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Polytope of Type {6,152}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,152}*1824
Also Known As : {6,152|2}. if this polytope has another name.
Group : SmallGroup(1824,397)
Rank : 3
Schlafli Type : {6,152}
Number of vertices, edges, etc : 6, 456, 152
Order of s0s1s2 : 456
Order of s0s1s2s1 : 2
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) :
   2-fold quotients : {6,76}*912a
   3-fold quotients : {2,152}*608
   4-fold quotients : {6,38}*456
   6-fold quotients : {2,76}*304
   12-fold quotients : {2,38}*152
   19-fold quotients : {6,8}*96
   24-fold quotients : {2,19}*76
   38-fold quotients : {6,4}*48a
   57-fold quotients : {2,8}*32
   76-fold quotients : {6,2}*24
   114-fold quotients : {2,4}*16
   152-fold quotients : {3,2}*12
   228-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)( 27, 46)
( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)( 35, 54)
( 36, 55)( 37, 56)( 38, 57)( 77, 96)( 78, 97)( 79, 98)( 80, 99)( 81,100)
( 82,101)( 83,102)( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)( 89,108)
( 90,109)( 91,110)( 92,111)( 93,112)( 94,113)( 95,114)(134,153)(135,154)
(136,155)(137,156)(138,157)(139,158)(140,159)(141,160)(142,161)(143,162)
(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)(150,169)(151,170)
(152,171)(191,210)(192,211)(193,212)(194,213)(195,214)(196,215)(197,216)
(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)(205,224)
(206,225)(207,226)(208,227)(209,228)(248,267)(249,268)(250,269)(251,270)
(252,271)(253,272)(254,273)(255,274)(256,275)(257,276)(258,277)(259,278)
(260,279)(261,280)(262,281)(263,282)(264,283)(265,284)(266,285)(305,324)
(306,325)(307,326)(308,327)(309,328)(310,329)(311,330)(312,331)(313,332)
(314,333)(315,334)(316,335)(317,336)(318,337)(319,338)(320,339)(321,340)
(322,341)(323,342)(362,381)(363,382)(364,383)(365,384)(366,385)(367,386)
(368,387)(369,388)(370,389)(371,390)(372,391)(373,392)(374,393)(375,394)
(376,395)(377,396)(378,397)(379,398)(380,399)(419,438)(420,439)(421,440)
(422,441)(423,442)(424,443)(425,444)(426,445)(427,446)(428,447)(429,448)
(430,449)(431,450)(432,451)(433,452)(434,453)(435,454)(436,455)(437,456);;
s1 := (  1, 20)(  2, 38)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)(  8, 32)
(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)( 16, 24)
( 17, 23)( 18, 22)( 19, 21)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 58, 77)( 59, 95)( 60, 94)( 61, 93)
( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)( 69, 85)
( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 76, 78)( 97,114)
( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)
(115,191)(116,209)(117,208)(118,207)(119,206)(120,205)(121,204)(122,203)
(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)(129,196)(130,195)
(131,194)(132,193)(133,192)(134,172)(135,190)(136,189)(137,188)(138,187)
(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)(146,179)
(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)(153,210)(154,228)
(155,227)(156,226)(157,225)(158,224)(159,223)(160,222)(161,221)(162,220)
(163,219)(164,218)(165,217)(166,216)(167,215)(168,214)(169,213)(170,212)
(171,211)(229,362)(230,380)(231,379)(232,378)(233,377)(234,376)(235,375)
(236,374)(237,373)(238,372)(239,371)(240,370)(241,369)(242,368)(243,367)
(244,366)(245,365)(246,364)(247,363)(248,343)(249,361)(250,360)(251,359)
(252,358)(253,357)(254,356)(255,355)(256,354)(257,353)(258,352)(259,351)
(260,350)(261,349)(262,348)(263,347)(264,346)(265,345)(266,344)(267,381)
(268,399)(269,398)(270,397)(271,396)(272,395)(273,394)(274,393)(275,392)
(276,391)(277,390)(278,389)(279,388)(280,387)(281,386)(282,385)(283,384)
(284,383)(285,382)(286,419)(287,437)(288,436)(289,435)(290,434)(291,433)
(292,432)(293,431)(294,430)(295,429)(296,428)(297,427)(298,426)(299,425)
(300,424)(301,423)(302,422)(303,421)(304,420)(305,400)(306,418)(307,417)
(308,416)(309,415)(310,414)(311,413)(312,412)(313,411)(314,410)(315,409)
(316,408)(317,407)(318,406)(319,405)(320,404)(321,403)(322,402)(323,401)
(324,438)(325,456)(326,455)(327,454)(328,453)(329,452)(330,451)(331,450)
(332,449)(333,448)(334,447)(335,446)(336,445)(337,444)(338,443)(339,442)
(340,441)(341,440)(342,439);;
s2 := (  1,230)(  2,229)(  3,247)(  4,246)(  5,245)(  6,244)(  7,243)(  8,242)
(  9,241)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)( 16,234)
( 17,233)( 18,232)( 19,231)( 20,249)( 21,248)( 22,266)( 23,265)( 24,264)
( 25,263)( 26,262)( 27,261)( 28,260)( 29,259)( 30,258)( 31,257)( 32,256)
( 33,255)( 34,254)( 35,253)( 36,252)( 37,251)( 38,250)( 39,268)( 40,267)
( 41,285)( 42,284)( 43,283)( 44,282)( 45,281)( 46,280)( 47,279)( 48,278)
( 49,277)( 50,276)( 51,275)( 52,274)( 53,273)( 54,272)( 55,271)( 56,270)
( 57,269)( 58,287)( 59,286)( 60,304)( 61,303)( 62,302)( 63,301)( 64,300)
( 65,299)( 66,298)( 67,297)( 68,296)( 69,295)( 70,294)( 71,293)( 72,292)
( 73,291)( 74,290)( 75,289)( 76,288)( 77,306)( 78,305)( 79,323)( 80,322)
( 81,321)( 82,320)( 83,319)( 84,318)( 85,317)( 86,316)( 87,315)( 88,314)
( 89,313)( 90,312)( 91,311)( 92,310)( 93,309)( 94,308)( 95,307)( 96,325)
( 97,324)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)(104,336)
(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)(112,328)
(113,327)(114,326)(115,401)(116,400)(117,418)(118,417)(119,416)(120,415)
(121,414)(122,413)(123,412)(124,411)(125,410)(126,409)(127,408)(128,407)
(129,406)(130,405)(131,404)(132,403)(133,402)(134,420)(135,419)(136,437)
(137,436)(138,435)(139,434)(140,433)(141,432)(142,431)(143,430)(144,429)
(145,428)(146,427)(147,426)(148,425)(149,424)(150,423)(151,422)(152,421)
(153,439)(154,438)(155,456)(156,455)(157,454)(158,453)(159,452)(160,451)
(161,450)(162,449)(163,448)(164,447)(165,446)(166,445)(167,444)(168,443)
(169,442)(170,441)(171,440)(172,344)(173,343)(174,361)(175,360)(176,359)
(177,358)(178,357)(179,356)(180,355)(181,354)(182,353)(183,352)(184,351)
(185,350)(186,349)(187,348)(188,347)(189,346)(190,345)(191,363)(192,362)
(193,380)(194,379)(195,378)(196,377)(197,376)(198,375)(199,374)(200,373)
(201,372)(202,371)(203,370)(204,369)(205,368)(206,367)(207,366)(208,365)
(209,364)(210,382)(211,381)(212,399)(213,398)(214,397)(215,396)(216,395)
(217,394)(218,393)(219,392)(220,391)(221,390)(222,389)(223,388)(224,387)
(225,386)(226,385)(227,384)(228,383);;
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, s0*s1*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(456)!( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)
( 27, 46)( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)
( 35, 54)( 36, 55)( 37, 56)( 38, 57)( 77, 96)( 78, 97)( 79, 98)( 80, 99)
( 81,100)( 82,101)( 83,102)( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)
( 89,108)( 90,109)( 91,110)( 92,111)( 93,112)( 94,113)( 95,114)(134,153)
(135,154)(136,155)(137,156)(138,157)(139,158)(140,159)(141,160)(142,161)
(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)(150,169)
(151,170)(152,171)(191,210)(192,211)(193,212)(194,213)(195,214)(196,215)
(197,216)(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)
(205,224)(206,225)(207,226)(208,227)(209,228)(248,267)(249,268)(250,269)
(251,270)(252,271)(253,272)(254,273)(255,274)(256,275)(257,276)(258,277)
(259,278)(260,279)(261,280)(262,281)(263,282)(264,283)(265,284)(266,285)
(305,324)(306,325)(307,326)(308,327)(309,328)(310,329)(311,330)(312,331)
(313,332)(314,333)(315,334)(316,335)(317,336)(318,337)(319,338)(320,339)
(321,340)(322,341)(323,342)(362,381)(363,382)(364,383)(365,384)(366,385)
(367,386)(368,387)(369,388)(370,389)(371,390)(372,391)(373,392)(374,393)
(375,394)(376,395)(377,396)(378,397)(379,398)(380,399)(419,438)(420,439)
(421,440)(422,441)(423,442)(424,443)(425,444)(426,445)(427,446)(428,447)
(429,448)(430,449)(431,450)(432,451)(433,452)(434,453)(435,454)(436,455)
(437,456);
s1 := Sym(456)!(  1, 20)(  2, 38)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)
(  8, 32)(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)
( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 40, 57)( 41, 56)( 42, 55)( 43, 54)
( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 58, 77)( 59, 95)( 60, 94)
( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)
( 69, 85)( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 76, 78)
( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)
(105,106)(115,191)(116,209)(117,208)(118,207)(119,206)(120,205)(121,204)
(122,203)(123,202)(124,201)(125,200)(126,199)(127,198)(128,197)(129,196)
(130,195)(131,194)(132,193)(133,192)(134,172)(135,190)(136,189)(137,188)
(138,187)(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)
(146,179)(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)(153,210)
(154,228)(155,227)(156,226)(157,225)(158,224)(159,223)(160,222)(161,221)
(162,220)(163,219)(164,218)(165,217)(166,216)(167,215)(168,214)(169,213)
(170,212)(171,211)(229,362)(230,380)(231,379)(232,378)(233,377)(234,376)
(235,375)(236,374)(237,373)(238,372)(239,371)(240,370)(241,369)(242,368)
(243,367)(244,366)(245,365)(246,364)(247,363)(248,343)(249,361)(250,360)
(251,359)(252,358)(253,357)(254,356)(255,355)(256,354)(257,353)(258,352)
(259,351)(260,350)(261,349)(262,348)(263,347)(264,346)(265,345)(266,344)
(267,381)(268,399)(269,398)(270,397)(271,396)(272,395)(273,394)(274,393)
(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)(281,386)(282,385)
(283,384)(284,383)(285,382)(286,419)(287,437)(288,436)(289,435)(290,434)
(291,433)(292,432)(293,431)(294,430)(295,429)(296,428)(297,427)(298,426)
(299,425)(300,424)(301,423)(302,422)(303,421)(304,420)(305,400)(306,418)
(307,417)(308,416)(309,415)(310,414)(311,413)(312,412)(313,411)(314,410)
(315,409)(316,408)(317,407)(318,406)(319,405)(320,404)(321,403)(322,402)
(323,401)(324,438)(325,456)(326,455)(327,454)(328,453)(329,452)(330,451)
(331,450)(332,449)(333,448)(334,447)(335,446)(336,445)(337,444)(338,443)
(339,442)(340,441)(341,440)(342,439);
s2 := Sym(456)!(  1,230)(  2,229)(  3,247)(  4,246)(  5,245)(  6,244)(  7,243)
(  8,242)(  9,241)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)
( 16,234)( 17,233)( 18,232)( 19,231)( 20,249)( 21,248)( 22,266)( 23,265)
( 24,264)( 25,263)( 26,262)( 27,261)( 28,260)( 29,259)( 30,258)( 31,257)
( 32,256)( 33,255)( 34,254)( 35,253)( 36,252)( 37,251)( 38,250)( 39,268)
( 40,267)( 41,285)( 42,284)( 43,283)( 44,282)( 45,281)( 46,280)( 47,279)
( 48,278)( 49,277)( 50,276)( 51,275)( 52,274)( 53,273)( 54,272)( 55,271)
( 56,270)( 57,269)( 58,287)( 59,286)( 60,304)( 61,303)( 62,302)( 63,301)
( 64,300)( 65,299)( 66,298)( 67,297)( 68,296)( 69,295)( 70,294)( 71,293)
( 72,292)( 73,291)( 74,290)( 75,289)( 76,288)( 77,306)( 78,305)( 79,323)
( 80,322)( 81,321)( 82,320)( 83,319)( 84,318)( 85,317)( 86,316)( 87,315)
( 88,314)( 89,313)( 90,312)( 91,311)( 92,310)( 93,309)( 94,308)( 95,307)
( 96,325)( 97,324)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)
(104,336)(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)
(112,328)(113,327)(114,326)(115,401)(116,400)(117,418)(118,417)(119,416)
(120,415)(121,414)(122,413)(123,412)(124,411)(125,410)(126,409)(127,408)
(128,407)(129,406)(130,405)(131,404)(132,403)(133,402)(134,420)(135,419)
(136,437)(137,436)(138,435)(139,434)(140,433)(141,432)(142,431)(143,430)
(144,429)(145,428)(146,427)(147,426)(148,425)(149,424)(150,423)(151,422)
(152,421)(153,439)(154,438)(155,456)(156,455)(157,454)(158,453)(159,452)
(160,451)(161,450)(162,449)(163,448)(164,447)(165,446)(166,445)(167,444)
(168,443)(169,442)(170,441)(171,440)(172,344)(173,343)(174,361)(175,360)
(176,359)(177,358)(178,357)(179,356)(180,355)(181,354)(182,353)(183,352)
(184,351)(185,350)(186,349)(187,348)(188,347)(189,346)(190,345)(191,363)
(192,362)(193,380)(194,379)(195,378)(196,377)(197,376)(198,375)(199,374)
(200,373)(201,372)(202,371)(203,370)(204,369)(205,368)(206,367)(207,366)
(208,365)(209,364)(210,382)(211,381)(212,399)(213,398)(214,397)(215,396)
(216,395)(217,394)(218,393)(219,392)(220,391)(221,390)(222,389)(223,388)
(224,387)(225,386)(226,385)(227,384)(228,383);
poly := sub<Sym(456)|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, s0*s1*s2*s1*s0*s1*s2*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 >; 
 
References : None.
to this polytope