Shey-lhiattaghan

My vel anaase ayd ayns keeall elley yn 'ockle shoh, lhaih Shey-lhiattaghan (reddaghey).

Shey-lhiattaghan cadjin
Shey-lhiattaghan cadjin, {6}
Oirryn as mullee	6
Cowraghyn Schläfli	{6} t{3}
Diagramyn Coxeter-Dynkin
Possan shimmeadraght	Daa-heedragh (D6)
Eaghtyr (lesh t=lhiurid yn oirr)	$A={\frac {3{\sqrt {3}}}{2}}t^{2}$ $\simeq 2.598076211t^{2}.$
Uillin sthie (keimyn)	120°
Troyn	dronnagh, 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

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 $t\,\!$ currit liorish $A={\frac {3{\sqrt {3}}}{2}}t^{2}\simeq 2.598076211t^{2}.$

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 $t\,\!$ currit sheese myr $6t\,\!$, y crantessen smoo $2t\,\!$, as y crantessen sloo $t{\sqrt {3}}\,\!$.

Cha nel stooaltane platoanagh ayn ta jeant seose jeh shey-lhiattaghanyn cadjin.