Three Orthographic Views of Geometric Solids
2020-12-10 02:59
This GeoGebra applet dynamically demonstrates the three orthographic views (front, side, top) of common spatial solids like prisms, pyramids, cylinders, cones, and spheres. Using interactive buttons and 3D vectors, users can switch between solids and observe their 2D projections on orthogonal planes, enhancing spatial visualization and understanding of solid geometry.
In collections
Exploring the World of Shapes in GeoGebra
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.2.817.0" app="classic" platform="w" id="E5B8FEDF-EE7E-41D4-9A94-4FE03923F538" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="800" height="600" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.35125" orientation="1" />
</panes>
<views>
<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 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="1" visible="true" inframe="false" stylebar="false" location="3" size="281" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="320" tab="ALGEBRA" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="true" location="3" size="300" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="100" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="22" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" 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="4097" visible="false" inframe="false" stylebar="true" location="1" size="279" window="100,100,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" window="50,50,500,500" />
<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="false" location="1" size="509" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 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 | 100001 100001" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="281" height="598"/>
<coordSystem xZero="-2107.829210633601" yZero="2937.0288112012445" scale="118.29553022049801" yscale="118.29553022050233"/>
<evSettings axes="false" 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="11" grid="0"/>
<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="4"/>
<angleUnit val="degree"/>
<algebraStyle val="3" 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="-0.8591412011995159" scale="41.122321438697355" xAngle="30.000000000000004" zAngle="-125.26438968275468"/>
<evSettings axes="false" grid="true" 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="几何体的三视图" author="" date="">
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="29" y="74"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetViewDirection[Vector[G,O]]"/>
<caption val="主视图"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<element type="button" label="button2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="29" y="144"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetViewDirection[Rotate[Vector[G,O],-90°,O]]"/>
<caption val="左视图"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<element type="button" label="button3">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="29" y="214"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetViewDirection[Vector[(0,0,-1)]]"/>
<caption val="俯视图"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<element type="button" label="button4">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="29" y="285"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetViewDirection[Vector((1,sqrt[2],-1))]
G=(0,-6,0)"/>
<caption val="复位"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<expression label="A" exp="(0, 1, 0)" type="point"/>
<element type="point3d" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<pointSize val="5"/>
<coords x="0" y="1" z="0" w="1"/>
</element>
<element type="numeric" label="n">
<value val="4"/>
<slider min="3" max="6" absoluteScreenLocation="true" width="200" x="28" y="417" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="Rotate[A, (360° * i / n), (0, 0)]" a1="i" a2="1" a3="n"/>
<output a0="l1"/>
</command>
<element type="list" label="l1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Polygon">
<input a0="l1"/>
<output a0="t1"/>
</command>
<element type="polygon3d" label="t1">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="false" label="false" ev="4"/>
<condition showObject="p ∨ q"/>
<objColor r="204" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<command name="Prism">
<input a0="t1" a1="Element[l1, 1] + (0, 0, 5)"/>
<output a0="a" a1="B" a2="C" a3="D" a4="E" a5="F" a6="face1" a7="face2" a8="face3" a9="face5" a10="face6" a11="face7" a12="face4" a13="edge1" a14="edge2" a15="edge3" a16="edge7" a17="edge9" a18="edge11" a19="edge4" a20="edge5" a21="edge6" a22="edge8" a23="edge10" a24="edge12"/>
</command>
<element type="polyhedron" label="a">
<lineStyle thickness="5" type="0" typeHidden="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="point3d" label="B">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<pointSize val="4"/>
<coords x="-1.2246467991473532e-16" y="-1" z="5" w="1"/>
</element>
<element type="point3d" label="C">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<pointSize val="4"/>
<coords x="1" y="-1.8369701987210297e-16" z="5" w="1"/>
</element>
<element type="point3d" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<pointSize val="4"/>
<coords x="2.4492935982947064e-16" y="1" z="5" w="1"/>
</element>
<element type="point3d" label="E">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<pointSize val="4"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
</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"/>
<pointSize val="4"/>
<coords x="NaN" y="NaN" z="NaN" w="NaN"/>
</element>
<element type="polygon3d" label="face1">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face2">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face3">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face5">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face6">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face7">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face4">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="edge1">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge2">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge3">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge7">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge9">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge11">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge4">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge5">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge6">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge8">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge10">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge12">
<show object="true" label="false" ev="4"/>
<condition showObject="p"/>
<objColor r="216" g="27" b="96" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="polygon3d" label="t1">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="false" label="false" ev="4"/>
<condition showObject="p ∨ q"/>
<objColor r="204" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<expression label="G" exp="(0, -6, 0)" type="point"/>
<element type="point3d" label="G">
<show object="true" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-20" y="-4"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<caption val="人"/>
<pointSize val="5"/>
<coords x="0" y="-6" z="0" w="1"/>
</element>
<command name="Midpoint">
<input a0="G" a1="(0, 0)"/>
<output a0="H"/>
</command>
<element type="point3d" label="H">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<pointSize val="5"/>
<coords x="0" y="-3" z="0" w="1"/>
</element>
<command name="Vector">
<input a0="G" a1="H"/>
<output a0="u"/>
</command>
<element type="vector3d" label="u">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="25" y="40"/>
<labelMode val="3"/>
<caption val="人"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<startPoint exp="G"/>
<coords x="0" y="3" z="0" w="0"/>
</element>
<element type="button" label="button5">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="150" y="74"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[p,!p]"/>
<caption val="棱柱"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<element type="button" label="button6">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="150" y="128"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[q,!q]"/>
<caption val="棱锥"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<element type="button" label="button7">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="150" y="184"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[r,!r]"/>
<caption val="圆柱"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<element type="button" label="button8">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="150" y="245"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[s,!s]"/>
<caption val="圆锥"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<element type="button" label="button9">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="152" y="304"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,!t]"/>
<caption val="球"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<expression label="P" exp="(0, 0, 5)" type="point"/>
<element type="point3d" label="P">
<show object="true" label="false" ev="4"/>
<condition showObject="q ∨ s"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<pointSize val="3"/>
<coords x="0" y="0" z="5" w="1"/>
</element>
<command name="Pyramid">
<input a0="t1" a1="P"/>
<output a0="b" a1="face8" a2="face10" a3="face9" a4="face11" a5="face12" a6="face13" a7="edge13" a8="edge14" a9="edge15" a10="edge16" a11="edge17" a12="edge18"/>
</command>
<element type="polyhedron" label="b">
<lineStyle thickness="5" type="0" typeHidden="0"/>
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face8">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face10">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face9">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face11">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face12">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="face13">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="edge13">
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge14">
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge15">
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge16">
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge17">
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge18">
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="219" g="97" b="20" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="0"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="polygon3d" label="t1">
<lineStyle thickness="5" type="0" typeHidden="0" opacity="178"/>
<show object="false" label="false" ev="4"/>
<condition showObject="p ∨ q"/>
<objColor r="204" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="boolean" label="p">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="q">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Cylinder">
<input a0="(0, 0)" a1="P" a2="1"/>
<output a0="c" a1="d" a2="e" a3="f"/>
</command>
<element type="quadriclimited" label="c">
<show object="true" label="false" ev="4"/>
<condition showObject="r"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="conic3d" label="d">
<show object="true" label="false" ev="4"/>
<condition showObject="r"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eqnStyle style="parametric"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-1" A3="0" A4="0" A5="0"/>
</element>
<element type="conic3d" label="e">
<show object="true" label="false" ev="4"/>
<condition showObject="r"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eqnStyle style="parametric"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-1" A3="0" A4="0" A5="0"/>
</element>
<element type="quadricpart" label="f">
<show object="true" label="false" ev="4"/>
<condition showObject="r"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
</element>
<element type="boolean" label="r">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Cone">
<input a0="(0, 0)" a1="P" a2="1"/>
<output a0="g" a1="g_{2}" a2="g_{3}"/>
</command>
<element type="quadriclimited" label="g">
<show object="true" label="false" ev="4"/>
<condition showObject="s"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="conic3d" label="g_{2}">
<show object="true" label="false" ev="4"/>
<condition showObject="s"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eqnStyle style="parametric"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-1.0000000000000002" A3="0" A4="0" A5="0"/>
</element>
<element type="quadricpart" label="g_{3}">
<show object="true" label="false" ev="4"/>
<condition showObject="s"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
</element>
<element type="boolean" label="s">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Sphere">
<input a0="(0, 0, 2.5)" a1="2.5"/>
<output a0="h"/>
</command>
<element type="quadric" label="h">
<show object="true" label="false" ev="4"/>
<condition showObject="t"/>
<objColor r="211" g="47" b="47" alpha="0.6499999761581421"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eqnStyle style="specific"/>
<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="0" A4="0" A5="0" A6="0" A7="0" A8="0" A9="-2.5"/>
</element>
<element type="boolean" label="t">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
</construction>
</geogebra>