Polytope of Type {153,6}

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

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