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Polytope of Type {22,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,34}*1496
Also Known As : {22,34|2}. if this polytope has another name.
Group : SmallGroup(1496,37)
Rank : 3
Schlafli Type : {22,34}
Number of vertices, edges, etc : 22, 374, 34
Order of s0s1s2 : 374
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) :
   11-fold quotients : {2,34}*136
   17-fold quotients : {22,2}*88
   22-fold quotients : {2,17}*68
   34-fold quotients : {11,2}*44
   187-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 18,171)( 19,172)( 20,173)( 21,174)( 22,175)( 23,176)( 24,177)( 25,178)
( 26,179)( 27,180)( 28,181)( 29,182)( 30,183)( 31,184)( 32,185)( 33,186)
( 34,187)( 35,154)( 36,155)( 37,156)( 38,157)( 39,158)( 40,159)( 41,160)
( 42,161)( 43,162)( 44,163)( 45,164)( 46,165)( 47,166)( 48,167)( 49,168)
( 50,169)( 51,170)( 52,137)( 53,138)( 54,139)( 55,140)( 56,141)( 57,142)
( 58,143)( 59,144)( 60,145)( 61,146)( 62,147)( 63,148)( 64,149)( 65,150)
( 66,151)( 67,152)( 68,153)( 69,120)( 70,121)( 71,122)( 72,123)( 73,124)
( 74,125)( 75,126)( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)( 81,132)
( 82,133)( 83,134)( 84,135)( 85,136)( 86,103)( 87,104)( 88,105)( 89,106)
( 90,107)( 91,108)( 92,109)( 93,110)( 94,111)( 95,112)( 96,113)( 97,114)
( 98,115)( 99,116)(100,117)(101,118)(102,119)(205,358)(206,359)(207,360)
(208,361)(209,362)(210,363)(211,364)(212,365)(213,366)(214,367)(215,368)
(216,369)(217,370)(218,371)(219,372)(220,373)(221,374)(222,341)(223,342)
(224,343)(225,344)(226,345)(227,346)(228,347)(229,348)(230,349)(231,350)
(232,351)(233,352)(234,353)(235,354)(236,355)(237,356)(238,357)(239,324)
(240,325)(241,326)(242,327)(243,328)(244,329)(245,330)(246,331)(247,332)
(248,333)(249,334)(250,335)(251,336)(252,337)(253,338)(254,339)(255,340)
(256,307)(257,308)(258,309)(259,310)(260,311)(261,312)(262,313)(263,314)
(264,315)(265,316)(266,317)(267,318)(268,319)(269,320)(270,321)(271,322)
(272,323)(273,290)(274,291)(275,292)(276,293)(277,294)(278,295)(279,296)
(280,297)(281,298)(282,299)(283,300)(284,301)(285,302)(286,303)(287,304)
(288,305)(289,306);;
s1 := (  1, 18)(  2, 34)(  3, 33)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 28)
(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)
( 17, 19)( 35,171)( 36,187)( 37,186)( 38,185)( 39,184)( 40,183)( 41,182)
( 42,181)( 43,180)( 44,179)( 45,178)( 46,177)( 47,176)( 48,175)( 49,174)
( 50,173)( 51,172)( 52,154)( 53,170)( 54,169)( 55,168)( 56,167)( 57,166)
( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)( 65,158)
( 66,157)( 67,156)( 68,155)( 69,137)( 70,153)( 71,152)( 72,151)( 73,150)
( 74,149)( 75,148)( 76,147)( 77,146)( 78,145)( 79,144)( 80,143)( 81,142)
( 82,141)( 83,140)( 84,139)( 85,138)( 86,120)( 87,136)( 88,135)( 89,134)
( 90,133)( 91,132)( 92,131)( 93,130)( 94,129)( 95,128)( 96,127)( 97,126)
( 98,125)( 99,124)(100,123)(101,122)(102,121)(104,119)(105,118)(106,117)
(107,116)(108,115)(109,114)(110,113)(111,112)(188,205)(189,221)(190,220)
(191,219)(192,218)(193,217)(194,216)(195,215)(196,214)(197,213)(198,212)
(199,211)(200,210)(201,209)(202,208)(203,207)(204,206)(222,358)(223,374)
(224,373)(225,372)(226,371)(227,370)(228,369)(229,368)(230,367)(231,366)
(232,365)(233,364)(234,363)(235,362)(236,361)(237,360)(238,359)(239,341)
(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,351)(247,350)
(248,349)(249,348)(250,347)(251,346)(252,345)(253,344)(254,343)(255,342)
(256,324)(257,340)(258,339)(259,338)(260,337)(261,336)(262,335)(263,334)
(264,333)(265,332)(266,331)(267,330)(268,329)(269,328)(270,327)(271,326)
(272,325)(273,307)(274,323)(275,322)(276,321)(277,320)(278,319)(279,318)
(280,317)(281,316)(282,315)(283,314)(284,313)(285,312)(286,311)(287,310)
(288,309)(289,308)(291,306)(292,305)(293,304)(294,303)(295,302)(296,301)
(297,300)(298,299);;
s2 := (  1,189)(  2,188)(  3,204)(  4,203)(  5,202)(  6,201)(  7,200)(  8,199)
(  9,198)( 10,197)( 11,196)( 12,195)( 13,194)( 14,193)( 15,192)( 16,191)
( 17,190)( 18,206)( 19,205)( 20,221)( 21,220)( 22,219)( 23,218)( 24,217)
( 25,216)( 26,215)( 27,214)( 28,213)( 29,212)( 30,211)( 31,210)( 32,209)
( 33,208)( 34,207)( 35,223)( 36,222)( 37,238)( 38,237)( 39,236)( 40,235)
( 41,234)( 42,233)( 43,232)( 44,231)( 45,230)( 46,229)( 47,228)( 48,227)
( 49,226)( 50,225)( 51,224)( 52,240)( 53,239)( 54,255)( 55,254)( 56,253)
( 57,252)( 58,251)( 59,250)( 60,249)( 61,248)( 62,247)( 63,246)( 64,245)
( 65,244)( 66,243)( 67,242)( 68,241)( 69,257)( 70,256)( 71,272)( 72,271)
( 73,270)( 74,269)( 75,268)( 76,267)( 77,266)( 78,265)( 79,264)( 80,263)
( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,274)( 87,273)( 88,289)
( 89,288)( 90,287)( 91,286)( 92,285)( 93,284)( 94,283)( 95,282)( 96,281)
( 97,280)( 98,279)( 99,278)(100,277)(101,276)(102,275)(103,291)(104,290)
(105,306)(106,305)(107,304)(108,303)(109,302)(110,301)(111,300)(112,299)
(113,298)(114,297)(115,296)(116,295)(117,294)(118,293)(119,292)(120,308)
(121,307)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)(128,317)
(129,316)(130,315)(131,314)(132,313)(133,312)(134,311)(135,310)(136,309)
(137,325)(138,324)(139,340)(140,339)(141,338)(142,337)(143,336)(144,335)
(145,334)(146,333)(147,332)(148,331)(149,330)(150,329)(151,328)(152,327)
(153,326)(154,342)(155,341)(156,357)(157,356)(158,355)(159,354)(160,353)
(161,352)(162,351)(163,350)(164,349)(165,348)(166,347)(167,346)(168,345)
(169,344)(170,343)(171,359)(172,358)(173,374)(174,373)(175,372)(176,371)
(177,370)(178,369)(179,368)(180,367)(181,366)(182,365)(183,364)(184,363)
(185,362)(186,361)(187,360);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(374)!( 18,171)( 19,172)( 20,173)( 21,174)( 22,175)( 23,176)( 24,177)
( 25,178)( 26,179)( 27,180)( 28,181)( 29,182)( 30,183)( 31,184)( 32,185)
( 33,186)( 34,187)( 35,154)( 36,155)( 37,156)( 38,157)( 39,158)( 40,159)
( 41,160)( 42,161)( 43,162)( 44,163)( 45,164)( 46,165)( 47,166)( 48,167)
( 49,168)( 50,169)( 51,170)( 52,137)( 53,138)( 54,139)( 55,140)( 56,141)
( 57,142)( 58,143)( 59,144)( 60,145)( 61,146)( 62,147)( 63,148)( 64,149)
( 65,150)( 66,151)( 67,152)( 68,153)( 69,120)( 70,121)( 71,122)( 72,123)
( 73,124)( 74,125)( 75,126)( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)
( 81,132)( 82,133)( 83,134)( 84,135)( 85,136)( 86,103)( 87,104)( 88,105)
( 89,106)( 90,107)( 91,108)( 92,109)( 93,110)( 94,111)( 95,112)( 96,113)
( 97,114)( 98,115)( 99,116)(100,117)(101,118)(102,119)(205,358)(206,359)
(207,360)(208,361)(209,362)(210,363)(211,364)(212,365)(213,366)(214,367)
(215,368)(216,369)(217,370)(218,371)(219,372)(220,373)(221,374)(222,341)
(223,342)(224,343)(225,344)(226,345)(227,346)(228,347)(229,348)(230,349)
(231,350)(232,351)(233,352)(234,353)(235,354)(236,355)(237,356)(238,357)
(239,324)(240,325)(241,326)(242,327)(243,328)(244,329)(245,330)(246,331)
(247,332)(248,333)(249,334)(250,335)(251,336)(252,337)(253,338)(254,339)
(255,340)(256,307)(257,308)(258,309)(259,310)(260,311)(261,312)(262,313)
(263,314)(264,315)(265,316)(266,317)(267,318)(268,319)(269,320)(270,321)
(271,322)(272,323)(273,290)(274,291)(275,292)(276,293)(277,294)(278,295)
(279,296)(280,297)(281,298)(282,299)(283,300)(284,301)(285,302)(286,303)
(287,304)(288,305)(289,306);
s1 := Sym(374)!(  1, 18)(  2, 34)(  3, 33)(  4, 32)(  5, 31)(  6, 30)(  7, 29)
(  8, 28)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 35,171)( 36,187)( 37,186)( 38,185)( 39,184)( 40,183)
( 41,182)( 42,181)( 43,180)( 44,179)( 45,178)( 46,177)( 47,176)( 48,175)
( 49,174)( 50,173)( 51,172)( 52,154)( 53,170)( 54,169)( 55,168)( 56,167)
( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)
( 65,158)( 66,157)( 67,156)( 68,155)( 69,137)( 70,153)( 71,152)( 72,151)
( 73,150)( 74,149)( 75,148)( 76,147)( 77,146)( 78,145)( 79,144)( 80,143)
( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,120)( 87,136)( 88,135)
( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)( 94,129)( 95,128)( 96,127)
( 97,126)( 98,125)( 99,124)(100,123)(101,122)(102,121)(104,119)(105,118)
(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(188,205)(189,221)
(190,220)(191,219)(192,218)(193,217)(194,216)(195,215)(196,214)(197,213)
(198,212)(199,211)(200,210)(201,209)(202,208)(203,207)(204,206)(222,358)
(223,374)(224,373)(225,372)(226,371)(227,370)(228,369)(229,368)(230,367)
(231,366)(232,365)(233,364)(234,363)(235,362)(236,361)(237,360)(238,359)
(239,341)(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,351)
(247,350)(248,349)(249,348)(250,347)(251,346)(252,345)(253,344)(254,343)
(255,342)(256,324)(257,340)(258,339)(259,338)(260,337)(261,336)(262,335)
(263,334)(264,333)(265,332)(266,331)(267,330)(268,329)(269,328)(270,327)
(271,326)(272,325)(273,307)(274,323)(275,322)(276,321)(277,320)(278,319)
(279,318)(280,317)(281,316)(282,315)(283,314)(284,313)(285,312)(286,311)
(287,310)(288,309)(289,308)(291,306)(292,305)(293,304)(294,303)(295,302)
(296,301)(297,300)(298,299);
s2 := Sym(374)!(  1,189)(  2,188)(  3,204)(  4,203)(  5,202)(  6,201)(  7,200)
(  8,199)(  9,198)( 10,197)( 11,196)( 12,195)( 13,194)( 14,193)( 15,192)
( 16,191)( 17,190)( 18,206)( 19,205)( 20,221)( 21,220)( 22,219)( 23,218)
( 24,217)( 25,216)( 26,215)( 27,214)( 28,213)( 29,212)( 30,211)( 31,210)
( 32,209)( 33,208)( 34,207)( 35,223)( 36,222)( 37,238)( 38,237)( 39,236)
( 40,235)( 41,234)( 42,233)( 43,232)( 44,231)( 45,230)( 46,229)( 47,228)
( 48,227)( 49,226)( 50,225)( 51,224)( 52,240)( 53,239)( 54,255)( 55,254)
( 56,253)( 57,252)( 58,251)( 59,250)( 60,249)( 61,248)( 62,247)( 63,246)
( 64,245)( 65,244)( 66,243)( 67,242)( 68,241)( 69,257)( 70,256)( 71,272)
( 72,271)( 73,270)( 74,269)( 75,268)( 76,267)( 77,266)( 78,265)( 79,264)
( 80,263)( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,274)( 87,273)
( 88,289)( 89,288)( 90,287)( 91,286)( 92,285)( 93,284)( 94,283)( 95,282)
( 96,281)( 97,280)( 98,279)( 99,278)(100,277)(101,276)(102,275)(103,291)
(104,290)(105,306)(106,305)(107,304)(108,303)(109,302)(110,301)(111,300)
(112,299)(113,298)(114,297)(115,296)(116,295)(117,294)(118,293)(119,292)
(120,308)(121,307)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)
(128,317)(129,316)(130,315)(131,314)(132,313)(133,312)(134,311)(135,310)
(136,309)(137,325)(138,324)(139,340)(140,339)(141,338)(142,337)(143,336)
(144,335)(145,334)(146,333)(147,332)(148,331)(149,330)(150,329)(151,328)
(152,327)(153,326)(154,342)(155,341)(156,357)(157,356)(158,355)(159,354)
(160,353)(161,352)(162,351)(163,350)(164,349)(165,348)(166,347)(167,346)
(168,345)(169,344)(170,343)(171,359)(172,358)(173,374)(174,373)(175,372)
(176,371)(177,370)(178,369)(179,368)(180,367)(181,366)(182,365)(183,364)
(184,363)(185,362)(186,361)(187,360);
poly := sub<Sym(374)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s1*s2 >; 
 
References : None.
to this polytope