Polytope of Type {6,132}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,132}*1584c
if this polytope has a name.
Group : SmallGroup(1584,562)
Rank : 3
Schlafli Type : {6,132}
Number of vertices, edges, etc : 6, 396, 132
Order of s₀s₁s₂ : 132
Order of s₀s₁s₂s₁ : 6
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 : {6,66}*792c
   3-fold quotients : {2,132}*528
   4-fold quotients : {6,33}*396
   6-fold quotients : {2,66}*264
   9-fold quotients : {2,44}*176
   11-fold quotients : {6,12}*144b
   12-fold quotients : {2,33}*132
   18-fold quotients : {2,22}*88
   22-fold quotients : {6,6}*72b
   33-fold quotients : {2,12}*48
   36-fold quotients : {2,11}*44
   44-fold quotients : {6,3}*36
   66-fold quotients : {2,6}*24
   99-fold quotients : {2,4}*16
   132-fold quotients : {2,3}*12
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope