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Polytope of Type {148,6}

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