Polytope of Type {124,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope