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Polytope of Type {6,148}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,148}*1776a
Also Known As : {6,148|2}. if this polytope has another name.
Group : SmallGroup(1776,179)
Rank : 3
Schlafli Type : {6,148}
Number of vertices, edges, etc : 6, 444, 148
Order of s0s1s2 : 444
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 : {6,74}*888
   3-fold quotients : {2,148}*592
   6-fold quotients : {2,74}*296
   12-fold quotients : {2,37}*148
   37-fold quotients : {6,4}*48a
   74-fold quotients : {6,2}*24
   111-fold quotients : {2,4}*16
   148-fold quotients : {3,2}*12
   222-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 38, 75)( 39, 76)( 40, 77)( 41, 78)( 42, 79)( 43, 80)( 44, 81)( 45, 82)
( 46, 83)( 47, 84)( 48, 85)( 49, 86)( 50, 87)( 51, 88)( 52, 89)( 53, 90)
( 54, 91)( 55, 92)( 56, 93)( 57, 94)( 58, 95)( 59, 96)( 60, 97)( 61, 98)
( 62, 99)( 63,100)( 64,101)( 65,102)( 66,103)( 67,104)( 68,105)( 69,106)
( 70,107)( 71,108)( 72,109)( 73,110)( 74,111)(149,186)(150,187)(151,188)
(152,189)(153,190)(154,191)(155,192)(156,193)(157,194)(158,195)(159,196)
(160,197)(161,198)(162,199)(163,200)(164,201)(165,202)(166,203)(167,204)
(168,205)(169,206)(170,207)(171,208)(172,209)(173,210)(174,211)(175,212)
(176,213)(177,214)(178,215)(179,216)(180,217)(181,218)(182,219)(183,220)
(184,221)(185,222)(260,297)(261,298)(262,299)(263,300)(264,301)(265,302)
(266,303)(267,304)(268,305)(269,306)(270,307)(271,308)(272,309)(273,310)
(274,311)(275,312)(276,313)(277,314)(278,315)(279,316)(280,317)(281,318)
(282,319)(283,320)(284,321)(285,322)(286,323)(287,324)(288,325)(289,326)
(290,327)(291,328)(292,329)(293,330)(294,331)(295,332)(296,333)(371,408)
(372,409)(373,410)(374,411)(375,412)(376,413)(377,414)(378,415)(379,416)
(380,417)(381,418)(382,419)(383,420)(384,421)(385,422)(386,423)(387,424)
(388,425)(389,426)(390,427)(391,428)(392,429)(393,430)(394,431)(395,432)
(396,433)(397,434)(398,435)(399,436)(400,437)(401,438)(402,439)(403,440)
(404,441)(405,442)(406,443)(407,444);;
s1 := (  1, 38)(  2, 74)(  3, 73)(  4, 72)(  5, 71)(  6, 70)(  7, 69)(  8, 68)
(  9, 67)( 10, 66)( 11, 65)( 12, 64)( 13, 63)( 14, 62)( 15, 61)( 16, 60)
( 17, 59)( 18, 58)( 19, 57)( 20, 56)( 21, 55)( 22, 54)( 23, 53)( 24, 52)
( 25, 51)( 26, 50)( 27, 49)( 28, 48)( 29, 47)( 30, 46)( 31, 45)( 32, 44)
( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 76,111)( 77,110)( 78,109)
( 79,108)( 80,107)( 81,106)( 82,105)( 83,104)( 84,103)( 85,102)( 86,101)
( 87,100)( 88, 99)( 89, 98)( 90, 97)( 91, 96)( 92, 95)( 93, 94)(112,149)
(113,185)(114,184)(115,183)(116,182)(117,181)(118,180)(119,179)(120,178)
(121,177)(122,176)(123,175)(124,174)(125,173)(126,172)(127,171)(128,170)
(129,169)(130,168)(131,167)(132,166)(133,165)(134,164)(135,163)(136,162)
(137,161)(138,160)(139,159)(140,158)(141,157)(142,156)(143,155)(144,154)
(145,153)(146,152)(147,151)(148,150)(187,222)(188,221)(189,220)(190,219)
(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)
(199,210)(200,209)(201,208)(202,207)(203,206)(204,205)(223,371)(224,407)
(225,406)(226,405)(227,404)(228,403)(229,402)(230,401)(231,400)(232,399)
(233,398)(234,397)(235,396)(236,395)(237,394)(238,393)(239,392)(240,391)
(241,390)(242,389)(243,388)(244,387)(245,386)(246,385)(247,384)(248,383)
(249,382)(250,381)(251,380)(252,379)(253,378)(254,377)(255,376)(256,375)
(257,374)(258,373)(259,372)(260,334)(261,370)(262,369)(263,368)(264,367)
(265,366)(266,365)(267,364)(268,363)(269,362)(270,361)(271,360)(272,359)
(273,358)(274,357)(275,356)(276,355)(277,354)(278,353)(279,352)(280,351)
(281,350)(282,349)(283,348)(284,347)(285,346)(286,345)(287,344)(288,343)
(289,342)(290,341)(291,340)(292,339)(293,338)(294,337)(295,336)(296,335)
(297,408)(298,444)(299,443)(300,442)(301,441)(302,440)(303,439)(304,438)
(305,437)(306,436)(307,435)(308,434)(309,433)(310,432)(311,431)(312,430)
(313,429)(314,428)(315,427)(316,426)(317,425)(318,424)(319,423)(320,422)
(321,421)(322,420)(323,419)(324,418)(325,417)(326,416)(327,415)(328,414)
(329,413)(330,412)(331,411)(332,410)(333,409);;
s2 := (  1,224)(  2,223)(  3,259)(  4,258)(  5,257)(  6,256)(  7,255)(  8,254)
(  9,253)( 10,252)( 11,251)( 12,250)( 13,249)( 14,248)( 15,247)( 16,246)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,240)( 23,239)( 24,238)
( 25,237)( 26,236)( 27,235)( 28,234)( 29,233)( 30,232)( 31,231)( 32,230)
( 33,229)( 34,228)( 35,227)( 36,226)( 37,225)( 38,261)( 39,260)( 40,296)
( 41,295)( 42,294)( 43,293)( 44,292)( 45,291)( 46,290)( 47,289)( 48,288)
( 49,287)( 50,286)( 51,285)( 52,284)( 53,283)( 54,282)( 55,281)( 56,280)
( 57,279)( 58,278)( 59,277)( 60,276)( 61,275)( 62,274)( 63,273)( 64,272)
( 65,271)( 66,270)( 67,269)( 68,268)( 69,267)( 70,266)( 71,265)( 72,264)
( 73,263)( 74,262)( 75,298)( 76,297)( 77,333)( 78,332)( 79,331)( 80,330)
( 81,329)( 82,328)( 83,327)( 84,326)( 85,325)( 86,324)( 87,323)( 88,322)
( 89,321)( 90,320)( 91,319)( 92,318)( 93,317)( 94,316)( 95,315)( 96,314)
( 97,313)( 98,312)( 99,311)(100,310)(101,309)(102,308)(103,307)(104,306)
(105,305)(106,304)(107,303)(108,302)(109,301)(110,300)(111,299)(112,335)
(113,334)(114,370)(115,369)(116,368)(117,367)(118,366)(119,365)(120,364)
(121,363)(122,362)(123,361)(124,360)(125,359)(126,358)(127,357)(128,356)
(129,355)(130,354)(131,353)(132,352)(133,351)(134,350)(135,349)(136,348)
(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)(144,340)
(145,339)(146,338)(147,337)(148,336)(149,372)(150,371)(151,407)(152,406)
(153,405)(154,404)(155,403)(156,402)(157,401)(158,400)(159,399)(160,398)
(161,397)(162,396)(163,395)(164,394)(165,393)(166,392)(167,391)(168,390)
(169,389)(170,388)(171,387)(172,386)(173,385)(174,384)(175,383)(176,382)
(177,381)(178,380)(179,379)(180,378)(181,377)(182,376)(183,375)(184,374)
(185,373)(186,409)(187,408)(188,444)(189,443)(190,442)(191,441)(192,440)
(193,439)(194,438)(195,437)(196,436)(197,435)(198,434)(199,433)(200,432)
(201,431)(202,430)(203,429)(204,428)(205,427)(206,426)(207,425)(208,424)
(209,423)(210,422)(211,421)(212,420)(213,419)(214,418)(215,417)(216,416)
(217,415)(218,414)(219,413)(220,412)(221,411)(222,410);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(444)!( 38, 75)( 39, 76)( 40, 77)( 41, 78)( 42, 79)( 43, 80)( 44, 81)
( 45, 82)( 46, 83)( 47, 84)( 48, 85)( 49, 86)( 50, 87)( 51, 88)( 52, 89)
( 53, 90)( 54, 91)( 55, 92)( 56, 93)( 57, 94)( 58, 95)( 59, 96)( 60, 97)
( 61, 98)( 62, 99)( 63,100)( 64,101)( 65,102)( 66,103)( 67,104)( 68,105)
( 69,106)( 70,107)( 71,108)( 72,109)( 73,110)( 74,111)(149,186)(150,187)
(151,188)(152,189)(153,190)(154,191)(155,192)(156,193)(157,194)(158,195)
(159,196)(160,197)(161,198)(162,199)(163,200)(164,201)(165,202)(166,203)
(167,204)(168,205)(169,206)(170,207)(171,208)(172,209)(173,210)(174,211)
(175,212)(176,213)(177,214)(178,215)(179,216)(180,217)(181,218)(182,219)
(183,220)(184,221)(185,222)(260,297)(261,298)(262,299)(263,300)(264,301)
(265,302)(266,303)(267,304)(268,305)(269,306)(270,307)(271,308)(272,309)
(273,310)(274,311)(275,312)(276,313)(277,314)(278,315)(279,316)(280,317)
(281,318)(282,319)(283,320)(284,321)(285,322)(286,323)(287,324)(288,325)
(289,326)(290,327)(291,328)(292,329)(293,330)(294,331)(295,332)(296,333)
(371,408)(372,409)(373,410)(374,411)(375,412)(376,413)(377,414)(378,415)
(379,416)(380,417)(381,418)(382,419)(383,420)(384,421)(385,422)(386,423)
(387,424)(388,425)(389,426)(390,427)(391,428)(392,429)(393,430)(394,431)
(395,432)(396,433)(397,434)(398,435)(399,436)(400,437)(401,438)(402,439)
(403,440)(404,441)(405,442)(406,443)(407,444);
s1 := Sym(444)!(  1, 38)(  2, 74)(  3, 73)(  4, 72)(  5, 71)(  6, 70)(  7, 69)
(  8, 68)(  9, 67)( 10, 66)( 11, 65)( 12, 64)( 13, 63)( 14, 62)( 15, 61)
( 16, 60)( 17, 59)( 18, 58)( 19, 57)( 20, 56)( 21, 55)( 22, 54)( 23, 53)
( 24, 52)( 25, 51)( 26, 50)( 27, 49)( 28, 48)( 29, 47)( 30, 46)( 31, 45)
( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 76,111)( 77,110)
( 78,109)( 79,108)( 80,107)( 81,106)( 82,105)( 83,104)( 84,103)( 85,102)
( 86,101)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 91, 96)( 92, 95)( 93, 94)
(112,149)(113,185)(114,184)(115,183)(116,182)(117,181)(118,180)(119,179)
(120,178)(121,177)(122,176)(123,175)(124,174)(125,173)(126,172)(127,171)
(128,170)(129,169)(130,168)(131,167)(132,166)(133,165)(134,164)(135,163)
(136,162)(137,161)(138,160)(139,159)(140,158)(141,157)(142,156)(143,155)
(144,154)(145,153)(146,152)(147,151)(148,150)(187,222)(188,221)(189,220)
(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)(197,212)
(198,211)(199,210)(200,209)(201,208)(202,207)(203,206)(204,205)(223,371)
(224,407)(225,406)(226,405)(227,404)(228,403)(229,402)(230,401)(231,400)
(232,399)(233,398)(234,397)(235,396)(236,395)(237,394)(238,393)(239,392)
(240,391)(241,390)(242,389)(243,388)(244,387)(245,386)(246,385)(247,384)
(248,383)(249,382)(250,381)(251,380)(252,379)(253,378)(254,377)(255,376)
(256,375)(257,374)(258,373)(259,372)(260,334)(261,370)(262,369)(263,368)
(264,367)(265,366)(266,365)(267,364)(268,363)(269,362)(270,361)(271,360)
(272,359)(273,358)(274,357)(275,356)(276,355)(277,354)(278,353)(279,352)
(280,351)(281,350)(282,349)(283,348)(284,347)(285,346)(286,345)(287,344)
(288,343)(289,342)(290,341)(291,340)(292,339)(293,338)(294,337)(295,336)
(296,335)(297,408)(298,444)(299,443)(300,442)(301,441)(302,440)(303,439)
(304,438)(305,437)(306,436)(307,435)(308,434)(309,433)(310,432)(311,431)
(312,430)(313,429)(314,428)(315,427)(316,426)(317,425)(318,424)(319,423)
(320,422)(321,421)(322,420)(323,419)(324,418)(325,417)(326,416)(327,415)
(328,414)(329,413)(330,412)(331,411)(332,410)(333,409);
s2 := Sym(444)!(  1,224)(  2,223)(  3,259)(  4,258)(  5,257)(  6,256)(  7,255)
(  8,254)(  9,253)( 10,252)( 11,251)( 12,250)( 13,249)( 14,248)( 15,247)
( 16,246)( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,240)( 23,239)
( 24,238)( 25,237)( 26,236)( 27,235)( 28,234)( 29,233)( 30,232)( 31,231)
( 32,230)( 33,229)( 34,228)( 35,227)( 36,226)( 37,225)( 38,261)( 39,260)
( 40,296)( 41,295)( 42,294)( 43,293)( 44,292)( 45,291)( 46,290)( 47,289)
( 48,288)( 49,287)( 50,286)( 51,285)( 52,284)( 53,283)( 54,282)( 55,281)
( 56,280)( 57,279)( 58,278)( 59,277)( 60,276)( 61,275)( 62,274)( 63,273)
( 64,272)( 65,271)( 66,270)( 67,269)( 68,268)( 69,267)( 70,266)( 71,265)
( 72,264)( 73,263)( 74,262)( 75,298)( 76,297)( 77,333)( 78,332)( 79,331)
( 80,330)( 81,329)( 82,328)( 83,327)( 84,326)( 85,325)( 86,324)( 87,323)
( 88,322)( 89,321)( 90,320)( 91,319)( 92,318)( 93,317)( 94,316)( 95,315)
( 96,314)( 97,313)( 98,312)( 99,311)(100,310)(101,309)(102,308)(103,307)
(104,306)(105,305)(106,304)(107,303)(108,302)(109,301)(110,300)(111,299)
(112,335)(113,334)(114,370)(115,369)(116,368)(117,367)(118,366)(119,365)
(120,364)(121,363)(122,362)(123,361)(124,360)(125,359)(126,358)(127,357)
(128,356)(129,355)(130,354)(131,353)(132,352)(133,351)(134,350)(135,349)
(136,348)(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)
(144,340)(145,339)(146,338)(147,337)(148,336)(149,372)(150,371)(151,407)
(152,406)(153,405)(154,404)(155,403)(156,402)(157,401)(158,400)(159,399)
(160,398)(161,397)(162,396)(163,395)(164,394)(165,393)(166,392)(167,391)
(168,390)(169,389)(170,388)(171,387)(172,386)(173,385)(174,384)(175,383)
(176,382)(177,381)(178,380)(179,379)(180,378)(181,377)(182,376)(183,375)
(184,374)(185,373)(186,409)(187,408)(188,444)(189,443)(190,442)(191,441)
(192,440)(193,439)(194,438)(195,437)(196,436)(197,435)(198,434)(199,433)
(200,432)(201,431)(202,430)(203,429)(204,428)(205,427)(206,426)(207,425)
(208,424)(209,423)(210,422)(211,421)(212,420)(213,419)(214,418)(215,417)
(216,416)(217,415)(218,414)(219,413)(220,412)(221,411)(222,410);
poly := sub<Sym(444)|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 >; 
 
References : None.
to this polytope