Polytope of Type {33,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {33,22}*1452
if this polytope has a name.
Group : SmallGroup(1452,30)
Rank : 3
Schlafli Type : {33,22}
Number of vertices, edges, etc : 33, 363, 22
Order of s₀s₁s₂ : 66
Order of s₀s₁s₂s₁ : 22
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) :
   3-fold quotients : {11,22}*484
   11-fold quotients : {33,2}*132
   33-fold quotients : {11,2}*44
   121-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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