" z="1" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="E">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1" y="1" z="1" w="1"/>
<pointSize val="3"/>
</element>
<element type="polygon3d" label="face1">
<lineStyle thickness="4" type="-1" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.4099999964237213"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face3">
<lineStyle thickness="4" type="-1" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.4099999964237213"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face2">
<lineStyle thickness="4" type="-1" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.4099999964237213"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face4">
<lineStyle thickness="4" type="-1" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.4099999964237213"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face5">
<lineStyle thickness="4" type="-1" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.4099999964237213"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="faceBCDE">
<lineStyle thickness="4" type="-1" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.4099999964237213"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="edge2">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge1">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge4">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge6">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge3">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAE">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBE">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" 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="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge5">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" 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="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge7">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeDE">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="-1" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Sphere">
<input a0="(0, 0, 0)" a1="r"/>
<output a0="b"/>
</command>
<element type="quadric" label="b">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.6600000262260437"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" 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="-2.0736" A4="0" A5="0" A6="0" A7="0" A8="0" A9="0"/>
<eqnStyle style="specific"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="40" y="92"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(r,1)"/>
<font serif="false" sizeM="2" size="12" style="0"/>
<caption val="内切球"/>
</element>
<expression label="O" exp="(0, 0, 0)" type="point"/>
<element type="point3d" label="O">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="0" z="0" w="1"/>
<pointSize val="5"/>
</element>
<expression label="F" exp="(0, 0, -1)" type="point"/>
<element type="point3d" label="F">
<show object="true" label="false" ev="4"/>
<condition showObject="r ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="0" z="-1" w="1"/>
<pointSize val="3"/>
</element>
<expression label="G" exp="(0, 0, 1)" type="point"/>
<element type="point3d" label="G">
<show object="true" label="false" ev="4"/>
<condition showObject="r ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="0" z="1" w="1"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="F" a1="G"/>
<output a0="f"/>
</command>
<element type="segment3d" label="f">
<show object="true" label="false" ev="4"/>
<condition showObject="r ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="button" label="button2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="32" y="154"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(r,sqrt(2))"/>
<font serif="false" sizeM="2" size="12" style="0"/>
<caption val="与棱相切"/>
</element>
<expression label="H" exp="(-1, 0, 1)" type="point"/>
<element type="point3d" label="H">
<show object="true" label="false" ev="4"/>
<condition showObject="r ≟ sqrt(2)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-1" y="0" z="1" w="1"/>
<pointSize val="3"/>
</element>
<expression label="I" exp="(1, 0, -1)" type="point"/>
<element type="point3d" label="I">
<show object="true" label="false" ev="4"/>
<condition showObject="r ≟ sqrt(2)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1" y="0" z="-1" w="1"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="H" a1="I"/>
<output a0="g"/>
</command>
<element type="segment3d" label="g">
<show object="true" label="false" ev="4"/>
<condition showObject="r ≟ sqrt(2)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="button" label="button3">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="41" y="209"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(r,sqrt(3))"/>
<font serif="false" sizeM="2" size="12" style="0"/>
<caption val="外接球"/>
</element>
<command name="Segment">
<input a0="C" a1="A"/>
<output a0="h"/>
</command>
<element type="segment3d" label="h">
<show object="true" label="false" ev="4"/>
<condition showObject="r ≟ sqrt(3)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="J" exp="(-1, -1, -1)" type="point"/>
<element type="point3d" label="J">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-1" y="-1" z="-1" w="1"/>
<pointSize val="3"/>
</element>
<expression label="K" exp="(1, -1, -1)" type="point"/>
<element type="point3d" label="K">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1" y="-1" z="-1" w="1"/>
<pointSize val="3"/>
</element>
<expression label="L" exp="(1, 1, -1)" type="point"/>
<element type="point3d" label="L">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1" y="1" z="-1" w="1"/>
<pointSize val="3"/>
</element>
<command name="Pyramid">
<input a0="L" a1="J" a2="C" a3="E"/>
<output a0="c" a1="faceCJL" a2="faceEJL" a3="faceCEJ" a4="faceCEL" a5="edgeJL" a6="edgeCJ" a7="edgeCL" a8="edgeEL" a9="edgeEJ" a10="edgeCE"/>
</command>
<element type="polyhedron" label="c">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0.5199999809265137"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="faceCJL">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0.5199999809265137"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="faceEJL">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0.5199999809265137"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="faceCEJ">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0.5199999809265137"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="faceCEL">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0.5199999809265137"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="edgeJL">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeCJ">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeCL">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeEL">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeEJ">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeCE">
<show object="true" label="false" ev="4"/>
<condition showObject="d"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="boolean" label="d">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="37" y="265"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="隐藏＼显示正四面体"/>
</element>
</construction>
</geogebra>