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class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_no.wikipedia.org&uselang=nb" class=""><span>Doner</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesial:Opprett_konto&returnto=Kube&returntoquery=action%3Dedit" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk" class=""><span>Opprett konto</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spesial:Logg_inn&returnto=Kube&returntoquery=action%3Dedit" title="Du oppfordres til å 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aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Artikkelen finnes kun på dette språket. Legg til artikkelen på andre språk" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-0" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">Legg til språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> <div class="after-portlet after-portlet-lang"><span class="uls-after-portlet-link"></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Navnerom"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Kube" title="Vis innholdssiden [c]" accesskey="c"><span>Artikkel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskusjon:Kube" rel="discussion" title="Diskusjon om innholdssiden [t]" accesskey="t"><span>Diskusjon</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Bytt språkvariant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">norsk bokmål</span> </label> 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Husk å ta med alle detaljene ovenfor.</div></div><hr /> <p>Du kan se og kopiere kildekoden til denne siden: </p><textarea readonly="" accesskey="," id="wpTextbox1" cols="80" rows="25" style="" class="mw-editfont-monospace" lang="nb" dir="ltr" name="wpTextbox1">{{Kildeløs|Helt uten kilder.|dato=10. okt. 2015}} {{Infoboks polyeder |navn=Kube |bilde=Hexahedron.svg |bildebredde=185px |bildetekst= |animasjon=hexahedron.gif |type=[[Platonsk legeme]] |dual=[[Oktaeder]] |sider=6 |sidetype=[[kvadrat]]er |kanter=12 |hjørner=8 |sidefordeling=4.4.4 |schläfli={4,3} }} [[Fil:Dice.jpg|180px|thumb|Den velkjente sekssidede [[terning]]en er kubeformet]] En '''kube''' eller '''terning''' er et [[tredimensjonal]]t romlegeme som begrenses av seks [[kvadrat]]iske [[side (geometri)|sider]] hvor tre møtes i hvert [[hjørne]]. Kuben kan også bli kalt et '''[[regulært polyeder|regulært]] [[heksaeder]]''' og er en av de fem [[platonsk legeme|platonske legemene]]. Kube er en spesiell type rektangulært [[prisme (geometri)|prisme]], rektangulært [[parallellepiped]] og tresidet [[trapesoeder]]. Kuben er ''[[dualt polyeder|dual]]'' med [[oktaeder]]et. Kuben er det eneste platonske legemet som kan stables uten at det blir gap mellom dem. ==Formler== Hvis en kube har kanter med lengde <math>a</math>, er {|class="wikitable" |- |[[areal]] |align=center|<math>6 a^2\,</math> |- |[[volum]] |align=center|<math>a^3\,</math> |- |side[[diagonal]] |align=center|<math>\sqrt 2a</math> |- |romdiagonal |align=center|<math>\sqrt 3a</math> |- |[[radius]] til en omskrevet [[kule (geometri)|kule]]<br />(fyller hele figuren) |align=center|<math>\frac{\sqrt 3}{2} a</math> |- |midtradius<br />(radius til kule som dekker midten av hver kant) |align=center|<math>\frac{a}{\sqrt 2}</math> |- |radius av en innskrevet kule |align=center|<math>\frac{a}{2}</math> |- |vinkel mellom sidene (i [[radianer]]) |align=center|<math>\frac{\pi}{2}</math> |} Slik som volumet av en kube er tredje potens av en side, <math>a \times a \times a</math>, kalles gjerne tredjepotensen for ''[[kube (aritmetikk)|kuber]]'', på samme måte som med [[kvadrat (aritmetikk)|kvadrater]] og andrepotenser. En kube har det største volumet av [[kuboide]]r (rektangulære bokser) med et gitt [[overflateareal]]. I tillegg har en kube det største arealet av kuboider med likt sammenlagt lineær størrelse (lengde+bredde+høyde). == Kartesiske koordinater == En kube sentrert ved origo, og med hjørneavstander på 2 får kartesiske koordinater : (±1,±1,±1) Da vil innsiden bestå av alle punkt (x0, x1, x2) der -1 < xi < 1. [[Fil:Unitcube.svg|150px|thumb|Enhetskube]] [[Fil:دوران المكعب.gif |150px|miniatyr|høyre|Animert perspektiv av enhetskube]] == Enhetskuben == En enhetskube er en kube der alle sider er 1 enhet lang. Volum av en 3 dimensjonal enhetskube er 1, og totalt overflateareal er 6 kvadrat. Begrepet enhetskube er også brukt om "kuber" i n-dimensjonale rom. ==Relaterte polyedre== [[Image:Dual Cube-Octahedron.svg|thumb|200px|right|Dualen av en kube er et [[oktaeder]].]] [[File:Hemicube2.PNG|200px|thumb|[[Hemikube|Hemikuben]] er 2-til-1-kvotienten av en kube.]] Kvotienten til en kube ved dets motstående avbildning, avkaster et projektivt polyeder, [[hemikube]]n. Hvis vi tar utgangspunkt i en kube med kantlengde 1, vil det [[dualt polyeder|duale polyeder]]et dets (et [[oktaeder]]) ha kantlengder på <math>\scriptstyle \sqrt{2}</math>. Kuben er et spesialtilfelle av en rekke grupper mer generelle polyedre: {|class=wikitable !Navn!!Like kantlengder?!!Like vinkler?!!Rette vinkler? |- |'''Kube'''||'''Ja'''||'''Ja'''||'''Ja''' |- |[[Romboeder]]||Ja||Ja||Nei |- |[[Kuboide]]||Nei||Ja||Ja |- |[[Parallellepiped]]||Nei||Ja||Nei |- |[[Firkant]]sidet heksaeder||Nei||Nei||Nei |} Hjørnene på en kube kan deles inn i to grupper på fire som danner hvert sitt [[tetraeder]]. Mer generelt blir denne omtalt som en [[demikube]]. Disse to sammen former en regulær polyedersammensetning, et [[stjernetetraeder]]. Skjæringen mellom de to danner et oktaeder. Et slikt regulært tetraeder kan ha {{frac|1|3}} av volumet til den kuben. Det resterende volumet består av fire irregulære tetraedre med henholdsvis et volum på {{frac|1|6}} av den samme kuben. Ved å kutte av hjørnene på en kube uten at de nye sidene møter hverandre, får vi et polyeder med seks [[oktogon]]ale sider og åtte [[trekant]]ede. Spesielt kan vi få regulære oktogoner som gir en [[avstumpet kube]]. Hvis de møter hverandre i hjørner som er felles med de gamle, får vi et [[kuboktaeder]]. Vi får et [[rombkuboktaeder]] ved å kutte av både hjørner og kanter en spesiell lengde. En kube kan innskrives i et [[dodekaeder]] slik at alle kubens hjørner også er et hjørne hos dodekaederet og alle kantene er en diagonal på en av dodekaederets sideflater. Kombinasjonen av alle slike kuber gir opphav til den regulære sammensetningen av fem kuber. Hvis to motstående hjørner av en kube avstumpes på dybden av de tre hosliggende kantene, får vi et irregulært oktaeder. Åtte av disse irregulære oktaedrene kan festes til de likesidede trakant-sidene hos et regulært oktaeder slik at vi får et kuboktaeder. Kuben er topologisk relatert til en serie kuleformede polyedre og tesseleringer hvor tre sider møtes i hvert hjørne. {| class="wikitable" !Kule-<br />polyedre !colspan=3|[[Regulært polyeder|Polyeder]] ![[Regulær tesselering|Euklidisk]] !colspan=4|Hyperbolsk tesselering |- align=center |[[File:Spherical trigonal hosohedron.svg|50px]]<br />[[Hosoeder|{2,3}]]<br />{{CDD|node_1|2|node|3|node}} |[[Image:Uniform polyhedron-33-t0.png|50px]]<br />[[Tetraeder|{3,3}]]<br />{{CDD|node_1|3|node|3|node}} |[[Image:Uniform polyhedron-43-t0.png|50px]]<br />[[Kube|{4,3}]]<br />{{CDD|node_1|4|node|3|node}} |[[Image:Uniform polyhedron-53-t0.png|50px]]<br />[[Dodekaeder|{5,3}]]<br />{{CDD|node_1|5|node|3|node}} |[[Image:Uniform polyhedron-63-t0.png|50px]]<br />[[Heksagonal tesselering|{6,3}]]<br />{{CDD|node_1|6|node|3|node}} |[[File:H2_tiling_237-1.png|50px]]<br />[[Heptagonal tesselering|{7,3}]]<br />{{CDD|node_1|7|node|3|node}} |[[File:H2_tiling_238-1.png|50px]]<br />[[Oktogonal tesselering|{8,3}]]<br />{{CDD|node_1|8|node|3|node}} |... |[[File:H2_tiling_23i-1.png|50px]]<br />(∞,3}<br />{{CDD|node_1|infin|node|3|node}} |} == Se også == * [[Kuben]], pekerside til bestemt form av sustantivet, med flere betydninger * [[Bikube]], bolig for honningbier som brukes i [[birøkt]] * [[Rubiks kube]], et mekanisk puslespill * [[Kubikk]] {{polyedre}} {{Autoritetsdata}} [[Kategori:Platonske legemer]] </textarea><div class="templatesUsed"><div class="mw-templatesUsedExplanation"><p>Maler som brukes på denne siden: </p></div><ul> <li><a href="/wiki/Mal:," title="Mal:,">Mal:,</a> (<a href="/w/index.php?title=Mal:,&action=edit" title="Mal:,">vis kilde</a>) (halvbeskyttet)</li><li><a href="/wiki/Mal:Amboks" title="Mal:Amboks">Mal:Amboks</a> (<a href="/w/index.php?title=Mal:Amboks&action=edit" title="Mal:Amboks">vis kilde</a>) (beskyttet)</li><li><a href="/wiki/Mal:Autoritetsdata" title="Mal:Autoritetsdata">Mal:Autoritetsdata</a> (<a href="/w/index.php?title=Mal:Autoritetsdata&action=edit" 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