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Polytope of Type {24,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,34}*1632
Also Known As : {24,34|2}. if this polytope has another name.
Group : SmallGroup(1632,320)
Rank : 3
Schlafli Type : {24,34}
Number of vertices, edges, etc : 24, 408, 34
Order of s0s1s2 : 408
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) :
   2-fold quotients : {12,34}*816
   3-fold quotients : {8,34}*544
   4-fold quotients : {6,34}*408
   6-fold quotients : {4,34}*272
   12-fold quotients : {2,34}*136
   17-fold quotients : {24,2}*96
   24-fold quotients : {2,17}*68
   34-fold quotients : {12,2}*48
   51-fold quotients : {8,2}*32
   68-fold quotients : {6,2}*24
   102-fold quotients : {4,2}*16
   136-fold quotients : {3,2}*12
   204-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 18, 35)( 19, 36)( 20, 37)( 21, 38)( 22, 39)( 23, 40)( 24, 41)( 25, 42)
( 26, 43)( 27, 44)( 28, 45)( 29, 46)( 30, 47)( 31, 48)( 32, 49)( 33, 50)
( 34, 51)( 69, 86)( 70, 87)( 71, 88)( 72, 89)( 73, 90)( 74, 91)( 75, 92)
( 76, 93)( 77, 94)( 78, 95)( 79, 96)( 80, 97)( 81, 98)( 82, 99)( 83,100)
( 84,101)( 85,102)(103,154)(104,155)(105,156)(106,157)(107,158)(108,159)
(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)
(117,168)(118,169)(119,170)(120,188)(121,189)(122,190)(123,191)(124,192)
(125,193)(126,194)(127,195)(128,196)(129,197)(130,198)(131,199)(132,200)
(133,201)(134,202)(135,203)(136,204)(137,171)(138,172)(139,173)(140,174)
(141,175)(142,176)(143,177)(144,178)(145,179)(146,180)(147,181)(148,182)
(149,183)(150,184)(151,185)(152,186)(153,187)(205,307)(206,308)(207,309)
(208,310)(209,311)(210,312)(211,313)(212,314)(213,315)(214,316)(215,317)
(216,318)(217,319)(218,320)(219,321)(220,322)(221,323)(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)
(256,358)(257,359)(258,360)(259,361)(260,362)(261,363)(262,364)(263,365)
(264,366)(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,373)
(272,374)(273,392)(274,393)(275,394)(276,395)(277,396)(278,397)(279,398)
(280,399)(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)(287,406)
(288,407)(289,408)(290,375)(291,376)(292,377)(293,378)(294,379)(295,380)
(296,381)(297,382)(298,383)(299,384)(300,385)(301,386)(302,387)(303,388)
(304,389)(305,390)(306,391);;
s1 := (  1,222)(  2,238)(  3,237)(  4,236)(  5,235)(  6,234)(  7,233)(  8,232)
(  9,231)( 10,230)( 11,229)( 12,228)( 13,227)( 14,226)( 15,225)( 16,224)
( 17,223)( 18,205)( 19,221)( 20,220)( 21,219)( 22,218)( 23,217)( 24,216)
( 25,215)( 26,214)( 27,213)( 28,212)( 29,211)( 30,210)( 31,209)( 32,208)
( 33,207)( 34,206)( 35,239)( 36,255)( 37,254)( 38,253)( 39,252)( 40,251)
( 41,250)( 42,249)( 43,248)( 44,247)( 45,246)( 46,245)( 47,244)( 48,243)
( 49,242)( 50,241)( 51,240)( 52,273)( 53,289)( 54,288)( 55,287)( 56,286)
( 57,285)( 58,284)( 59,283)( 60,282)( 61,281)( 62,280)( 63,279)( 64,278)
( 65,277)( 66,276)( 67,275)( 68,274)( 69,256)( 70,272)( 71,271)( 72,270)
( 73,269)( 74,268)( 75,267)( 76,266)( 77,265)( 78,264)( 79,263)( 80,262)
( 81,261)( 82,260)( 83,259)( 84,258)( 85,257)( 86,290)( 87,306)( 88,305)
( 89,304)( 90,303)( 91,302)( 92,301)( 93,300)( 94,299)( 95,298)( 96,297)
( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,375)(104,391)
(105,390)(106,389)(107,388)(108,387)(109,386)(110,385)(111,384)(112,383)
(113,382)(114,381)(115,380)(116,379)(117,378)(118,377)(119,376)(120,358)
(121,374)(122,373)(123,372)(124,371)(125,370)(126,369)(127,368)(128,367)
(129,366)(130,365)(131,364)(132,363)(133,362)(134,361)(135,360)(136,359)
(137,392)(138,408)(139,407)(140,406)(141,405)(142,404)(143,403)(144,402)
(145,401)(146,400)(147,399)(148,398)(149,397)(150,396)(151,395)(152,394)
(153,393)(154,324)(155,340)(156,339)(157,338)(158,337)(159,336)(160,335)
(161,334)(162,333)(163,332)(164,331)(165,330)(166,329)(167,328)(168,327)
(169,326)(170,325)(171,307)(172,323)(173,322)(174,321)(175,320)(176,319)
(177,318)(178,317)(179,316)(180,315)(181,314)(182,313)(183,312)(184,311)
(185,310)(186,309)(187,308)(188,341)(189,357)(190,356)(191,355)(192,354)
(193,353)(194,352)(195,351)(196,350)(197,349)(198,348)(199,347)(200,346)
(201,345)(202,344)(203,343)(204,342);;
s2 := (  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)
( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)
( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)
( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)
( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)
(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)(111,113)
(120,121)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130)
(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)
(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)
(171,172)(173,187)(174,186)(175,185)(176,184)(177,183)(178,182)(179,181)
(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)
(205,206)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)(213,215)
(222,223)(224,238)(225,237)(226,236)(227,235)(228,234)(229,233)(230,232)
(239,240)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)
(256,257)(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)(264,266)
(273,274)(275,289)(276,288)(277,287)(278,286)(279,285)(280,284)(281,283)
(290,291)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)(298,300)
(307,308)(309,323)(310,322)(311,321)(312,320)(313,319)(314,318)(315,317)
(324,325)(326,340)(327,339)(328,338)(329,337)(330,336)(331,335)(332,334)
(341,342)(343,357)(344,356)(345,355)(346,354)(347,353)(348,352)(349,351)
(358,359)(360,374)(361,373)(362,372)(363,371)(364,370)(365,369)(366,368)
(375,376)(377,391)(378,390)(379,389)(380,388)(381,387)(382,386)(383,385)
(392,393)(394,408)(395,407)(396,406)(397,405)(398,404)(399,403)(400,402);;
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*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(408)!( 18, 35)( 19, 36)( 20, 37)( 21, 38)( 22, 39)( 23, 40)( 24, 41)
( 25, 42)( 26, 43)( 27, 44)( 28, 45)( 29, 46)( 30, 47)( 31, 48)( 32, 49)
( 33, 50)( 34, 51)( 69, 86)( 70, 87)( 71, 88)( 72, 89)( 73, 90)( 74, 91)
( 75, 92)( 76, 93)( 77, 94)( 78, 95)( 79, 96)( 80, 97)( 81, 98)( 82, 99)
( 83,100)( 84,101)( 85,102)(103,154)(104,155)(105,156)(106,157)(107,158)
(108,159)(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)
(116,167)(117,168)(118,169)(119,170)(120,188)(121,189)(122,190)(123,191)
(124,192)(125,193)(126,194)(127,195)(128,196)(129,197)(130,198)(131,199)
(132,200)(133,201)(134,202)(135,203)(136,204)(137,171)(138,172)(139,173)
(140,174)(141,175)(142,176)(143,177)(144,178)(145,179)(146,180)(147,181)
(148,182)(149,183)(150,184)(151,185)(152,186)(153,187)(205,307)(206,308)
(207,309)(208,310)(209,311)(210,312)(211,313)(212,314)(213,315)(214,316)
(215,317)(216,318)(217,319)(218,320)(219,321)(220,322)(221,323)(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)(256,358)(257,359)(258,360)(259,361)(260,362)(261,363)(262,364)
(263,365)(264,366)(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)
(271,373)(272,374)(273,392)(274,393)(275,394)(276,395)(277,396)(278,397)
(279,398)(280,399)(281,400)(282,401)(283,402)(284,403)(285,404)(286,405)
(287,406)(288,407)(289,408)(290,375)(291,376)(292,377)(293,378)(294,379)
(295,380)(296,381)(297,382)(298,383)(299,384)(300,385)(301,386)(302,387)
(303,388)(304,389)(305,390)(306,391);
s1 := Sym(408)!(  1,222)(  2,238)(  3,237)(  4,236)(  5,235)(  6,234)(  7,233)
(  8,232)(  9,231)( 10,230)( 11,229)( 12,228)( 13,227)( 14,226)( 15,225)
( 16,224)( 17,223)( 18,205)( 19,221)( 20,220)( 21,219)( 22,218)( 23,217)
( 24,216)( 25,215)( 26,214)( 27,213)( 28,212)( 29,211)( 30,210)( 31,209)
( 32,208)( 33,207)( 34,206)( 35,239)( 36,255)( 37,254)( 38,253)( 39,252)
( 40,251)( 41,250)( 42,249)( 43,248)( 44,247)( 45,246)( 46,245)( 47,244)
( 48,243)( 49,242)( 50,241)( 51,240)( 52,273)( 53,289)( 54,288)( 55,287)
( 56,286)( 57,285)( 58,284)( 59,283)( 60,282)( 61,281)( 62,280)( 63,279)
( 64,278)( 65,277)( 66,276)( 67,275)( 68,274)( 69,256)( 70,272)( 71,271)
( 72,270)( 73,269)( 74,268)( 75,267)( 76,266)( 77,265)( 78,264)( 79,263)
( 80,262)( 81,261)( 82,260)( 83,259)( 84,258)( 85,257)( 86,290)( 87,306)
( 88,305)( 89,304)( 90,303)( 91,302)( 92,301)( 93,300)( 94,299)( 95,298)
( 96,297)( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,375)
(104,391)(105,390)(106,389)(107,388)(108,387)(109,386)(110,385)(111,384)
(112,383)(113,382)(114,381)(115,380)(116,379)(117,378)(118,377)(119,376)
(120,358)(121,374)(122,373)(123,372)(124,371)(125,370)(126,369)(127,368)
(128,367)(129,366)(130,365)(131,364)(132,363)(133,362)(134,361)(135,360)
(136,359)(137,392)(138,408)(139,407)(140,406)(141,405)(142,404)(143,403)
(144,402)(145,401)(146,400)(147,399)(148,398)(149,397)(150,396)(151,395)
(152,394)(153,393)(154,324)(155,340)(156,339)(157,338)(158,337)(159,336)
(160,335)(161,334)(162,333)(163,332)(164,331)(165,330)(166,329)(167,328)
(168,327)(169,326)(170,325)(171,307)(172,323)(173,322)(174,321)(175,320)
(176,319)(177,318)(178,317)(179,316)(180,315)(181,314)(182,313)(183,312)
(184,311)(185,310)(186,309)(187,308)(188,341)(189,357)(190,356)(191,355)
(192,354)(193,353)(194,352)(195,351)(196,350)(197,349)(198,348)(199,347)
(200,346)(201,345)(202,344)(203,343)(204,342);
s2 := Sym(408)!(  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)
(  9, 11)( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)
( 26, 28)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 45)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)
( 60, 62)( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)
( 94, 96)(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)
(111,113)(120,121)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)
(128,130)(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)
(145,147)(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)
(162,164)(171,172)(173,187)(174,186)(175,185)(176,184)(177,183)(178,182)
(179,181)(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)
(196,198)(205,206)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)
(213,215)(222,223)(224,238)(225,237)(226,236)(227,235)(228,234)(229,233)
(230,232)(239,240)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)
(247,249)(256,257)(258,272)(259,271)(260,270)(261,269)(262,268)(263,267)
(264,266)(273,274)(275,289)(276,288)(277,287)(278,286)(279,285)(280,284)
(281,283)(290,291)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)
(298,300)(307,308)(309,323)(310,322)(311,321)(312,320)(313,319)(314,318)
(315,317)(324,325)(326,340)(327,339)(328,338)(329,337)(330,336)(331,335)
(332,334)(341,342)(343,357)(344,356)(345,355)(346,354)(347,353)(348,352)
(349,351)(358,359)(360,374)(361,373)(362,372)(363,371)(364,370)(365,369)
(366,368)(375,376)(377,391)(378,390)(379,389)(380,388)(381,387)(382,386)
(383,385)(392,393)(394,408)(395,407)(396,406)(397,405)(398,404)(399,403)
(400,402);
poly := sub<Sym(408)|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*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