
staar polyhedron

jyamithiyil, oru nakshatra polyhedron oru polyhedrone, athinu nakshatram polulla drishya gunanilavaaram nalkunna nonkonveksittiyude aavarthichulla gunamundu.
pothuvaayi rund tharam staar polyhedronukalundu
staar polyhedrayude ganithashaasthra padanangal saadhaaranayaayi saadhaarana, ekeekritha polyheadra allengil ekeekritha polyhedrayude erattakalumaayi bandhappettirikkunnu. eee nakshathrangalellam svayam verthirikkunna tharathilullavayaanu.
svayam-verthirikkunna nakshatra polyheadra.
saadhaarana staar polyheadra.
saadhaarana nakshatramaaya polyheadra svayam verthirikkunna polyhedrayaanu. avaykku onnukil svayam-verthirikkunna mukhangalo allengil svayam-verthirikkunna sheershaka roopangalo undayirikkaam.
keppler-poinsot polyheadra ennariyappedunna naalu saadhaarana staar polyhedrakalundu. schlufly chihnam {"p", "q"} "p" vashangalulla mukhangaleyum "q" vashangalulla sheershakachithrangaleyum soochippikkunnu. avayil randennam pentagramic mukhangalum randennam pentegraamik vertex chithrangalumaanu.
<eee chithrangal oro roopavum kaanikkunnu, aaa mukhatthinte drishyamaaya bhagam kaanikkunnathin orotta mukham manja niratthilaanu.
eathenkilum nakshathratthinte bahubhujathin ananthamaaya ennam saadhaarana nakshatrangalaaya deehedra hoshaheadra (2, "p/q"), {"p/q", 2) ennivayum undu. euclidean bahiraakaashath avaa degenerate cheyyumbol, avaye golaakrithiyil nondeejanarettu roopathil thirichariyaan kazhiyum.
unifom unifom eratta nakshatra polyheadra.
rund ananthamaaya srenikalaaya prisangaludeyum aantiprisangaludeyum erattakalum avayude erattakalum ulppede niravadhi ekeekritha nakshatra polyhedrakalundu.
unifom, duval unifom staar polyheadra ennivayum svayam-verthirikkunna polyhedrayaanu. avaykku onnukil svayam-verthirikkunna mukhangalo allengil svayam-verthirikkunna sheershaka roopangalo allengil randum undakam.
ekeekritha nakshatramaaya polyhedraykku sthiramaaya mukhangalo saadhaarana nakshatra bahubhuja mukhangalo undu. eratta unifom staar polyhedraykku saadhaarana mukhangalo saadhaarana staar pooligoon vertex chithrangalo undu.
stelleshanukalum vashangalum.
mukalilulla roopangalkkappuram, svayam-verthirikkunna (nakshatram) polyhedrayude paridhiyillaattha klaasukalundu.
convex polyhedrayude stelleshanukalum avayude duvalukalum, duval polyhedrayude vashangalumaan rund pradhana klaasukal.
udaaharanathinu, icosahedroninte (chithreekaricha) poornnamaaya steleshane 20 samana mukhangal ulkkollunna svayam-verthirikkunna polyhedronaayi vyaakhyaanikkaam, oronnum (9/4) murivulla bahubhujamaan. manja niratthil varacha oru mukhamulla eee polyhedroninte oru chithram chuvadeyundu.
staar polytopukal.
ethra alavukalilum samanamaaya svayam-verthirikkunna polytoppine staar polytope ennu vilikkunnu.
oru saadhaarana polytope {"p", "q", "r"..., s", "t"} ennathu oru staar polytoppaanu, athinte vasham {"p", "q" aanenkil..."s" "} allengil athinte sheershakam {" "q", "r"..., s", "t"} oru staar polytoppaanu.
naalu alavukalil, 10 saadhaarana nakshatra polycorakale schlafly-hess polycora ennu vilikkunnu. saadhaarana nakshatra polyhedraykku samaanamaayi, eee 10 ennavum anchu saadhaarana platonic kharapadaarthangalil onno allengil naalu saadhaarana nakshatramaaya keppler-poinsot polyhedrayil onno aaya vashangalal nirmmithamaan.
udaaharanathinu, orthogonalaayi 3-space aayi project cheythirikkunna grettu grand stelletted 120-sell ithupole kaanapedunnu
4-ll kooduthal alavukalulla staar polytopukal illa.
staar-domaine staar polyheadra.
oru interior pooyintil ninnu muzhuvan interior kaanaan kazhiyunna vidhathil svayam kadakkaatha oru polyhedron oru staar domaininte udaaharanamaanu. svayam verthirikkunna niravadhi nakshatra polyhedrayude drishyamaaya baahya bhagangal nakshatra domainukalude athirthikal roopappeduthunnu.
ennaal avayude roopam samaanamaanengilum, amoorthamaaya polyheadra enna nilayil iva vyathyastha gadanakalaanu. udaaharanathinu, cheria stelletted dodecahedroninu 12 pentagraam mukhangalundu, ennaal anubandha nakshatra domaine 60 isosilus trikona mukhangalundu, athinanusarichu vyathyastha ennam konukalum arikukalum undu.
polyhedral staar domainukal vividha tharatthilulla vaasthuvidyakalil prathyakshappedunnu, saadhaaranayaayi mathaparamaya swabhaavam. udaaharanathinu, pala barok pallikalilum avaye palli nirmmicha maarppaappayude pratheekangalayi kaanapedunnu, hangarian pallikalilum mattu mathaparamaya kettidangalilum. eee nakshathrangal alankaaravasthukkalaayum upayogikkaam. moravian nakshathrangal rund aavasyangalkkum upayogikkunnu, avaa vividha roopangalil nirmmikkaan kazhiyum.