
kataa huaa octahedron

jyaamiti mein, kataa huaa octahedron archimedian thhos haye joe ack niyamit octahedron seey chhah pyramids koo hataakar utpann hotaa haye, octahedron key sheershon mein seey pratyek parr ack. kataa huaa octahedrone mein 14 chehare (8 niyamit shatkon aur 6 varg), 36 kinare aur 24 sheersh hain. choonki isake pratyek chehare mein bindu samroopata hoti haye, isaliye kataa huaa octahedron 6-zonohedron hotaa haye. yeh swarn-stambh bahu-hedron bhee haye, jisamen varg aur shatkon chehare hain. ghana kii tarah, yeh ack permutohedron key roop mein tri-ayami sthaan koo tesslet (yaa "paik") curr sakata haye.
kataaya gayaa octahedrone buckminster fuller dwara "meekan" kahaa jaataa thaa.
iska dohra bahu-hedron tetrakis hexahedrone haye. yadi mool kataa huaa octahedrone ikai kinare kii lambai rakhta haye, tou isake dohare tetrakis hexahedrone kii kinare kii lambai aur lambai hoti haye.
nirmaan.
ack kataa huaa octahedrone ack niyamit octahedrone seey banaaya jaataa haye jisaki taraf kii lambai 3 "aeye" hoti haye, jisamen chhah daahine vargakar pyramid koo hataaya jaataa haye, pratyek bindu seey ack. inn pyramids mein sambahu trikon banaane key liye aadhar paksh kii lambai ("aeye") aur paarshv paksh kii lambai ("ee") donon hoti hain. taba aadhar kshetra "a" 2 haye. dhyaan dein kii yeh aakar bilkul aadhe octahedrone yaa johnson solid jey1 key samaan haye.
vargakar pyramid key gunon seey, abb humm pyramid kii tirchhi oonchaai, "s", aur oonchaai, "h", paa sakate hainh
pyramid kaa aayatan, "v", iss prakaar diyaa gayaa haih
kyonki chhah pyramids koo katkar hataa diyaa jaataa haye, isaliye kull "a" 3 kii matra khou jaati haye.
orthogonal anuman.
kataa huaa octahedrone mein paanch vishesh orthogonal prakshepan hotey hain, joe ack sheersh parr, dou prakaar key kinaaron parr kendrit hotey hain, aur dou prakaar key chehare hotey hainh shatkon aur varg. antim dou bee2 aur aeye2 coxitor vimaanon key anuroop hain.
golakar tiling.
kataa huaa octahedrone 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.
nirdeshank.
(0, ±1, ±2) key sabhi kramparivartan mool mein kendrit a = ±2 kii lambai key ack katey hue octahedron key sheershon key cartasian nirdeshank hain. iss prakaar sheersh 12 ayaton key koney bhee hain jinake lambe kinare nirdeshank akshon key samanantar hain.
kinare key vactor mein cartasian nirdeshank aur inke kramparivartan hotey hain. 6 vargakar cheharon key chehare key samanya (kinaaron key samanya cross utpaad joe ack samanya sheersh saajha karate hain) hain, aur. 8 shatkon cheharon key chehare samanya hain. dou chehare key samanya key jode key beach bindu utpaad aasann cheharon key beach dihedral konn kii cosine haye, yaa tou-yaa-. dwi-parichal konn lagbhag 1.910633 radian (109.471 °) haye joe dou shatkonon dwara saajha kiye gaye kinaaron parr yaa 2.186276 radian (125.263 °) ack shatkon aur ack varg dwara saajha kiye gaye kinaaron parr haye.
vichhedan.
kataa huaa octahedron koo ack kendriya octahedron mein vichhedit kiya jaa sakata haye, joe pratyek chehare parr 8 trikoniya kapol seey ghiraa huaa haye, aur sheershon key oopar 6 vargakar pyramid hain.
kendriya octahedrone aur 2 yaa 4 trikoniya kapol koo hataakar dihedral aur tetrahedral samroopata key saath dou stevert toroid banate hainh
permutohedron.
kataa huaa octahedrone koo chaar aayamon mein aur bhee adhik samamit nirdeshank dwara darshaaya jaa sakata haih (1,2,3,4) key sabhi kramparivartan tri-ayami upasthaan mein ack kataa huaa octahedrone key sheersh banaate hain. isaliye, kataa huaa octahedrone crum 4 kaa permutohedron haih pratyek sheersh (1,2,3,4) key kramparivartan seey mell khaata haye aur pratyek kinara dou tatvon kii ack jodee key anusaar adla-badali kaa pratinidhitva kartaa haye.
kshetrafal aur matra.
satah kshetra "s" aur ack kataa huaa octahedrone kii aayatan "v" joe kinare kii lambai "a" haye, way hainh
ack samaan rung.
tetrahedral samroopata aur octahedral samroopata key saath dou samaan rung hain, aur "kataa huaa trikoniya antiprism" key roop mein dihedral samroopata key saath dou 2-samaan rung hain. pratyek key liye nirmaan naam diye gaye hain. unake kanave polyhedrone sanketan koshthak mein diye gaye hain.
rasayan vigyaan.
kataa huaa octahedrone faujacite chrystal kii sanrachana mein maujood haye.
detta chhipaana.
kataai octahedron (vaastav mein, saamaanyikrit kataai octahedron) punaravritti coding key sanyojan mein quantisation index modulan (qim) key truti vishleshan mein dikhaai detaa haye.
sambandhit polyheadra.
kataa huaa octahedron ghana aur niyamit octahedron seey sambandhit ack samaan polyheader key parivaar mein seey ack haye.
yeh tetrahedron parivaar key sarvavyaapi key roop mein bhee maujood haih
samroopata utparivartan.
yeh polyhedrone sheersh aakriti (4.6.2 "pee") aur coxter-dyankin aarekh key saath samaan pattern key anukram kaa ack sadasya haye. pee" <6 key liye, anukram key sadasya sarvavyaapi bahu-parichhed (zonohedra) hain, jinhen neeche golakar jhukaav key roop mein dikhaaya gayaa haye. pee"> 6 key liye, way atee-dhruviya tala key jhukaav hain, joe katey hue tribhujakar tiling seey shuru hotey hain.
kataa huaa octahedron sheershik roop seey samaan polyheader aur sheersh aakritiyon "aine" key saath jhukaav key anukram key ack hisse key roop mein sambandhit haye.
kataa huaa octahedron samroop bahu-parichhed key anukram key ack bhaag key roop mein sthalvaigyaanik roop seey sambandhit haye aur sheersh aakritiyon key saath jhukaav 4.2 "aine". 2 "aine", atee-javic tala mein vistaarit haih
sambandhit polytope.
kataa huaa octahedrone" (bitrancated cube), bitrancated hypercubes key anukram mein pahala haih
ack atee-tala dwara ack tesseract koo kaatna sambhav haye taaki iska kataa huaa cross-section ack kataa huaa octahedron hoe.
tessellation.
kataa huaa octahedrone teen alag-alag uttal samaan honeycomb (antariksh-bharane vaale tessellation) mein maujood haih
koshika-sanchari bitrancated cubic honeycomb koo shareer-kendrit cubic jaali key voronoi tessellation key roop mein bhee dekhaa jaa sakata haye. kataa huaa octahedron paanch tri-ayami praathamik samanantar mein seey ack haye.
kataa huaa octahedral graph.
graph siddhant key ganitiya kshetra mein, ack kataa huaa octahedral graph, kaataa huaa octahedron key sheershon aur kinaaron kaa graph haye. isamen 24 sheersh aur 36 kinare hain, aur yeh ack ghana archimedian graph haye. isamen pustak kii motai 3 aur kataar sankhya 2 haye.
hamiltonian ghana graph key roop mein, ise kaee tarikon seey ell. see. aff. sanketan dwara darshaaya jaa sakata haih [3, −7,7, −3] 6, [5, −11,11,7,5, −5, −7, −11,11, −5, −7,7] 2, aur [−11,5, −3, −7, −9,3, −5,5, −3,9,7,3, −5,11, −3,7, −7, −9,9,7, −5,7, −5,7, −3, −7, −7, −7, −7, −7, −7, −7, −7, −7, −7, −7, −7, −7, −7, −7, −3].

