Polytope of Type {22,33}

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

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

Permutation Representation (Magma) :

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