Polytope of Type {85,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {85,10}*1700
if this polytope has a name.
Group : SmallGroup(1700,43)
Rank : 3
Schlafli Type : {85,10}
Number of vertices, edges, etc : 85, 425, 10
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 : {85,2}*340
   17-fold quotients : {5,10}*100
   25-fold quotients : {17,2}*68
   85-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope