Polytope of Type {132,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {132,6}*1584b
Also Known As : {132,6|2}. if this polytope has another name.
Group : SmallGroup(1584,562)
Rank : 3
Schlafli Type : {132,6}
Number of vertices, edges, etc : 132, 396, 6
Order of s₀s₁s₂ : 132
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {66,6}*792b
   3-fold quotients : {44,6}*528a, {132,2}*528
   6-fold quotients : {22,6}*264, {66,2}*264
   9-fold quotients : {44,2}*176
   11-fold quotients : {12,6}*144a
   12-fold quotients : {33,2}*132
   18-fold quotients : {22,2}*88
   22-fold quotients : {6,6}*72a
   33-fold quotients : {12,2}*48, {4,6}*48a
   36-fold quotients : {11,2}*44
   66-fold quotients : {2,6}*24, {6,2}*24
   99-fold quotients : {4,2}*16
   132-fold quotients : {2,3}*12, {3,2}*12
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 12, 23)( 13, 33)( 14, 32)
( 15, 31)( 16, 30)( 17, 29)( 18, 28)( 19, 27)( 20, 26)( 21, 25)( 22, 24)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)
( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 78, 89)( 79, 99)( 80, 98)
( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)
(101,110)(102,109)(103,108)(104,107)(105,106)(111,122)(112,132)(113,131)
(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)(121,123)
(134,143)(135,142)(136,141)(137,140)(138,139)(144,155)(145,165)(146,164)
(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)
(167,176)(168,175)(169,174)(170,173)(171,172)(177,188)(178,198)(179,197)
(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)
(199,298)(200,308)(201,307)(202,306)(203,305)(204,304)(205,303)(206,302)
(207,301)(208,300)(209,299)(210,320)(211,330)(212,329)(213,328)(214,327)
(215,326)(216,325)(217,324)(218,323)(219,322)(220,321)(221,309)(222,319)
(223,318)(224,317)(225,316)(226,315)(227,314)(228,313)(229,312)(230,311)
(231,310)(232,331)(233,341)(234,340)(235,339)(236,338)(237,337)(238,336)
(239,335)(240,334)(241,333)(242,332)(243,353)(244,363)(245,362)(246,361)
(247,360)(248,359)(249,358)(250,357)(251,356)(252,355)(253,354)(254,342)
(255,352)(256,351)(257,350)(258,349)(259,348)(260,347)(261,346)(262,345)
(263,344)(264,343)(265,364)(266,374)(267,373)(268,372)(269,371)(270,370)
(271,369)(272,368)(273,367)(274,366)(275,365)(276,386)(277,396)(278,395)
(279,394)(280,393)(281,392)(282,391)(283,390)(284,389)(285,388)(286,387)
(287,375)(288,385)(289,384)(290,383)(291,382)(292,381)(293,380)(294,379)
(295,378)(296,377)(297,376);;
s1 := (  1,211)(  2,210)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)(  8,215)
(  9,214)( 10,213)( 11,212)( 12,200)( 13,199)( 14,209)( 15,208)( 16,207)
( 17,206)( 18,205)( 19,204)( 20,203)( 21,202)( 22,201)( 23,222)( 24,221)
( 25,231)( 26,230)( 27,229)( 28,228)( 29,227)( 30,226)( 31,225)( 32,224)
( 33,223)( 34,277)( 35,276)( 36,286)( 37,285)( 38,284)( 39,283)( 40,282)
( 41,281)( 42,280)( 43,279)( 44,278)( 45,266)( 46,265)( 47,275)( 48,274)
( 49,273)( 50,272)( 51,271)( 52,270)( 53,269)( 54,268)( 55,267)( 56,288)
( 57,287)( 58,297)( 59,296)( 60,295)( 61,294)( 62,293)( 63,292)( 64,291)
( 65,290)( 66,289)( 67,244)( 68,243)( 69,253)( 70,252)( 71,251)( 72,250)
( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,233)( 79,232)( 80,242)
( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)( 88,234)
( 89,255)( 90,254)( 91,264)( 92,263)( 93,262)( 94,261)( 95,260)( 96,259)
( 97,258)( 98,257)( 99,256)(100,310)(101,309)(102,319)(103,318)(104,317)
(105,316)(106,315)(107,314)(108,313)(109,312)(110,311)(111,299)(112,298)
(113,308)(114,307)(115,306)(116,305)(117,304)(118,303)(119,302)(120,301)
(121,300)(122,321)(123,320)(124,330)(125,329)(126,328)(127,327)(128,326)
(129,325)(130,324)(131,323)(132,322)(133,376)(134,375)(135,385)(136,384)
(137,383)(138,382)(139,381)(140,380)(141,379)(142,378)(143,377)(144,365)
(145,364)(146,374)(147,373)(148,372)(149,371)(150,370)(151,369)(152,368)
(153,367)(154,366)(155,387)(156,386)(157,396)(158,395)(159,394)(160,393)
(161,392)(162,391)(163,390)(164,389)(165,388)(166,343)(167,342)(168,352)
(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)(176,344)
(177,332)(178,331)(179,341)(180,340)(181,339)(182,338)(183,337)(184,336)
(185,335)(186,334)(187,333)(188,354)(189,353)(190,363)(191,362)(192,361)
(193,360)(194,359)(195,358)(196,357)(197,356)(198,355);;
s2 := (  1, 34)(  2, 35)(  3, 36)(  4, 37)(  5, 38)(  6, 39)(  7, 40)(  8, 41)
(  9, 42)( 10, 43)( 11, 44)( 12, 45)( 13, 46)( 14, 47)( 15, 48)( 16, 49)
( 17, 50)( 18, 51)( 19, 52)( 20, 53)( 21, 54)( 22, 55)( 23, 56)( 24, 57)
( 25, 58)( 26, 59)( 27, 60)( 28, 61)( 29, 62)( 30, 63)( 31, 64)( 32, 65)
( 33, 66)(100,133)(101,134)(102,135)(103,136)(104,137)(105,138)(106,139)
(107,140)(108,141)(109,142)(110,143)(111,144)(112,145)(113,146)(114,147)
(115,148)(116,149)(117,150)(118,151)(119,152)(120,153)(121,154)(122,155)
(123,156)(124,157)(125,158)(126,159)(127,160)(128,161)(129,162)(130,163)
(131,164)(132,165)(199,232)(200,233)(201,234)(202,235)(203,236)(204,237)
(205,238)(206,239)(207,240)(208,241)(209,242)(210,243)(211,244)(212,245)
(213,246)(214,247)(215,248)(216,249)(217,250)(218,251)(219,252)(220,253)
(221,254)(222,255)(223,256)(224,257)(225,258)(226,259)(227,260)(228,261)
(229,262)(230,263)(231,264)(298,331)(299,332)(300,333)(301,334)(302,335)
(303,336)(304,337)(305,338)(306,339)(307,340)(308,341)(309,342)(310,343)
(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)(318,351)
(319,352)(320,353)(321,354)(322,355)(323,356)(324,357)(325,358)(326,359)
(327,360)(328,361)(329,362)(330,363);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(396)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 12, 23)( 13, 33)
( 14, 32)( 15, 31)( 16, 30)( 17, 29)( 18, 28)( 19, 27)( 20, 26)( 21, 25)
( 22, 24)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)
( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)
( 55, 57)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 78, 89)( 79, 99)
( 80, 98)( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)
( 88, 90)(101,110)(102,109)(103,108)(104,107)(105,106)(111,122)(112,132)
(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)
(121,123)(134,143)(135,142)(136,141)(137,140)(138,139)(144,155)(145,165)
(146,164)(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)
(154,156)(167,176)(168,175)(169,174)(170,173)(171,172)(177,188)(178,198)
(179,197)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)
(187,189)(199,298)(200,308)(201,307)(202,306)(203,305)(204,304)(205,303)
(206,302)(207,301)(208,300)(209,299)(210,320)(211,330)(212,329)(213,328)
(214,327)(215,326)(216,325)(217,324)(218,323)(219,322)(220,321)(221,309)
(222,319)(223,318)(224,317)(225,316)(226,315)(227,314)(228,313)(229,312)
(230,311)(231,310)(232,331)(233,341)(234,340)(235,339)(236,338)(237,337)
(238,336)(239,335)(240,334)(241,333)(242,332)(243,353)(244,363)(245,362)
(246,361)(247,360)(248,359)(249,358)(250,357)(251,356)(252,355)(253,354)
(254,342)(255,352)(256,351)(257,350)(258,349)(259,348)(260,347)(261,346)
(262,345)(263,344)(264,343)(265,364)(266,374)(267,373)(268,372)(269,371)
(270,370)(271,369)(272,368)(273,367)(274,366)(275,365)(276,386)(277,396)
(278,395)(279,394)(280,393)(281,392)(282,391)(283,390)(284,389)(285,388)
(286,387)(287,375)(288,385)(289,384)(290,383)(291,382)(292,381)(293,380)
(294,379)(295,378)(296,377)(297,376);
s1 := Sym(396)!(  1,211)(  2,210)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)
(  8,215)(  9,214)( 10,213)( 11,212)( 12,200)( 13,199)( 14,209)( 15,208)
( 16,207)( 17,206)( 18,205)( 19,204)( 20,203)( 21,202)( 22,201)( 23,222)
( 24,221)( 25,231)( 26,230)( 27,229)( 28,228)( 29,227)( 30,226)( 31,225)
( 32,224)( 33,223)( 34,277)( 35,276)( 36,286)( 37,285)( 38,284)( 39,283)
( 40,282)( 41,281)( 42,280)( 43,279)( 44,278)( 45,266)( 46,265)( 47,275)
( 48,274)( 49,273)( 50,272)( 51,271)( 52,270)( 53,269)( 54,268)( 55,267)
( 56,288)( 57,287)( 58,297)( 59,296)( 60,295)( 61,294)( 62,293)( 63,292)
( 64,291)( 65,290)( 66,289)( 67,244)( 68,243)( 69,253)( 70,252)( 71,251)
( 72,250)( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,233)( 79,232)
( 80,242)( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)
( 88,234)( 89,255)( 90,254)( 91,264)( 92,263)( 93,262)( 94,261)( 95,260)
( 96,259)( 97,258)( 98,257)( 99,256)(100,310)(101,309)(102,319)(103,318)
(104,317)(105,316)(106,315)(107,314)(108,313)(109,312)(110,311)(111,299)
(112,298)(113,308)(114,307)(115,306)(116,305)(117,304)(118,303)(119,302)
(120,301)(121,300)(122,321)(123,320)(124,330)(125,329)(126,328)(127,327)
(128,326)(129,325)(130,324)(131,323)(132,322)(133,376)(134,375)(135,385)
(136,384)(137,383)(138,382)(139,381)(140,380)(141,379)(142,378)(143,377)
(144,365)(145,364)(146,374)(147,373)(148,372)(149,371)(150,370)(151,369)
(152,368)(153,367)(154,366)(155,387)(156,386)(157,396)(158,395)(159,394)
(160,393)(161,392)(162,391)(163,390)(164,389)(165,388)(166,343)(167,342)
(168,352)(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)
(176,344)(177,332)(178,331)(179,341)(180,340)(181,339)(182,338)(183,337)
(184,336)(185,335)(186,334)(187,333)(188,354)(189,353)(190,363)(191,362)
(192,361)(193,360)(194,359)(195,358)(196,357)(197,356)(198,355);
s2 := Sym(396)!(  1, 34)(  2, 35)(  3, 36)(  4, 37)(  5, 38)(  6, 39)(  7, 40)
(  8, 41)(  9, 42)( 10, 43)( 11, 44)( 12, 45)( 13, 46)( 14, 47)( 15, 48)
( 16, 49)( 17, 50)( 18, 51)( 19, 52)( 20, 53)( 21, 54)( 22, 55)( 23, 56)
( 24, 57)( 25, 58)( 26, 59)( 27, 60)( 28, 61)( 29, 62)( 30, 63)( 31, 64)
( 32, 65)( 33, 66)(100,133)(101,134)(102,135)(103,136)(104,137)(105,138)
(106,139)(107,140)(108,141)(109,142)(110,143)(111,144)(112,145)(113,146)
(114,147)(115,148)(116,149)(117,150)(118,151)(119,152)(120,153)(121,154)
(122,155)(123,156)(124,157)(125,158)(126,159)(127,160)(128,161)(129,162)
(130,163)(131,164)(132,165)(199,232)(200,233)(201,234)(202,235)(203,236)
(204,237)(205,238)(206,239)(207,240)(208,241)(209,242)(210,243)(211,244)
(212,245)(213,246)(214,247)(215,248)(216,249)(217,250)(218,251)(219,252)
(220,253)(221,254)(222,255)(223,256)(224,257)(225,258)(226,259)(227,260)
(228,261)(229,262)(230,263)(231,264)(298,331)(299,332)(300,333)(301,334)
(302,335)(303,336)(304,337)(305,338)(306,339)(307,340)(308,341)(309,342)
(310,343)(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)
(318,351)(319,352)(320,353)(321,354)(322,355)(323,356)(324,357)(325,358)
(326,359)(327,360)(328,361)(329,362)(330,363);
poly := sub<Sym(396)|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 >;

References : None.
to this polytope