Volume of a Pyramid
2015-08-13 17:24
This GeoGebra applet demonstrates the calculation and 3D geometric construction of a pyramid's volume. Using commands like Translate, Rotate, and Pyramid, it builds a 3D pyramid model and dynamically displays its volume, helping users understand the volume formula and spatial structure in solid geometry.
In collections
S3 Area and Volume
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.132.0" id="dae32782-2adb-4db9-96dc-f89c55e036f7" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1179" height="996" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.6445783132530121" orientation="0" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="1011,327,700,550" />
<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="1" visible="true" inframe="false" stylebar="false" location="2" size="237" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" 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="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="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" 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 | 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 | 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="0" size="642" window="100,100,600,400" />
</views>
<toolbar show="true" 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="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1168" height="218"/>
<coordSystem xZero="-52.9361382419234" yZero="793.4906085649889" scale="37.56574004507885" yscale="37.56574004507884"/>
<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="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" 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"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="-0.7071739453731747" yZero="-0.8641208749059026" zZero="-0.655253929936587" scale="118.96745332641116" xAngle="24.0" zAngle="-391.4376717148683"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="0"/>
<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="l">
<value val="2.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="1" max="5" absoluteScreenLocation="true" width="200.0" x="38.0" y="196.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<caption val="Height"/>
</element>
<element type="vector3d" label="w">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0.0" y="0.0" z="1.0" w="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<element type="numeric" label="k">
<value val="2.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="1" max="5" absoluteScreenLocation="true" width="200.0" x="37.0" y="86.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<caption val="Length"/>
</element>
<element type="vector3d" label="v">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0.0" y="1.0" z="0.0" w="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<element type="numeric" label="j">
<value val="2.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="1" max="5" absoluteScreenLocation="true" width="200.0" x="39.0" y="143.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<caption val="Width"/>
</element>
<element type="vector3d" label="u">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="1.0" y="0.0" z="0.0" w="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<element type="point" label="A">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.0" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Translate">
<input a0="(0, 0)" a1="Vector[(j * u)]"/>
<output a0="B"/>
</command>
<element type="point3d" label="B">
<show object="false" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="0.0" z="0.0" w="1.0"/>
<coordStyle style="cartesian"/>
<pointSize val="4"/>
</element>
<command name="Translate">
<input a0="(0, 0)" a1="Vector[(k * v)]"/>
<output a0="C"/>
</command>
<element type="point3d" label="C">
<show object="false" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="2.0" z="0.0" w="1.0"/>
<coordStyle style="cartesian"/>
<pointSize val="4"/>
</element>
<expression label="D" exp="(x(B), y(C))" type="point" />
<element type="point" label="D">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="C" a1="A" a2="B" a3="D"/>
<output a0="poly1" a1="c" a2="a" a3="b" a4="d"/>
</command>
<element type="polygon3d" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬f"/>
<objColor r="255" g="102" b="0" alpha="0.7"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="a">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="b">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="d">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Translate">
<input a0="(0, 0)" a1="Vector[(l * w)]"/>
<output a0="E"/>
</command>
<element type="point3d" label="E">
<show object="false" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="2.0" w="1.0"/>
<coordStyle style="cartesian"/>
<pointSize val="4"/>
</element>
<element type="numeric" label="n">
<value val="1.0"/>
<show object="true" label="true"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200.0" x="386.0" y="86.0" fixed="true" horizontal="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.001" speed="2" type="0" playing="true"/>
<caption val="Rotate"/>
</element>
<command name="Prism">
<input a0="poly1" a1="z(E)"/>
<output a0="e" a1="F" a2="G" a3="H" a4="I" a5="faceACFG" a6="faceABHG" a7="faceBDIH_1" a8="faceCDIF" a9="faceFGHI" a10="edgeCF_1" a11="edgeAG" a12="edgeBH_1" a13="edgeDI_1" a14="edgeFG" a15="edgeGH" a16="edgeHI_1" a17="edgeFI_1"/>
</command>
<element type="polyhedron" label="e">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬f"/>
<objColor r="255" g="102" b="0" alpha="0.7"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="point3d" label="F">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="2.0" z="2.0" w="1.0"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="G">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="2.0" w="1.0"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="H">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="0.0" z="2.0" w="1.0"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="I">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="2.0" z="2.0" w="1.0"/>
<pointSize val="3"/>
</element>
<element type="polygon3d" label="faceACFG">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬f"/>
<objColor r="255" g="102" b="0" alpha="0.7"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceABHG">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬f"/>
<objColor r="255" g="102" b="0" alpha="0.7"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceBDIH_1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬f"/>
<objColor r="255" g="102" b="0" alpha="0.7"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceCDIF">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬f"/>
<objColor r="255" g="102" b="0" alpha="0.7"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceFGHI">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="¬f"/>
<objColor r="255" g="102" b="0" alpha="0.7"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="edgeCF_1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAG">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBH_1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeDI_1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeFG">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeGH">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeHI_1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeFI_1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="boolean" label="f">
<value val="true"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="373" y="16"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="Split cuboid"/>
</element>
<command name="Pyramid">
<input a0="C" a1="A" a2="B" a3="D" a4="F"/>
<output a0="g" a1="faceABDC" a2="faceACF" a3="faceABF_1" a4="faceBDF_1" a5="faceCDF" a6="edgeAC" a7="edgeAB_1" a8="edgeBD_1" a9="edgeCD" a10="edgeCF" a11="edgeAF_1" a12="edgeBF_1" a13="edgeDF_1"/>
</command>
<element type="polyhedron" label="g">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="faceABDC">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceACF">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceABF_1">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceBDF_1">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceCDF">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="255" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="edgeAC">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAB_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBD_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<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"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeCF">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAF_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBF_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeDF_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="edgeHI_1" a1="edgeDI_1"/>
<output a0="J"/>
</command>
<element type="point3d" label="J">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="2.0" z="2.0" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Pyramid">
<input a0="I" a1="D" a2="B" a3="H" a4="F"/>
<output a0="h" a1="faceBDIH" a2="faceDFI" a3="faceBDF" a4="faceBFH_1" a5="faceFHI" a6="edgeDI" a7="edgeBD" a8="edgeBH_2" a9="edgeHI_2" a10="edgeFI_2" a11="edgeDF" a12="edgeBF_2" a13="edgeFH_1"/>
</command>
<element type="polyhedron" label="h">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="51" g="51" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="faceBDIH">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="51" g="51" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceDFI">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="51" g="51" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceBDF">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="51" g="51" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceBFH_1">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="51" g="51" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceFHI">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="51" g="51" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="edgeDI">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<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"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-25" y="24"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBH_2">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeHI_2">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeFI_2">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeDF">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBF_2">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeFH_1">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Pyramid">
<input a0="E" a1="A" a2="B" a3="H" a4="F"/>
<output a0="i" a1="faceABHE" a2="faceAEF" a3="faceABF" a4="faceBFH" a5="faceEFH" a6="edgeAE_1" a7="edgeAB" a8="edgeBH" a9="edgeEH_1" a10="edgeEF_1" a11="edgeAF" a12="edgeBF" a13="edgeFH"/>
</command>
<element type="polyhedron" label="i">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="153" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="polygon3d" label="faceABHE">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="153" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceAEF">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="153" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceABF">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="153" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceBFH">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="153" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceEFH">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="153" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="edgeAE_1">
<show object="false" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<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"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBH">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeEH_1">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeEF_1">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAF">
<show object="false" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBF">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeFH">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 0 ∧ f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="i" a1="(n * π / 2)" a2="edgeAB"/>
<output a0="i'"/>
</command>
<element type="polyhedron" label="i'">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="(¬(n ≟ 0)) ∧ f"/>
<objColor r="0" g="153" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Rotate">
<input a0="h" a1="((-n) * π / 2)" a2="edgeBD"/>
<output a0="h'"/>
</command>
<element type="polyhedron" label="h'">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="(¬(n ≟ 0)) ∧ f"/>
<objColor r="0" g="0" b="255" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="104" y="17"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="j=2 k=2 l=2 "/>
<font serif="false" sizeM="1.4" size="5" style="0"/>
<caption val="Cube"/>
</element>
<command name="Volume">
<input a0="i'"/>
<output a0="volumei'"/>
</command>
<element type="numeric" label="volumei'">
<value val="2.6666666666666665"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="Texti'" exp=""Volume of " + (Name[i']) + " = " + volumei'" />
<element type="text" label="Texti'">
<show object="false" label="true" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<startPoint exp="Pointi'"/>
</element>
<command name="Point">
<input a0="i'"/>
<output a0="Pointi'"/>
</command>
<element type="point3d" label="Pointi'">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="0.5682113653019307" y="-2.0" z="1.2246467991473532E-16" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Volume">
<input a0="h'"/>
<output a0="volumeh'"/>
</command>
<element type="numeric" label="volumeh'">
<value val="2.6666666666666665"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="Texth'" exp=""Volume of " + (Name[h']) + " = " + volumeh'" />
<element type="text" label="Texth'">
<show object="false" label="true" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<startPoint exp="Pointh'"/>
</element>
<command name="Point">
<input a0="h'"/>
<output a0="Pointh'"/>
</command>
<element type="point3d" label="Pointh'">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="2.431339234843147" y="2.0" z="0.43133923484314707" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Volume">
<input a0="g"/>
<output a0="volumeg"/>
</command>
<element type="numeric" label="volumeg">
<value val="2.6666666666666665"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="Textg" exp=""Volume of " + (Name[g]) + " = " + volumeg" />
<element type="text" label="Textg">
<show object="false" label="true" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<startPoint exp="Pointg"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="Pointg"/>
</command>
<element type="point3d" label="Pointg">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="0.8828161378032302" y="1.1171838621967698" z="1.1171838621967698" w="1.0"/>
<pointSize val="3"/>
</element>
<expression label="text1" exp=""Volume = " + (LaTeX[volumei']) + """ />
<element type="text" label="text1">
<show object="true" label="true" ev="8"/>
<condition showObject="f"/>
<objColor r="0" g="153" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="3.0" size="24" style="0"/>
<auxiliary val="false"/>
<startPoint x="22.492200000000018" y="20.403980000000022" z="1.0"/>
</element>
<expression label="text2" exp=""Volume =" + (LaTeX[volumeg]) + """ />
<element type="text" label="text2">
<show object="true" label="true" ev="8"/>
<condition showObject="f"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="3.0" size="24" style="0"/>
<auxiliary val="false"/>
<startPoint x="22.521360000000048" y="17.35086000000004" z="1.0"/>
</element>
<expression label="text3" exp=""Volume = " + (LaTeX[volumei']) + """ />
<element type="text" label="text3">
<show object="true" label="true" ev="8"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="3.0" size="24" style="0"/>
<auxiliary val="false"/>
<startPoint x="22.49220000000002" y="18.913260000000022" z="1.0"/>
</element>
<command name="Rotate">
<input a0="H" a1="(n * π / 2)" a2="edgeAB"/>
<output a0="H'"/>
</command>
<element type="point3d" label="H'">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="-2.0" z="1.2246467991473532E-16" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Rotate">
<input a0="G" a1="(n * π / 2)" a2="edgeAB"/>
<output a0="G'"/>
</command>
<element type="point3d" label="G'">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-2.0" z="1.2246467991473532E-16" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Rotate">
<input a0="F" a1="(n * π / 2)" a2="edgeAB"/>
<output a0="F'"/>
</command>
<element type="point3d" label="F'">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-1.9999999999999998" z="2.0" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="F'" a1="G'"/>
<output a0="m"/>
</command>
<element type="segment3d" label="m">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="F'" a1="H'"/>
<output a0="p"/>
</command>
<element type="segment3d" label="p">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="F'"/>
<output a0="q"/>
</command>
<element type="segment3d" label="q">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="F'"/>
<output a0="r"/>
</command>
<element type="segment3d" label="r">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="G'"/>
<output a0="s"/>
</command>
<element type="segment3d" label="s">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="H'"/>
<output a0="t"/>
</command>
<element type="segment3d" label="t">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="G'" a1="H'"/>
<output a0="a_1"/>
</command>
<element type="segment3d" label="a_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="J" a1="((-n) * π / 2)" a2="edgeBD"/>
<output a0="J'"/>
</command>
<element type="point3d" label="J'">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.0" y="2.0" z="1.2246467991473532E-16" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Rotate">
<input a0="H" a1="((-n) * π / 2)" a2="edgeBD"/>
<output a0="H'_1"/>
</command>
<element type="point3d" label="H'_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.0" y="0.0" z="1.2246467991473532E-16" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Rotate">
<input a0="F" a1="((-n) * π / 2)" a2="edgeBD"/>
<output a0="F'_1"/>
</command>
<element type="point3d" label="F'_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.0" y="2.0" z="2.0" w="1.0"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="F'_1" a1="J'"/>
<output a0="b_1"/>
</command>
<element type="segment3d" label="b_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="F'_1" a1="D"/>
<output a0="c_1"/>
</command>
<element type="segment3d" label="c_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="F'_1" a1="B"/>
<output a0="d_1"/>
</command>
<element type="segment3d" label="d_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="F'_1" a1="H'_1"/>
<output a0="e_1"/>
</command>
<element type="segment3d" label="e_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="H'_1"/>
<output a0="f_1"/>
</command>
<element type="segment3d" label="f_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="H'_1" a1="J'"/>
<output a0="g_1"/>
</command>
<element type="segment3d" label="g_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="J'" a1="D"/>
<output a0="h_1"/>
</command>
<element type="segment3d" label="h_1">
<show object="true" label="false" ev="4"/>
<condition showObject="f"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>