Polytope of Type {141,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {141,6}*1692
if this polytope has a name.
Group : SmallGroup(1692,22)
Rank : 3
Schlafli Type : {141,6}
Number of vertices, edges, etc : 141, 423, 6
Order of s₀s₁s₂ : 282
Order of s₀s₁s₂s₁ : 6
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) :
   3-fold quotients : {141,2}*564
   9-fold quotients : {47,2}*188
   47-fold quotients : {3,6}*36
   141-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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