Polytope of Type {6,153}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,153}*1836
if this polytope has a name.
Group : SmallGroup(1836,51)
Rank : 3
Schlafli Type : {6,153}
Number of vertices, edges, etc : 6, 459, 153
Order of s₀s₁s₂ : 306
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 : {2,153}*612, {6,51}*612
   9-fold quotients : {2,51}*204
   17-fold quotients : {6,9}*108
   27-fold quotients : {2,17}*68
   51-fold quotients : {2,9}*36, {6,3}*36
   153-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 52,103)( 53,104)( 54,105)( 55,106)( 56,107)( 57,108)( 58,109)( 59,110)
( 60,111)( 61,112)( 62,113)( 63,114)( 64,115)( 65,116)( 66,117)( 67,118)
( 68,119)( 69,120)( 70,121)( 71,122)( 72,123)( 73,124)( 74,125)( 75,126)
( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)( 81,132)( 82,133)( 83,134)
( 84,135)( 85,136)( 86,137)( 87,138)( 88,139)( 89,140)( 90,141)( 91,142)
( 92,143)( 93,144)( 94,145)( 95,146)( 96,147)( 97,148)( 98,149)( 99,150)
(100,151)(101,152)(102,153)(205,256)(206,257)(207,258)(208,259)(209,260)
(210,261)(211,262)(212,263)(213,264)(214,265)(215,266)(216,267)(217,268)
(218,269)(219,270)(220,271)(221,272)(222,273)(223,274)(224,275)(225,276)
(226,277)(227,278)(228,279)(229,280)(230,281)(231,282)(232,283)(233,284)
(234,285)(235,286)(236,287)(237,288)(238,289)(239,290)(240,291)(241,292)
(242,293)(243,294)(244,295)(245,296)(246,297)(247,298)(248,299)(249,300)
(250,301)(251,302)(252,303)(253,304)(254,305)(255,306)(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)(375,426)
(376,427)(377,428)(378,429)(379,430)(380,431)(381,432)(382,433)(383,434)
(384,435)(385,436)(386,437)(387,438)(388,439)(389,440)(390,441)(391,442)
(392,443)(393,444)(394,445)(395,446)(396,447)(397,448)(398,449)(399,450)
(400,451)(401,452)(402,453)(403,454)(404,455)(405,456)(406,457)(407,458)
(408,459);;
s1 := (  1, 52)(  2, 54)(  3, 53)(  4,100)(  5,102)(  6,101)(  7, 97)(  8, 99)
(  9, 98)( 10, 94)( 11, 96)( 12, 95)( 13, 91)( 14, 93)( 15, 92)( 16, 88)
( 17, 90)( 18, 89)( 19, 85)( 20, 87)( 21, 86)( 22, 82)( 23, 84)( 24, 83)
( 25, 79)( 26, 81)( 27, 80)( 28, 76)( 29, 78)( 30, 77)( 31, 73)( 32, 75)
( 33, 74)( 34, 70)( 35, 72)( 36, 71)( 37, 67)( 38, 69)( 39, 68)( 40, 64)
( 41, 66)( 42, 65)( 43, 61)( 44, 63)( 45, 62)( 46, 58)( 47, 60)( 48, 59)
( 49, 55)( 50, 57)( 51, 56)(104,105)(106,151)(107,153)(108,152)(109,148)
(110,150)(111,149)(112,145)(113,147)(114,146)(115,142)(116,144)(117,143)
(118,139)(119,141)(120,140)(121,136)(122,138)(123,137)(124,133)(125,135)
(126,134)(127,130)(128,132)(129,131)(154,359)(155,358)(156,360)(157,407)
(158,406)(159,408)(160,404)(161,403)(162,405)(163,401)(164,400)(165,402)
(166,398)(167,397)(168,399)(169,395)(170,394)(171,396)(172,392)(173,391)
(174,393)(175,389)(176,388)(177,390)(178,386)(179,385)(180,387)(181,383)
(182,382)(183,384)(184,380)(185,379)(186,381)(187,377)(188,376)(189,378)
(190,374)(191,373)(192,375)(193,371)(194,370)(195,372)(196,368)(197,367)
(198,369)(199,365)(200,364)(201,366)(202,362)(203,361)(204,363)(205,308)
(206,307)(207,309)(208,356)(209,355)(210,357)(211,353)(212,352)(213,354)
(214,350)(215,349)(216,351)(217,347)(218,346)(219,348)(220,344)(221,343)
(222,345)(223,341)(224,340)(225,342)(226,338)(227,337)(228,339)(229,335)
(230,334)(231,336)(232,332)(233,331)(234,333)(235,329)(236,328)(237,330)
(238,326)(239,325)(240,327)(241,323)(242,322)(243,324)(244,320)(245,319)
(246,321)(247,317)(248,316)(249,318)(250,314)(251,313)(252,315)(253,311)
(254,310)(255,312)(256,410)(257,409)(258,411)(259,458)(260,457)(261,459)
(262,455)(263,454)(264,456)(265,452)(266,451)(267,453)(268,449)(269,448)
(270,450)(271,446)(272,445)(273,447)(274,443)(275,442)(276,444)(277,440)
(278,439)(279,441)(280,437)(281,436)(282,438)(283,434)(284,433)(285,435)
(286,431)(287,430)(288,432)(289,428)(290,427)(291,429)(292,425)(293,424)
(294,426)(295,422)(296,421)(297,423)(298,419)(299,418)(300,420)(301,416)
(302,415)(303,417)(304,413)(305,412)(306,414);;
s2 := (  1,157)(  2,159)(  3,158)(  4,154)(  5,156)(  6,155)(  7,202)(  8,204)
(  9,203)( 10,199)( 11,201)( 12,200)( 13,196)( 14,198)( 15,197)( 16,193)
( 17,195)( 18,194)( 19,190)( 20,192)( 21,191)( 22,187)( 23,189)( 24,188)
( 25,184)( 26,186)( 27,185)( 28,181)( 29,183)( 30,182)( 31,178)( 32,180)
( 33,179)( 34,175)( 35,177)( 36,176)( 37,172)( 38,174)( 39,173)( 40,169)
( 41,171)( 42,170)( 43,166)( 44,168)( 45,167)( 46,163)( 47,165)( 48,164)
( 49,160)( 50,162)( 51,161)( 52,259)( 53,261)( 54,260)( 55,256)( 56,258)
( 57,257)( 58,304)( 59,306)( 60,305)( 61,301)( 62,303)( 63,302)( 64,298)
( 65,300)( 66,299)( 67,295)( 68,297)( 69,296)( 70,292)( 71,294)( 72,293)
( 73,289)( 74,291)( 75,290)( 76,286)( 77,288)( 78,287)( 79,283)( 80,285)
( 81,284)( 82,280)( 83,282)( 84,281)( 85,277)( 86,279)( 87,278)( 88,274)
( 89,276)( 90,275)( 91,271)( 92,273)( 93,272)( 94,268)( 95,270)( 96,269)
( 97,265)( 98,267)( 99,266)(100,262)(101,264)(102,263)(103,208)(104,210)
(105,209)(106,205)(107,207)(108,206)(109,253)(110,255)(111,254)(112,250)
(113,252)(114,251)(115,247)(116,249)(117,248)(118,244)(119,246)(120,245)
(121,241)(122,243)(123,242)(124,238)(125,240)(126,239)(127,235)(128,237)
(129,236)(130,232)(131,234)(132,233)(133,229)(134,231)(135,230)(136,226)
(137,228)(138,227)(139,223)(140,225)(141,224)(142,220)(143,222)(144,221)
(145,217)(146,219)(147,218)(148,214)(149,216)(150,215)(151,211)(152,213)
(153,212)(307,311)(308,310)(309,312)(313,356)(314,355)(315,357)(316,353)
(317,352)(318,354)(319,350)(320,349)(321,351)(322,347)(323,346)(324,348)
(325,344)(326,343)(327,345)(328,341)(329,340)(330,342)(331,338)(332,337)
(333,339)(334,335)(358,413)(359,412)(360,414)(361,410)(362,409)(363,411)
(364,458)(365,457)(366,459)(367,455)(368,454)(369,456)(370,452)(371,451)
(372,453)(373,449)(374,448)(375,450)(376,446)(377,445)(378,447)(379,443)
(380,442)(381,444)(382,440)(383,439)(384,441)(385,437)(386,436)(387,438)
(388,434)(389,433)(390,435)(391,431)(392,430)(393,432)(394,428)(395,427)
(396,429)(397,425)(398,424)(399,426)(400,422)(401,421)(402,423)(403,419)
(404,418)(405,420)(406,416)(407,415)(408,417);;
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*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(459)!( 52,103)( 53,104)( 54,105)( 55,106)( 56,107)( 57,108)( 58,109)
( 59,110)( 60,111)( 61,112)( 62,113)( 63,114)( 64,115)( 65,116)( 66,117)
( 67,118)( 68,119)( 69,120)( 70,121)( 71,122)( 72,123)( 73,124)( 74,125)
( 75,126)( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)( 81,132)( 82,133)
( 83,134)( 84,135)( 85,136)( 86,137)( 87,138)( 88,139)( 89,140)( 90,141)
( 91,142)( 92,143)( 93,144)( 94,145)( 95,146)( 96,147)( 97,148)( 98,149)
( 99,150)(100,151)(101,152)(102,153)(205,256)(206,257)(207,258)(208,259)
(209,260)(210,261)(211,262)(212,263)(213,264)(214,265)(215,266)(216,267)
(217,268)(218,269)(219,270)(220,271)(221,272)(222,273)(223,274)(224,275)
(225,276)(226,277)(227,278)(228,279)(229,280)(230,281)(231,282)(232,283)
(233,284)(234,285)(235,286)(236,287)(237,288)(238,289)(239,290)(240,291)
(241,292)(242,293)(243,294)(244,295)(245,296)(246,297)(247,298)(248,299)
(249,300)(250,301)(251,302)(252,303)(253,304)(254,305)(255,306)(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)
(375,426)(376,427)(377,428)(378,429)(379,430)(380,431)(381,432)(382,433)
(383,434)(384,435)(385,436)(386,437)(387,438)(388,439)(389,440)(390,441)
(391,442)(392,443)(393,444)(394,445)(395,446)(396,447)(397,448)(398,449)
(399,450)(400,451)(401,452)(402,453)(403,454)(404,455)(405,456)(406,457)
(407,458)(408,459);
s1 := Sym(459)!(  1, 52)(  2, 54)(  3, 53)(  4,100)(  5,102)(  6,101)(  7, 97)
(  8, 99)(  9, 98)( 10, 94)( 11, 96)( 12, 95)( 13, 91)( 14, 93)( 15, 92)
( 16, 88)( 17, 90)( 18, 89)( 19, 85)( 20, 87)( 21, 86)( 22, 82)( 23, 84)
( 24, 83)( 25, 79)( 26, 81)( 27, 80)( 28, 76)( 29, 78)( 30, 77)( 31, 73)
( 32, 75)( 33, 74)( 34, 70)( 35, 72)( 36, 71)( 37, 67)( 38, 69)( 39, 68)
( 40, 64)( 41, 66)( 42, 65)( 43, 61)( 44, 63)( 45, 62)( 46, 58)( 47, 60)
( 48, 59)( 49, 55)( 50, 57)( 51, 56)(104,105)(106,151)(107,153)(108,152)
(109,148)(110,150)(111,149)(112,145)(113,147)(114,146)(115,142)(116,144)
(117,143)(118,139)(119,141)(120,140)(121,136)(122,138)(123,137)(124,133)
(125,135)(126,134)(127,130)(128,132)(129,131)(154,359)(155,358)(156,360)
(157,407)(158,406)(159,408)(160,404)(161,403)(162,405)(163,401)(164,400)
(165,402)(166,398)(167,397)(168,399)(169,395)(170,394)(171,396)(172,392)
(173,391)(174,393)(175,389)(176,388)(177,390)(178,386)(179,385)(180,387)
(181,383)(182,382)(183,384)(184,380)(185,379)(186,381)(187,377)(188,376)
(189,378)(190,374)(191,373)(192,375)(193,371)(194,370)(195,372)(196,368)
(197,367)(198,369)(199,365)(200,364)(201,366)(202,362)(203,361)(204,363)
(205,308)(206,307)(207,309)(208,356)(209,355)(210,357)(211,353)(212,352)
(213,354)(214,350)(215,349)(216,351)(217,347)(218,346)(219,348)(220,344)
(221,343)(222,345)(223,341)(224,340)(225,342)(226,338)(227,337)(228,339)
(229,335)(230,334)(231,336)(232,332)(233,331)(234,333)(235,329)(236,328)
(237,330)(238,326)(239,325)(240,327)(241,323)(242,322)(243,324)(244,320)
(245,319)(246,321)(247,317)(248,316)(249,318)(250,314)(251,313)(252,315)
(253,311)(254,310)(255,312)(256,410)(257,409)(258,411)(259,458)(260,457)
(261,459)(262,455)(263,454)(264,456)(265,452)(266,451)(267,453)(268,449)
(269,448)(270,450)(271,446)(272,445)(273,447)(274,443)(275,442)(276,444)
(277,440)(278,439)(279,441)(280,437)(281,436)(282,438)(283,434)(284,433)
(285,435)(286,431)(287,430)(288,432)(289,428)(290,427)(291,429)(292,425)
(293,424)(294,426)(295,422)(296,421)(297,423)(298,419)(299,418)(300,420)
(301,416)(302,415)(303,417)(304,413)(305,412)(306,414);
s2 := Sym(459)!(  1,157)(  2,159)(  3,158)(  4,154)(  5,156)(  6,155)(  7,202)
(  8,204)(  9,203)( 10,199)( 11,201)( 12,200)( 13,196)( 14,198)( 15,197)
( 16,193)( 17,195)( 18,194)( 19,190)( 20,192)( 21,191)( 22,187)( 23,189)
( 24,188)( 25,184)( 26,186)( 27,185)( 28,181)( 29,183)( 30,182)( 31,178)
( 32,180)( 33,179)( 34,175)( 35,177)( 36,176)( 37,172)( 38,174)( 39,173)
( 40,169)( 41,171)( 42,170)( 43,166)( 44,168)( 45,167)( 46,163)( 47,165)
( 48,164)( 49,160)( 50,162)( 51,161)( 52,259)( 53,261)( 54,260)( 55,256)
( 56,258)( 57,257)( 58,304)( 59,306)( 60,305)( 61,301)( 62,303)( 63,302)
( 64,298)( 65,300)( 66,299)( 67,295)( 68,297)( 69,296)( 70,292)( 71,294)
( 72,293)( 73,289)( 74,291)( 75,290)( 76,286)( 77,288)( 78,287)( 79,283)
( 80,285)( 81,284)( 82,280)( 83,282)( 84,281)( 85,277)( 86,279)( 87,278)
( 88,274)( 89,276)( 90,275)( 91,271)( 92,273)( 93,272)( 94,268)( 95,270)
( 96,269)( 97,265)( 98,267)( 99,266)(100,262)(101,264)(102,263)(103,208)
(104,210)(105,209)(106,205)(107,207)(108,206)(109,253)(110,255)(111,254)
(112,250)(113,252)(114,251)(115,247)(116,249)(117,248)(118,244)(119,246)
(120,245)(121,241)(122,243)(123,242)(124,238)(125,240)(126,239)(127,235)
(128,237)(129,236)(130,232)(131,234)(132,233)(133,229)(134,231)(135,230)
(136,226)(137,228)(138,227)(139,223)(140,225)(141,224)(142,220)(143,222)
(144,221)(145,217)(146,219)(147,218)(148,214)(149,216)(150,215)(151,211)
(152,213)(153,212)(307,311)(308,310)(309,312)(313,356)(314,355)(315,357)
(316,353)(317,352)(318,354)(319,350)(320,349)(321,351)(322,347)(323,346)
(324,348)(325,344)(326,343)(327,345)(328,341)(329,340)(330,342)(331,338)
(332,337)(333,339)(334,335)(358,413)(359,412)(360,414)(361,410)(362,409)
(363,411)(364,458)(365,457)(366,459)(367,455)(368,454)(369,456)(370,452)
(371,451)(372,453)(373,449)(374,448)(375,450)(376,446)(377,445)(378,447)
(379,443)(380,442)(381,444)(382,440)(383,439)(384,441)(385,437)(386,436)
(387,438)(388,434)(389,433)(390,435)(391,431)(392,430)(393,432)(394,428)
(395,427)(396,429)(397,425)(398,424)(399,426)(400,422)(401,421)(402,423)
(403,419)(404,418)(405,420)(406,416)(407,415)(408,417);
poly := sub<Sym(459)|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*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