
ghana

jyaamiti mein, ack ghana ack tri-ayami thhos vastu haye joe chhah vargakar cheharon, pahaluon yaa bhujaaon seey ghiri hui haye, jisamen pratyek sheersh parr teen baithaken hoti hain. ack koney seey dekhaa jaae tou yeh ack shatkon haye aur isake jaal koo aamtaur parr ack cross key roop mein darshaaya jaataa haye.
ghana ekmatra niyamit shatkon haye aur paanch platonic thhos padarthon mein seey ack haye. isake 6 chehare, 12 kinare aur 8 sheersh hain.
ghana bhee ack varg samanantar haye, ack sambahu ghana aur ack daaen rhombohedron ack 3-zonohedron haye. yeh teen abhivinyason mein ack niyamit vargakar prism haye, aur chaar abhivinyason mein ack trikoniya trapezohedron haye.
ghana octahedrone key liye dohri haye. isamen ghana yaa ashtatal samroopata hoti haye.
ghana ekmatra uttal bahu-paridhiya haye jisake sabhi chehare vargakar hain.
orthogonal anuman.
ghana" mein chaar vishesh orthogonal anuman hotey hain, joe ack sheersh, kinaaron, chehare parr kendrit hotey hain aur isake sheersh aakriti key liye samanya hotey hain. pahala aur teesara aeye2 aur bee2 coxitor vimaanon key anuroop haye.
golakar tiling.
ghana koo ack golakar tiling key roop mein bhee darshaaya jaa sakata haye, aur ack stereographic prakshepan key madhyam seey vimaan parr prakshepit kiya jaa sakata haye. yeh prakshepan anuroop haye, konon koo sanrakshit kartaa haye lekin kshetra yaa lambai naheen. gole parr seedhi rekhaaon koo samtal parr golakar chaap key roop mein prakshepit kiya jaataa haye.
cartasian nirdeshank.
mool mein kendrit ack ghana key liye, akshon key samanantar kinaaron key saath aur 2 kii kinare kii lambai key saath, sheershon key cartasian nirdeshank hain
jabaki aantarik mein sabhi "i" key liye −1 <"x" i "<1 key saath sabhi bindu (" x "0", x "1", x "2) hotey hain.
tri-ayami sthaan mein sameekaran.
vishleshanatmak jyaamiti mein, kendra ("x" 0 ", y" 0 ", z" 0) key saath ack ghana kii satah aur "2a" kii kinare kii lambai sabhi binduon ("x", "y", "z") kaa sthaan haye jaise kii
ack ghana koo 3dee superalypsoid kaa seemit mamla bhee maanaa jaa sakata haye kyonki teenon pratipaadak anant taka pahunchate hain.
sootra.
kinare kii lambai key sootra _ 2 key ghana key liyeh
choonki ack ghana kii aayatan isake pakshon key sootra kii teesari shakti haye, teesari shaktiyon koo "cubes" kahaa jaataa haye, varg aur doosari shaktiyon key saath saadrishya dwara.
ack ghana mein ack diye gaye satah kshetra key saath ghana (aaytaakaar bakse) mein sabse badee matra hoti haye. saath hii, ack ghana mein samaan kull raikhik aakar (lambai + chaudaai + oonchaai) key saath ghanon mein sabse badee matra hoti haye.
antariksh mein bindu.
ack ghana key liye jisaki paridhi mein trijya "r" haye, aur usake tri-ayami sthaan mein ack diye gaye bindu key liye ghana key aathh sheershon seey doori "dee" key saath, hamaare paas haih
ghana koo doguna karein.
ghana koo doguna karna, yaa "delian samasya", pracheen yunani ganitvidon dwara kewal ack kampas aur seedhi dhaar kaa upayog karke diye gaye ghana key kinare kii lambai seey shuru karane aur mool ghana key dou baar aayatan key saath ack ghana key kinare kii lambai kaa nirmaan karane kii samasya thee. way iss samasya koo hull karane mein asamarth they, joe 1837 mein pier visale ney ise asambhav saabit curr diyaa kyonki 2 kaa ghana mool ack rachanaatmak sankhya naheen haye.
ack samaan rung aur samroopata.
ghana mein teen samaan rung hotey hain, jinhen pratyek sheersh key chaaron or vargakar cheharon key advitiya rangon dwara naamit kiya gayaa haih 111,112,123.
ghana mein samroopata key chaar varg hotey hain, jinhen sheersh-sankramankari rung dwara chehare koo darshaaya jaa sakata haye. uchchatam octahedral samroopata mein sabhi chehare ack hii rung key hotey hain. dihedral samroopata d4h ghana key thhos honey seey aatee haye, jisamen sabhi chhah paksh alag-alag rangon key hotey hain. prismatic upasamuchchay dee2dee mein pichhale key samaan rung haye aur dee2aich mein kull teen rangon key liye isake kinaaron key liye vaikalpik rung hain, jinhen vipareet pakshon dwara jodaa gayaa haye. pratyek samroopata roop mein ack alag waithoff prateek hotaa haye.
jyaamitiya sambandh.
ack ghana mein gyaarah jaal hotey hainh yaani, saat kinaaron koo katkar ack khokhale ghana koo samtal karane key gyaarah tareeke hain. ghana koo rangane key liye taaki kissy bhee dou aasann chehare kaa rung ack hii naa hoe, ack koo cumm seey cumm teen rangon kii aavashyakta hogi.
ghana tri-ayami euclidean sthaan kii ekmatra niyamit tiling kii koshika haye. yeh platonic thhos padarthon mein bhee advitiya haye, jisamen kinaaron kii ack samaan sankhya key saath chehare hotey hain aur isake parinamswarup, yeh usa samooh kaa ekmatra sadasya haye joe ack zonohedron haye (pratyek chehare mein bindu samroopata hoti haye).
ghana koo chhah samaan vargakar pyramids mein kaataa jaa sakata haye. yadi inn vargakar pyramids koo dusare ghana key chehare seey jodaa jaataa haye, tou ack sambhaajak dodecahedron praapt kiya jaataa haye (sambhaajak trikon key jode key saath sambhaajak chehare mein sanyukt).
dharamshastra mein.
cubes abrahamik dharmon mein dikhaai dete hain. makka mein kaaba ('ghana' key liye arabi) ack udaaharan haye. cubes bhee yahudi dharm mein tefilin key roop mein dikhaai dete hain, aur nae jerusalam koo nae vasiyatname mein ack cube key roop mein varnit kiya gayaa haye.
anya ayam.
chaar ayami euclidean sthaan mein ack ghana key anuroop kaa ack vishesh naam haye-ack tesseract yaa hypercube. adhik thheek seey, ack atee-ghana (yaa "aine"-ayami ghana yaa buss "aine"-ghana) "aine"-ayami euclidean sthaan mein ghana kaa anuroop haye aur ack tesseract crum-4 atee-ghana haye. ack atee-ghana koo "maap polytope" bhee kahaa jaataa haye.
nimn aayamon mein bhee ghana key anuroop hainh ayam 0 mein ack bindu, ack ayam mein ack rekha khand aur dou aayamon mein ack varg.
sambandhit polyheadra.
antipodal maanchitra dwara ghana kaa bhagfal ack prakshepya polyhedron, ardh-ghana utpann kartaa haye.
yadi mool ghana kii dhaar lambai 1 haye, tou isake dohare bahu-hedron (ack octahedron) kaa dhaar lambai sootra 5 haye.
samanya bahu-adhyetak key vibhinn vargon mein ghana ack vishesh mamla haih
ack ghana key sheershon koo chaar key dou samoohon mein baanta jaa sakata haye, pratyek ack niyamit tetrahedron banaata haye; adhik aam taur parr ise ack demicube key roop mein sandarbhit kiya jaataa haye. yeye donon ack saath ack niyamit yaugik, stella octangula banaate hain. donon kaa pratichhedan ack niyamit octahedrone banaata haye. ack niyamit tetrahedron kii samroopata ack ghana key anuroop hoti haye joe pratyek tetrahedron koo apane aap mein maanchitrit karati haye; ghana kii anya samroopata donon koo ack dusare key liye maanchitrit karati haye.
aise hii ack niyamit tetrahedron mein ghana kii matra hoti haye. shesh sthaan mein chaar barabar aniyamit chatushkoniya hotey hain, jinamen seey pratyek ghana kii matra key barabar hotaa haye.
sanshodhit ghana cuboctedron haye. yadi chhote konon koo kaat diyaa jaataa haye tou hamein chhah ashtakoniya chehare aur aathh trikoniya vaale ack bahu-paridhiya sootra milate hain. vishesh roop seey humm niyamit octagon (kataa huaa ghana) praapt curr sakate hain. donon konon aur kinaaron koo sahee matra mein katkar rombicuboctedron praapt kiya jaataa haye.
ack ghana koo ack dodecahedron mein utkeern kiya jaa sakata haye taaki ghana kaa pratyek sheersh dodecahedron kaa ack sheersh hoe aur pratyek kinara dodecahedron key cheharon mein seey ack kaa vikarn hoe; aise sabhi ghanon koo lene seey paanch ghanon key niyamit yaugik koo janm milata haye.
yadi ack ghana key dou vipareet konon koo seedhe unase judey teen sheershon kii gaharaai parr kaataa jaataa haye, tou ack aniyamit octahedrone praapt hotaa haye. inmein seey aathh aniyamit octahedron koo cuboctehedron praapt karane key liye ack niyamit octahedron key trikoniya cheharon seey jodaa jaa sakata haye.
ghana sthalvaigyaanik roop seey golakar bahu-ayami aur crum-3 sheersh aakritiyon key saath jhukaav kii ack shrinkhala seey sambandhit haye.
cuboctehdron ghana aur niyamit octahedron seey sambandhit ack samaan polyheader key parivaar mein seey ack haye.
ghana niyamit jhukaav key anukram key ack hisse key roop mein sthalvaigyaanik roop seey sambandhit haye, joe atee-javic tala mein failata haih {4, p}, p = 3,4,5..
dihedral samroopata, diach4 key saath, ghana samroop bahu-ganitiya aur jhukaav 4.2n.2n kii ack shrinkhala mein sthalvaigyaanik roop seey sambandhit haye, joe atee-javic tala mein vistaarit haih
inn sabhi aakritiyon mein octahedral samroopata haye.
ghana sambhaajak bahu-parichhed aur ["n", 3] coxitor samooh samroopata key saath jhukaav key anukram kaa ack hissa haye. ghana koo ack sambhaajak shatkon key roop mein dekhaa jaa sakata haye jahan sambhaajak varg hotey hain.
ghana ack vargakar prism haih
ack trikoniya trapezohedron key roop mein, ghana shatkon dihedral samroopata parivaar seey sambandhit haye.
ack samaan shahad aur polychora mein.
yeh 28 uttal samaan shahad key 9 kaa ack tatva haih 
yeh paanch chaar ayami samaan polychora kaa ack tatva bhee haih 
cubic graph.
ghana kaa kankal (sheersh aur kinare) 8 sheershon aur 12 kinaaron key saath ack graph banaata haye, jise ghana graph kahaa jaataa haye. yeh hypercube graph kaa ack vishesh mamla haye. yeh 5 platonic graphon mein seey ack haye, pratyek apane platonic thhos kaa ack kankal haye.
ack vistaar tri-ayami "key"-arrie hamming graph haye, joe "key" = 2 key liye ghana graph haye. iss prakaar key graph computer mein samanantar prasanskaran key siddhant mein hotey hain.