
billinsky dodecahedrone

jyaamiti mein, billinsky dodecahedron baarah sarvangsam sunhare samasthaanik vaale ack uttal bahusthaanik haye. isaki ack hii topology haye lekin chehare-sanchari samasthaanik dodecahedron kii tulanaa mein ack alag jyaamiti haye. yeh ack samanantar haye.
itihas.
yeh aakar johnn lodge kauli kii ack pustak mein dikhaai detaa haye, jise dodecarhambus key roop mein label kiya gayaa haye. iska naam stanko billinsky key naam parr rakhaa gayaa haye, jinhone ise phir seey khoja. billinsky ney khud ise doosari tarah kaa rombic dodecahedrone kahaa. billinsky kii khoj ney avgraph fedorov key uttal bahu-paridhiya key vargeekaran mein ack saal purani chook koo sarvangsam samang chehare key saath thheek kiya.
paribhasha aur guna.
paribhasha.
billinsky dodecahedrone baarah sarvangsam sunhare romby koo ack saath chipkakar banaaya jaataa haye. yeye rombi hain jinake vikarn swarn anupaat mein hainh
parinami polyhedron kaa graph samroop haye, lekin chehare alag-alag unmukh hainh vipareet romby kii ack jodee key lambe aur chhote vikarn vipareet hotey hain, apekshaakrit rombic dodecahedron mein sambandhit romby key abhivinyas key liye.
samroopata.
isake ulat honey key kaaran, bilinsky dodecahedron mein samroopata kaa ack nimn crum hotaa haye; iska samroopata samooh ack aaytaakaar ghana kaa hotaa haih crum kaa yeh octahedral samroopata kaa ack upsamooh haye; isake tatva hainh teen gunaa samroopata aksh, teen samamitata tala (joe iss thhos key akshiya tala bhee hain), aur vyutkram samroopata kaa ack kendra. billinsky dodecahedrone kaa ghoornan samooh crum kaa haye 
sheersh.
sambhoji dodecahedrone kii tarah, billinsky dodecahedrone mein degree key aathh sheersh aur degree key chhah sheersh hotey hain. isake urdhvaadhar aksh parr dou sheersh hotey hain, aur pratyek akshiya tala parr chaar sheersh hotey hain. lekin ulatane key kaaran, isake gair-apical sheersh dou varg (laal aur haraa) aur ack aayat (neela) banaate hain, aur isake chaudah sheersh sabhi mein chaar alag-alag prakaar key hotey hainh
chehare.
ack sunhare samasthaanik key poorak aantarik konn hainh
billinsky dodecahedrone key chehare baarah sarvangsam sunhare romby hain; lekin ulatafer key kaaran, way teen alag-alag prakaar key hainh
kinaaron.
bilinsky dodecahedrone key kinaaron kii lambai samaan hoti haye; lekin ulatane key kaaran, way chaar alag-alag prakaar key hotey hainh
cartasian nirdeshank, lambai.
billinsky dodecahedrone key sheershon kii motai mein cartasian nirdeshank hoe sakate hainh
swarn anupaat kahaan haye?
iss aakar key bilinsky dodecahedrone mein haih
polyheader key parivaaron mein.
billinsky dodecahedron ack samanantar haye; iss prakaar yeh ack antariksh bharane vaalaa polyhedron aur ack zonohedron bhee haye.
sambhoji dodecahedrone seey sambandh.
ack kagaj mein, aich. aiss. aim. coxter ney daavaa kiya kii bilinsky dodecahedron koo rombic dodecahedron seey ack affine parivartan dwara praapt kiya jaa sakata haye, lekin yeh galat haye. key liyeh
samasthaanik dodecahedrone menh pratyek lambe shareer vikarn (i.ee. vipareet degree-sheershon parr padaa huaa) chaar cheharon key chhote vikarnon key samanantar haye.
billinsky dodecahedrone menh sabse lamba shareer vikarn (i.ee. vipareet kaale degree-sheershon parr padaa huaa) dou cheharon key chhote vikarnon key samanantar haye, aur dou anya cheharon key lambe vikarnon key liye; chhote shareer vikarn (i.ee. vipareet neele rung key sheershon parr sthit) kissy bhee chehare key vikarn key samanantar naheen hotey hain.
sambhoji dodecahedron key kissy bhee affine parivartan menh pratyek lambe shareer vikarn (i.ee. vipareet degree-sheershon parr padaa huaa) chaar chehare key vikarn key samanantar rahata haye, aur yeye samaan (naee) lambai key baney rahate hain.
sunhare samroop chehare key saath zonohedra.
billinsky dodecahedron koo samaantar kinaaron key saath dou kshetron yaa duss aur aathh sunhare samaantar kinaaron key belt koo hataakar yaa dhwast karke samaantar trichontahedron (ack aur samaantar samaantar sunhare chehare vaale ack aur samaantar samaantar samaantar samaantar chehare vaale ack aur samaantar samaantar samaantar samaantar mukh vaale samaantar samaantar samaantar samaantar mukh vaale samaantar samaantar samaantar samaantar mukh vaale samaantar samaantar samaantar samaantar samaantar samaantar mukh vaale samaantar samaantar samaantar samaantar samaantar samaantar samaantar samaantar samaantar samaantar samaantar samaantar samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak samantarak summ duss cheharon key kewal ack kshetra koo hataane seey sambhoji icosahedron utpann hotaa haye. duss, aathh aur chhah cheharon key teen kshetron koo hataana ack sunhara rombohedron paida kartaa haye. iss prakaar billinsky dodecahedron seey chhah cheharon key kshetra koo hataakar ack sunhara rombohedron utpann hotaa haye. billinsky dodecahedron koo chaar sunhare romboheader mein vichhedit kiya jaa sakata haye, pratyek prakaar key dou.
sunhare sambhaajak cheharon vaale samasthaanik key sheershon kii ganana dou seey chhah utpann karane vaale kinare key vactors key raikhik sanyojan dwara kii jaa sakati haye, jisamen gunank yaa ack belt kaa arth haye ack belt joe dishaatmak vactor kaa pratinidhitva kartaa haye, aur jisamen samaan lambai key saath saha-samanantar kinare hotey hain. billinsky dodecahedron mein chhah saha-samanantar kinaaron key chaar belt hain.
yeye zonohedra hypercubes key prakshepan lifafe hain, joe-ayami prakshepan aadhar key saath, swarn anupaat () key saath hain. vishisht aadhar key liye haih
aadhar key liye-th collum key saath samaan haye. - th aur-th collum key liye hataa diye jaate hain.

