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