Polytope of Type {6,124}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,124}*1488a
Also Known As : {6,124|2}. if this polytope has another name.
Group : SmallGroup(1488,148)
Rank : 3
Schlafli Type : {6,124}
Number of vertices, edges, etc : 6, 372, 124
Order of s₀s₁s₂ : 372
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 : {6,62}*744
   3-fold quotients : {2,124}*496
   6-fold quotients : {2,62}*248
   12-fold quotients : {2,31}*124
   31-fold quotients : {6,4}*48a
   62-fold quotients : {6,2}*24
   93-fold quotients : {2,4}*16
   124-fold quotients : {3,2}*12
   186-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope