
kram-4 ashtakoniy farshi

bhoomitimadhye, kram-4 ashtakoniy tyle hii hyperbolic pratalachi niyamit tyle aahe. tyat 'schlafly' heey chinh {8,4} aahe. tyachya checkerboardchya rangala ashtakoniy tyle aanee aar {8,8} chey schlafly chinh mhatale jaau shakate.
eksaman bandhkame.
yaa farshanchya chaar eksaman rachana aahet, tyapaiki teen [8,8] caleidoscopemadhun aarshane kadhoon takalyamule bandhalya aahet. 2 aanee 4 kramankanmadhil aarsa kadhoon takalyas, [8,8,1 +], [(8,8,4)], (* 884) samamiti dete. done aarse [8,4 *] mhanoon kadhoon takalyas, bakiche aarse * 4444 samamitiche hotat.
samamiti.
hii farshi niyamit shatakonichya kadaa mhanoon bhetnanya 8 aarshanchya hyperbolic caleidoscope pratinidhitva karate. orbifold sanketanadvare yaa samamitila (* 22222222) kinwa (* 28) 8 kram-2 aarshanchya chhedanbindusaha mhanatat. coxitormadhye sanketan [8 *, 4] mhanoon darshavile jaau shakate, [8,4] samamitimadhye teenpaiki done aarse (ashtabhuj kendratoon jaanare) kadhoon takale jaau shakatat. ashtakoniy moolbhut kshetrachya 2 shirobindunmadhun dvibhajak aarsa jodane heey trapezohedral * 4422 samamiti paribhashit karate. shirobindunmadhun 4 dwibhajit aarse jodane * 444 samamiti paribhashit karate. kathavarun 4 dvibhajak aarse jodalyane * 4222 samamiti paribhashit hote. serve 8 dvibhajak jodalyane purn * 842 samamiti hote.
caleidoscopic kshetrankade dwirangi ashtakoniy tyle mhanoon pahile jaau shakate, jeey moolbhut kshetrachya aarshatil pratimanche pratinidhitva karate. haah rung aar {8,8} yaa eksaman tileche pratinidhitva karato, eka ardh-rekheey tyle aanee tyala ashtakoniy tyle mhatale jaau shakate.
sambandhit bahubhuj aanee farshi.
hii farshi ashtakoniy chehyansah niyamit jhukanyachya kramacha eka bhag mhanoon sthanikdrushtya sambandhit aahe, jyachi suruvat ashtakoniy farshipasoon hote, schlafly chinh {8, aine} aanee coxter aakrutisah, anantakade jaat aahe.
hii farshi niyamit bahupadi aanee prati shirobindu chaar faces asalelya jhukanyacha eka bhag mhanoon dekhil topologicaldrushtya sambandhit aahe, jyachi suruvat octahedronpasoon hote, schlafly chinh {n, 4} saha aanee coxter aakruti, n anantakade jaat aahe.