Polytope of Type {6,141}

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

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