Polytope of Type {10,85}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,85}*1700
if this polytope has a name.
Group : SmallGroup(1700,43)
Rank : 3
Schlafli Type : {10,85}
Number of vertices, edges, etc : 10, 425, 85
Order of s₀s₁s₂ : 170
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,85}*340
   17-fold quotients : {10,5}*100
   25-fold quotients : {2,17}*68
   85-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 18, 69)( 19, 70)( 20, 71)( 21, 72)( 22, 73)( 23, 74)( 24, 75)( 25, 76)
( 26, 77)( 27, 78)( 28, 79)( 29, 80)( 30, 81)( 31, 82)( 32, 83)( 33, 84)
( 34, 85)( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)( 41, 58)
( 42, 59)( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)( 49, 66)
( 50, 67)( 51, 68)(103,154)(104,155)(105,156)(106,157)(107,158)(108,159)
(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)
(117,168)(118,169)(119,170)(120,137)(121,138)(122,139)(123,140)(124,141)
(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)
(133,150)(134,151)(135,152)(136,153)(188,239)(189,240)(190,241)(191,242)
(192,243)(193,244)(194,245)(195,246)(196,247)(197,248)(198,249)(199,250)
(200,251)(201,252)(202,253)(203,254)(204,255)(205,222)(206,223)(207,224)
(208,225)(209,226)(210,227)(211,228)(212,229)(213,230)(214,231)(215,232)
(216,233)(217,234)(218,235)(219,236)(220,237)(221,238)(273,324)(274,325)
(275,326)(276,327)(277,328)(278,329)(279,330)(280,331)(281,332)(282,333)
(283,334)(284,335)(285,336)(286,337)(287,338)(288,339)(289,340)(290,307)
(291,308)(292,309)(293,310)(294,311)(295,312)(296,313)(297,314)(298,315)
(299,316)(300,317)(301,318)(302,319)(303,320)(304,321)(305,322)(306,323)
(358,409)(359,410)(360,411)(361,412)(362,413)(363,414)(364,415)(365,416)
(366,417)(367,418)(368,419)(369,420)(370,421)(371,422)(372,423)(373,424)
(374,425)(375,392)(376,393)(377,394)(378,395)(379,396)(380,397)(381,398)
(382,399)(383,400)(384,401)(385,402)(386,403)(387,404)(388,405)(389,406)
(390,407)(391,408);;
s1 := (  1, 18)(  2, 34)(  3, 33)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 28)
(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)
( 17, 19)( 35, 69)( 36, 85)( 37, 84)( 38, 83)( 39, 82)( 40, 81)( 41, 80)
( 42, 79)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 74)( 48, 73)( 49, 72)
( 50, 71)( 51, 70)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)
( 59, 62)( 60, 61)( 86,358)( 87,374)( 88,373)( 89,372)( 90,371)( 91,370)
( 92,369)( 93,368)( 94,367)( 95,366)( 96,365)( 97,364)( 98,363)( 99,362)
(100,361)(101,360)(102,359)(103,341)(104,357)(105,356)(106,355)(107,354)
(108,353)(109,352)(110,351)(111,350)(112,349)(113,348)(114,347)(115,346)
(116,345)(117,344)(118,343)(119,342)(120,409)(121,425)(122,424)(123,423)
(124,422)(125,421)(126,420)(127,419)(128,418)(129,417)(130,416)(131,415)
(132,414)(133,413)(134,412)(135,411)(136,410)(137,392)(138,408)(139,407)
(140,406)(141,405)(142,404)(143,403)(144,402)(145,401)(146,400)(147,399)
(148,398)(149,397)(150,396)(151,395)(152,394)(153,393)(154,375)(155,391)
(156,390)(157,389)(158,388)(159,387)(160,386)(161,385)(162,384)(163,383)
(164,382)(165,381)(166,380)(167,379)(168,378)(169,377)(170,376)(171,273)
(172,289)(173,288)(174,287)(175,286)(176,285)(177,284)(178,283)(179,282)
(180,281)(181,280)(182,279)(183,278)(184,277)(185,276)(186,275)(187,274)
(188,256)(189,272)(190,271)(191,270)(192,269)(193,268)(194,267)(195,266)
(196,265)(197,264)(198,263)(199,262)(200,261)(201,260)(202,259)(203,258)
(204,257)(205,324)(206,340)(207,339)(208,338)(209,337)(210,336)(211,335)
(212,334)(213,333)(214,332)(215,331)(216,330)(217,329)(218,328)(219,327)
(220,326)(221,325)(222,307)(223,323)(224,322)(225,321)(226,320)(227,319)
(228,318)(229,317)(230,316)(231,315)(232,314)(233,313)(234,312)(235,311)
(236,310)(237,309)(238,308)(239,290)(240,306)(241,305)(242,304)(243,303)
(244,302)(245,301)(246,300)(247,299)(248,298)(249,297)(250,296)(251,295)
(252,294)(253,293)(254,292)(255,291);;
s2 := (  1, 87)(  2, 86)(  3,102)(  4,101)(  5,100)(  6, 99)(  7, 98)(  8, 97)
(  9, 96)( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)
( 17, 88)( 18,155)( 19,154)( 20,170)( 21,169)( 22,168)( 23,167)( 24,166)
( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)( 32,158)
( 33,157)( 34,156)( 35,138)( 36,137)( 37,153)( 38,152)( 39,151)( 40,150)
( 41,149)( 42,148)( 43,147)( 44,146)( 45,145)( 46,144)( 47,143)( 48,142)
( 49,141)( 50,140)( 51,139)( 52,121)( 53,120)( 54,136)( 55,135)( 56,134)
( 57,133)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)( 64,126)
( 65,125)( 66,124)( 67,123)( 68,122)( 69,104)( 70,103)( 71,119)( 72,118)
( 73,117)( 74,116)( 75,115)( 76,114)( 77,113)( 78,112)( 79,111)( 80,110)
( 81,109)( 82,108)( 83,107)( 84,106)( 85,105)(171,342)(172,341)(173,357)
(174,356)(175,355)(176,354)(177,353)(178,352)(179,351)(180,350)(181,349)
(182,348)(183,347)(184,346)(185,345)(186,344)(187,343)(188,410)(189,409)
(190,425)(191,424)(192,423)(193,422)(194,421)(195,420)(196,419)(197,418)
(198,417)(199,416)(200,415)(201,414)(202,413)(203,412)(204,411)(205,393)
(206,392)(207,408)(208,407)(209,406)(210,405)(211,404)(212,403)(213,402)
(214,401)(215,400)(216,399)(217,398)(218,397)(219,396)(220,395)(221,394)
(222,376)(223,375)(224,391)(225,390)(226,389)(227,388)(228,387)(229,386)
(230,385)(231,384)(232,383)(233,382)(234,381)(235,380)(236,379)(237,378)
(238,377)(239,359)(240,358)(241,374)(242,373)(243,372)(244,371)(245,370)
(246,369)(247,368)(248,367)(249,366)(250,365)(251,364)(252,363)(253,362)
(254,361)(255,360)(256,257)(258,272)(259,271)(260,270)(261,269)(262,268)
(263,267)(264,266)(273,325)(274,324)(275,340)(276,339)(277,338)(278,337)
(279,336)(280,335)(281,334)(282,333)(283,332)(284,331)(285,330)(286,329)
(287,328)(288,327)(289,326)(290,308)(291,307)(292,323)(293,322)(294,321)
(295,320)(296,319)(297,318)(298,317)(299,316)(300,315)(301,314)(302,313)
(303,312)(304,311)(305,310)(306,309);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(425)!( 18, 69)( 19, 70)( 20, 71)( 21, 72)( 22, 73)( 23, 74)( 24, 75)
( 25, 76)( 26, 77)( 27, 78)( 28, 79)( 29, 80)( 30, 81)( 31, 82)( 32, 83)
( 33, 84)( 34, 85)( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)
( 41, 58)( 42, 59)( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)
( 49, 66)( 50, 67)( 51, 68)(103,154)(104,155)(105,156)(106,157)(107,158)
(108,159)(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)
(116,167)(117,168)(118,169)(119,170)(120,137)(121,138)(122,139)(123,140)
(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)
(132,149)(133,150)(134,151)(135,152)(136,153)(188,239)(189,240)(190,241)
(191,242)(192,243)(193,244)(194,245)(195,246)(196,247)(197,248)(198,249)
(199,250)(200,251)(201,252)(202,253)(203,254)(204,255)(205,222)(206,223)
(207,224)(208,225)(209,226)(210,227)(211,228)(212,229)(213,230)(214,231)
(215,232)(216,233)(217,234)(218,235)(219,236)(220,237)(221,238)(273,324)
(274,325)(275,326)(276,327)(277,328)(278,329)(279,330)(280,331)(281,332)
(282,333)(283,334)(284,335)(285,336)(286,337)(287,338)(288,339)(289,340)
(290,307)(291,308)(292,309)(293,310)(294,311)(295,312)(296,313)(297,314)
(298,315)(299,316)(300,317)(301,318)(302,319)(303,320)(304,321)(305,322)
(306,323)(358,409)(359,410)(360,411)(361,412)(362,413)(363,414)(364,415)
(365,416)(366,417)(367,418)(368,419)(369,420)(370,421)(371,422)(372,423)
(373,424)(374,425)(375,392)(376,393)(377,394)(378,395)(379,396)(380,397)
(381,398)(382,399)(383,400)(384,401)(385,402)(386,403)(387,404)(388,405)
(389,406)(390,407)(391,408);
s1 := Sym(425)!(  1, 18)(  2, 34)(  3, 33)(  4, 32)(  5, 31)(  6, 30)(  7, 29)
(  8, 28)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 35, 69)( 36, 85)( 37, 84)( 38, 83)( 39, 82)( 40, 81)
( 41, 80)( 42, 79)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 74)( 48, 73)
( 49, 72)( 50, 71)( 51, 70)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)
( 58, 63)( 59, 62)( 60, 61)( 86,358)( 87,374)( 88,373)( 89,372)( 90,371)
( 91,370)( 92,369)( 93,368)( 94,367)( 95,366)( 96,365)( 97,364)( 98,363)
( 99,362)(100,361)(101,360)(102,359)(103,341)(104,357)(105,356)(106,355)
(107,354)(108,353)(109,352)(110,351)(111,350)(112,349)(113,348)(114,347)
(115,346)(116,345)(117,344)(118,343)(119,342)(120,409)(121,425)(122,424)
(123,423)(124,422)(125,421)(126,420)(127,419)(128,418)(129,417)(130,416)
(131,415)(132,414)(133,413)(134,412)(135,411)(136,410)(137,392)(138,408)
(139,407)(140,406)(141,405)(142,404)(143,403)(144,402)(145,401)(146,400)
(147,399)(148,398)(149,397)(150,396)(151,395)(152,394)(153,393)(154,375)
(155,391)(156,390)(157,389)(158,388)(159,387)(160,386)(161,385)(162,384)
(163,383)(164,382)(165,381)(166,380)(167,379)(168,378)(169,377)(170,376)
(171,273)(172,289)(173,288)(174,287)(175,286)(176,285)(177,284)(178,283)
(179,282)(180,281)(181,280)(182,279)(183,278)(184,277)(185,276)(186,275)
(187,274)(188,256)(189,272)(190,271)(191,270)(192,269)(193,268)(194,267)
(195,266)(196,265)(197,264)(198,263)(199,262)(200,261)(201,260)(202,259)
(203,258)(204,257)(205,324)(206,340)(207,339)(208,338)(209,337)(210,336)
(211,335)(212,334)(213,333)(214,332)(215,331)(216,330)(217,329)(218,328)
(219,327)(220,326)(221,325)(222,307)(223,323)(224,322)(225,321)(226,320)
(227,319)(228,318)(229,317)(230,316)(231,315)(232,314)(233,313)(234,312)
(235,311)(236,310)(237,309)(238,308)(239,290)(240,306)(241,305)(242,304)
(243,303)(244,302)(245,301)(246,300)(247,299)(248,298)(249,297)(250,296)
(251,295)(252,294)(253,293)(254,292)(255,291);
s2 := Sym(425)!(  1, 87)(  2, 86)(  3,102)(  4,101)(  5,100)(  6, 99)(  7, 98)
(  8, 97)(  9, 96)( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 90)
( 16, 89)( 17, 88)( 18,155)( 19,154)( 20,170)( 21,169)( 22,168)( 23,167)
( 24,166)( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)
( 32,158)( 33,157)( 34,156)( 35,138)( 36,137)( 37,153)( 38,152)( 39,151)
( 40,150)( 41,149)( 42,148)( 43,147)( 44,146)( 45,145)( 46,144)( 47,143)
( 48,142)( 49,141)( 50,140)( 51,139)( 52,121)( 53,120)( 54,136)( 55,135)
( 56,134)( 57,133)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)
( 64,126)( 65,125)( 66,124)( 67,123)( 68,122)( 69,104)( 70,103)( 71,119)
( 72,118)( 73,117)( 74,116)( 75,115)( 76,114)( 77,113)( 78,112)( 79,111)
( 80,110)( 81,109)( 82,108)( 83,107)( 84,106)( 85,105)(171,342)(172,341)
(173,357)(174,356)(175,355)(176,354)(177,353)(178,352)(179,351)(180,350)
(181,349)(182,348)(183,347)(184,346)(185,345)(186,344)(187,343)(188,410)
(189,409)(190,425)(191,424)(192,423)(193,422)(194,421)(195,420)(196,419)
(197,418)(198,417)(199,416)(200,415)(201,414)(202,413)(203,412)(204,411)
(205,393)(206,392)(207,408)(208,407)(209,406)(210,405)(211,404)(212,403)
(213,402)(214,401)(215,400)(216,399)(217,398)(218,397)(219,396)(220,395)
(221,394)(222,376)(223,375)(224,391)(225,390)(226,389)(227,388)(228,387)
(229,386)(230,385)(231,384)(232,383)(233,382)(234,381)(235,380)(236,379)
(237,378)(238,377)(239,359)(240,358)(241,374)(242,373)(243,372)(244,371)
(245,370)(246,369)(247,368)(248,367)(249,366)(250,365)(251,364)(252,363)
(253,362)(254,361)(255,360)(256,257)(258,272)(259,271)(260,270)(261,269)
(262,268)(263,267)(264,266)(273,325)(274,324)(275,340)(276,339)(277,338)
(278,337)(279,336)(280,335)(281,334)(282,333)(283,332)(284,331)(285,330)
(286,329)(287,328)(288,327)(289,326)(290,308)(291,307)(292,323)(293,322)
(294,321)(295,320)(296,319)(297,318)(298,317)(299,316)(300,315)(301,314)
(302,313)(303,312)(304,311)(305,310)(306,309);
poly := sub<Sym(425)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope