Shey-lhiattaghan
{{ymmydynelley}}
{| border="1" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Shey-lhiattaghan cadjin
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|align=center colspan=2|[[Coadan:Regular hexagon.svg|250px]]<br />Shey-lhiattaghan [[Yl-lhiatteean cadjin|cadjin]], {6}
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|bgcolor=#e7dcc3|[[Oirr (towse-oaylleeaght)|Oirryn]] as [[Mullagh (towse-oaylleeaght)|mullee]]||6
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|bgcolor=#e7dcc3|[[Cowrey Schläfli|Cowraghyn Schläfli]]||{6}<br />t{3}
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|bgcolor=#e7dcc3|[[Diagram Coxeter–Dynkin|Diagramyn Coxeter-Dynkin]]||[[Coadan:CDW ring.svg]][[Coadan:CDW 6.png]][[Coadan:CDW dot.svg]]<br />[[Coadan:CDW ring.svg]][[Coadan:CDW 3.png]][[Coadan:CDW ring.svg]]
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|bgcolor=#e7dcc3|[[Rolley possanyn shimmeadraght phlaanagh|Possan shimmeadraght]]||[[Shimmeadraght ghaa-heedragh|Daa-heedragh]] (D<sub>6</sub>)
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|bgcolor=#e7dcc3|[[Eaghtyr]]<br />(lesh ''t''=lhiurid yn oirr)||<math>A = \frac{3 \sqrt{3}}{2}t^2</math><br /><math> \simeq 2.598076211 t^2.</math>
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|bgcolor=#e7dcc3|[[Uillin sthie]]<br />([[keim (uillin)|keimyn]])||120°
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|bgcolor=#e7dcc3|Troyn||[[Yl-lhiatteean dronnagh|dronnagh]], [[Yl-lhiatteean kiarklagh|kiarklagh]], [[co-lhiatteeagh]], [[jalloo co-uillinagh|co-uillinagh]], [[jalloo oirr-aistragh|oirr-aistragh]]
|}

Ayns [[towse-oaylleeaght]], ta'n '''shey-lhiattaghan''' ny [[yl-lhiatteean]] lesh shey oirryn as shey [[mullagh (towse-oaylleeaght)|mullee]]. She {6} y [[cowrey Schläfli]] ta currit er shey-lhiattaghan cadjin.

== Shey-lhiattaghan cadjin ==
[[Coadan:HexagonConstructionAni.gif|left|frame|Ta'n shey-lhiattaghan cadjin so-hroggalagh lesh combaase as reilleyder. Ta'n jalloo shoh taishbyney aght keim-er-cheim er kanys shey-lhiattaghan y chroo, currit liorish [[Euclid]] 'sy lioar ''[[Elmintyn Euclid|Elmintyn]]'', Lioar IV, Keisht 15.]]

Ta ny h-uillinyn sthie jeh shey-lhiattaghan cadjin (raad dy vel co-lhiurid ec dagh çheu) 120[[keim (uillin)|°]] er uillin, as ta 720 keimyn T ec y shey-lhiattaghan. Ta 6 [[shimmeadraght chiarklagh|shimmeadraghtyn kiarklagh]] as 6 [[shimmeeadraght aahoilshagh|shimmeadraghtyn aahoilshagh]] echey, as ad jannoo seose y [[possan daa-heedragh]] D<sub>6</sub>. Ta ny tessenaneyn s'liurey jeh shey-lhiattaghan cadjin, ta kiangley mullee chondaigagh chrantessenagh, daa cheayrt ny s'liurey na ny h-oirryn. Ayns cosoylaght rish [[kerrin (towse-oaylleeaght)|kerrinyn]] as [[troorane (towse-oaylleeaght)|trooraneyn]] [[co-lhiatteeagh]], ta shey-lhiattaghanyn kiangley rish y cheilley dys ''plaaney y çheeley'' gyn baarnaghyn (ta tree shey-lhiattaghanyn cruinnaghey ec dagh mullagh), as lesh shen t'ad so-ymmydagh son [[mosaic (obbraghey)|mosaicyn]] y hroggal.
Son yn oyr shen, ta killagyn shelleig jeant seose ayns cummey shey-lhiattagh as er oyr dy vel y cummey oc jannoo ymmyd fondagh jeh reamys as cooid hroggee. She mosaic kere volley jeh shey-lhiattaghanyn y [[diagram Voronoi]] jeh cleeah trooraneagh cadjin.

Ta eaghtyr jeh shey-lhiattaghan cadjin lesh liurid oirr <math>t\,\!</math> currit liorish
<math>A = \frac{3 \sqrt{3}}{2}t^2 \simeq 2.598076211 t^2.</math>

Myrane lesh shen, foddee eh y gheddyn magh lesh y formley A=ap/2, raad dy vel a yn [[apothem]] as p yn ym-linney.

Ta ym-linney y shey-lhiattaghan cadjin lesh liurid oirr <math>t\,\!</math> currit sheese myr <math>6t\,\!</math>, y crantessen smoo <math>2t\,\!</math>, as y crantessen sloo <math>t\sqrt{3}\,\!</math>.
 
Cha nel stooaltane platoanagh ayn ta jeant seose jeh shey-lhiattaghanyn cadjin.

{{bun}}

[[Ronney:Yl-lhiatteeanyn]]
[[Ronney:Towse-oaylleeaght]]
Shey-lhiattaghan cadjin250pxShey-lhiattaghan cadjin, {6}Oirryn as mullee6Cowraghyn Schläfli{6}t{3}Diagramyn Coxeter-DynkinCoadan:CDW ring.svgCoadan:CDW 6.pngCoadan:CDW dot.svgCoadan:CDW ring.svgCoadan:CDW 3.pngCoadan:CDW ring.svgPossan shimmeadraghtDaa-heedragh (D6)Eaghtyr(lesh t=lhiurid yn oirr)Uillin sthie(keimyn)120°Troyndronnagh, kiarklagh, co-lhiatteeagh, co-uillinagh, oirr-aistragh

Ayns towse-oaylleeaght, ta'n shey-lhiattaghan ny yl-lhiatteean lesh shey oirryn as shey mullee. She {6} y cowrey Schläfli ta currit er shey-lhiattaghan cadjin.

 Shey-lhiattaghan cadjin 
left|frame|Ta'n shey-lhiattaghan cadjin so-hroggalagh lesh combaase as reilleyder. Ta'n jalloo shoh taishbyney aght keim-er-cheim er kanys shey-lhiattaghan y chroo, currit liorish Euclid 'sy lioar Elmintyn, Lioar IV, Keisht 15.

Ta ny h-uillinyn sthie jeh shey-lhiattaghan cadjin (raad dy vel co-lhiurid ec dagh çheu) 120° er uillin, as ta 720 keimyn T ec y shey-lhiattaghan. Ta 6 shimmeadraghtyn kiarklagh as 6 shimmeadraghtyn aahoilshagh echey, as ad jannoo seose y possan daa-heedragh D6. Ta ny tessenaneyn s'liurey jeh shey-lhiattaghan cadjin, ta kiangley mullee chondaigagh chrantessenagh, daa cheayrt ny s'liurey na ny h-oirryn. Ayns cosoylaght rish kerrinyn as trooraneyn co-lhiatteeagh, ta shey-lhiattaghanyn kiangley rish y cheilley dys plaaney y çheeley gyn baarnaghyn (ta tree shey-lhiattaghanyn cruinnaghey ec dagh mullagh), as lesh shen t'ad so-ymmydagh son mosaicyn y hroggal.
Son yn oyr shen, ta killagyn shelleig jeant seose ayns cummey shey-lhiattagh as er oyr dy vel y cummey oc jannoo ymmyd fondagh jeh reamys as cooid hroggee. She mosaic kere volley jeh shey-lhiattaghanyn y diagram Voronoi jeh cleeah trooraneagh cadjin.

Ta eaghtyr jeh shey-lhiattaghan cadjin lesh liurid oirr  currit liorish

Myrane lesh shen, foddee eh y gheddyn magh lesh y formley A=ap/2, raad dy vel a yn apothem as p yn ym-linney.

Ta ym-linney y shey-lhiattaghan cadjin lesh liurid oirr  currit sheese myr , y crantessen smoo , as y crantessen sloo .
 
Cha nel stooaltane platoanagh ayn ta jeant seose jeh shey-lhiattaghanyn cadjin.

Ronney:Yl-lhiatteeanyn
Ronney:Towse-oaylleeaght