nett (polyhedron)

bhoomitimadhye, bahu-hedronche jaale hii pratalatil naan-aachchhadit kadaa-jodalelya bahubhujanchi eka vyavastha aahe jee bahu-hedronche chehare honyasathi dumadali jaau shakate (kathansah). polyhedral jaali hii polyheader aanee sarvasadharanpane ghan bhoomitichya abhyasasathi upayukt madat aahe, kaaran tyaa patal putthyasarkhya samgripasoon polyheadrache bhautik namune tayar karnyas anumati detat.
bahu -shastriy jaaliche prarambhik udaharan albrecht durerchya karyat disun yete, jyanchya 1525 madheel pustak 'aii course inn daad aart auph majerment with kampas andd ruller' ('untervisang dair mesang miit dame zirkel und richched') madhye platonic ghanpadarthansathi aanee anek archemedian ghanpadarthansathi jaali samavisht hotee. 1543 madhye augustein hirshavogelane yaa bandhkamanna pahilyanda jaali mhatale.
astitva aanee advitiyata.
konatya kadaa jodalya jaatat aanee konatya vegalya kelya jaatat hyachya nivadivar avalambun dilelya bahu-headronsathi anek bhinn jaali astitvat asoo shakatat. jaali tayar karnyasathi bahirmukh bahu-hedronpasoon kapalya gelelya kadaa bahu-hedronche pasarlele zaad tayar karane aavashyak aahe, parantu kahee pasarleli zaade kapalyane jaali tayar karnyaivaji ughadalyavar bahu-hedron swatahun aachchhadale jaau shakate. yaulat, dilelya jaalila tyachya kadaa konatya konatoon dumadalya jaatat aanee konatya kadaa ekatra chikatavanyachya nivadivar avalambun, ekapeksha jaast bhinn bahirmukh bahudhruviy madhye dumdu shakate. jarr jaale tyachya kadaa ekatra chikatavanyasathi asha namunyasah dile gele qee parinami aakarachya pratyek shirshamadhye sakaratmak koneey dosh asel aanee yaa doshanchi berries achook 4 asel, tarr tyatoon dumdu shakanare nemke eka bahu-hedron asane aavashyak aahe; heey alekzandrovche adviteey pramey aahe. tathapi, asha prakare tayar jhalelya bahubhujanche jaalicha bhag mhanoon nirdisht kelelya kelelya bhinn chehare asoo shakatatah kahee nivval bahubhujanna tyanchya palikade putt asoo shakatat aanee nivval bahubhujanmadhil kahee kadaa ughadi rahoo shakatat. yavyatirikt, ekach jaalyat anek vaidh gond namune asoo shakatat, jyamule bhinn dumadalele bahu-puttle tayar hote.
1975 madhye, jee. see. sheferdney vicharale qee pratyek bahirmukh bahu-headronmadhye kiman eka jaali aahe qaa, kinwa saral kadaa-unfolding aahe qaa? durers conjecture kinwa durers unfolding problem mhanoonahi olakhala jaanara haah prashna anuttarit aahe. tethe naun-convex polyheader astitvat aahe jyala jaali nasate aanee pratyek convex polyhedronchya polyhedronchya (udaharanarth kapalelya sthanasah) upavibhajan karane shakya aahe jenekarun upavibhajit asalelya sanchala jaale asel. 2014 madhye mohammed ghomi yanni dakhavun dile qee pratyek bahirmukh bahu-hedron eka sanlagn parivartananantar eka jaale swikarato. yavyatirikt, 2019 madhye barvinok aanee ghomi yanni dakhavun dile qee durerchya andajanche samanyikaran "chhadm kadaa" sathee ayashasvi hote, mhanje.eae., bhooganitiche eka jaale jeey bahu-hedronchya shirobinduna jodate aanee uttal uttal aalekh tayar karate.
eka sambandhit khula prashna vicharato qee bahirmukh bahu-hedronchya pratyek jaalyat eka fulanari, tyachya sapatpasoon tyachya dumadalelya avastheparyant satat gair-swayam-vichhedan gatee aahe qaa jee pratyek chehara sampoorn halchalit sapat thevate.
sarvat lahan marg.
polyhedronchya prushthbhagavaril done bindunmadhil prushthbhagavaril sarvat lahan marg haah margane sparsh kelelya asalelya upasanchasathi yogya jaalivaril saral resheshi sambandhit asato. jaali ashee asali pahije qee saral resha purnapane tyachya aat asel aanee konati sarvat lahan marg dete heey pahanyasathi ekhadyala anek jaali vicharat ghyavi lagtil. udaharanarth, ghankshetrachya babatit, jarr bindu shejarchya bajunvar asateel tarr sarvat lahan margasathi eka umedvar mhanje samaik kaath olandanara marg aahe; asha prakarcha sarvat lahan marg jaali vaparoon aadhalato jithe done chehare dekhil shejari aahet. sarvat lahan margasathiche itar umedvar donhichya shejari asalelya asalelya tisya prushthbhagavarun jaatat (jyapaiki done aahet) aanee pratyek shrenitil sarvat lahan marg shodhanyasathi sambandhit jaali vaparali jaau shakate.
kolee aanee mashichi samasya heey eka manoranjak ganitache kode aahe jyamadhye ghankshetravaril done bindunmadhil sarvat lahan marg shodhane samavisht aahe.
uchch-aayami polytope jaali.
4-bahupadiche jaale, eka chaar-aayami bahupadi, heey bahupadi peshinni banalele asate jeey tyanchya tyanchya jodalelya asatat aanee serve samaan trimiteey jaaga vyapatat, jyapramane bahupadichya jaalyache bahubhuj chehare tyanchya kathanni jodalele asatat aanee serve samaan pratal vyapatat. teseractche jaale, chaar-aayami hypercube, salvador dalichya 'crucifiction (corpus hypercubus)' (1954) yaa chitrat thalakpane vaparale gele aahe. teech tesseract jaali yaa laghukathechya kathanakachya kendrasthani aahe-aanee tyane eka vakr ghar bandhale-robbert aaa. henlein.
sootra _ 1-aayami hypercubechya sanyuktapane bhinn jaalichi sankhya, hya jaalila sootra _ 2 nodeswar eka vruksh mhanoon darshavoon, jyadvare hypercubechya asalelya jodya jaali tayar karnyasathi ekatra chikatalelya asatat, tyaa namunyache varnan karoon, dumadalelya hypercubever ekmekanchya viruddha asalelya asalelya jodyanche varnan varnan zadachya purak aalekhavar eka paripoorn julanisah shodhali jaau shakate. heey pratinidhitva vaparoon, 2,3,4, yaa parimananchya hypercubesathi vegvegalya ulgadyanchi sankhya... asey ganale jaate

