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Polytope of Type {134,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {134,6}*1608
Also Known As : {134,6|2}. if this polytope has another name.
Group : SmallGroup(1608,47)
Rank : 3
Schlafli Type : {134,6}
Number of vertices, edges, etc : 134, 402, 6
Order of s0s1s2 : 402
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) :
   3-fold quotients : {134,2}*536
   6-fold quotients : {67,2}*268
   67-fold quotients : {2,6}*24
   134-fold quotients : {2,3}*12
   201-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2, 67)(  3, 66)(  4, 65)(  5, 64)(  6, 63)(  7, 62)(  8, 61)(  9, 60)
( 10, 59)( 11, 58)( 12, 57)( 13, 56)( 14, 55)( 15, 54)( 16, 53)( 17, 52)
( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 45)( 25, 44)
( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)
( 34, 35)( 69,134)( 70,133)( 71,132)( 72,131)( 73,130)( 74,129)( 75,128)
( 76,127)( 77,126)( 78,125)( 79,124)( 80,123)( 81,122)( 82,121)( 83,120)
( 84,119)( 85,118)( 86,117)( 87,116)( 88,115)( 89,114)( 90,113)( 91,112)
( 92,111)( 93,110)( 94,109)( 95,108)( 96,107)( 97,106)( 98,105)( 99,104)
(100,103)(101,102)(136,201)(137,200)(138,199)(139,198)(140,197)(141,196)
(142,195)(143,194)(144,193)(145,192)(146,191)(147,190)(148,189)(149,188)
(150,187)(151,186)(152,185)(153,184)(154,183)(155,182)(156,181)(157,180)
(158,179)(159,178)(160,177)(161,176)(162,175)(163,174)(164,173)(165,172)
(166,171)(167,170)(168,169)(203,268)(204,267)(205,266)(206,265)(207,264)
(208,263)(209,262)(210,261)(211,260)(212,259)(213,258)(214,257)(215,256)
(216,255)(217,254)(218,253)(219,252)(220,251)(221,250)(222,249)(223,248)
(224,247)(225,246)(226,245)(227,244)(228,243)(229,242)(230,241)(231,240)
(232,239)(233,238)(234,237)(235,236)(270,335)(271,334)(272,333)(273,332)
(274,331)(275,330)(276,329)(277,328)(278,327)(279,326)(280,325)(281,324)
(282,323)(283,322)(284,321)(285,320)(286,319)(287,318)(288,317)(289,316)
(290,315)(291,314)(292,313)(293,312)(294,311)(295,310)(296,309)(297,308)
(298,307)(299,306)(300,305)(301,304)(302,303)(337,402)(338,401)(339,400)
(340,399)(341,398)(342,397)(343,396)(344,395)(345,394)(346,393)(347,392)
(348,391)(349,390)(350,389)(351,388)(352,387)(353,386)(354,385)(355,384)
(356,383)(357,382)(358,381)(359,380)(360,379)(361,378)(362,377)(363,376)
(364,375)(365,374)(366,373)(367,372)(368,371)(369,370);;
s1 := (  1,  2)(  3, 67)(  4, 66)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)
( 10, 60)( 11, 59)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)( 17, 53)
( 18, 52)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)( 25, 45)
( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)( 33, 37)
( 34, 36)( 68,136)( 69,135)( 70,201)( 71,200)( 72,199)( 73,198)( 74,197)
( 75,196)( 76,195)( 77,194)( 78,193)( 79,192)( 80,191)( 81,190)( 82,189)
( 83,188)( 84,187)( 85,186)( 86,185)( 87,184)( 88,183)( 89,182)( 90,181)
( 91,180)( 92,179)( 93,178)( 94,177)( 95,176)( 96,175)( 97,174)( 98,173)
( 99,172)(100,171)(101,170)(102,169)(103,168)(104,167)(105,166)(106,165)
(107,164)(108,163)(109,162)(110,161)(111,160)(112,159)(113,158)(114,157)
(115,156)(116,155)(117,154)(118,153)(119,152)(120,151)(121,150)(122,149)
(123,148)(124,147)(125,146)(126,145)(127,144)(128,143)(129,142)(130,141)
(131,140)(132,139)(133,138)(134,137)(202,203)(204,268)(205,267)(206,266)
(207,265)(208,264)(209,263)(210,262)(211,261)(212,260)(213,259)(214,258)
(215,257)(216,256)(217,255)(218,254)(219,253)(220,252)(221,251)(222,250)
(223,249)(224,248)(225,247)(226,246)(227,245)(228,244)(229,243)(230,242)
(231,241)(232,240)(233,239)(234,238)(235,237)(269,337)(270,336)(271,402)
(272,401)(273,400)(274,399)(275,398)(276,397)(277,396)(278,395)(279,394)
(280,393)(281,392)(282,391)(283,390)(284,389)(285,388)(286,387)(287,386)
(288,385)(289,384)(290,383)(291,382)(292,381)(293,380)(294,379)(295,378)
(296,377)(297,376)(298,375)(299,374)(300,373)(301,372)(302,371)(303,370)
(304,369)(305,368)(306,367)(307,366)(308,365)(309,364)(310,363)(311,362)
(312,361)(313,360)(314,359)(315,358)(316,357)(317,356)(318,355)(319,354)
(320,353)(321,352)(322,351)(323,350)(324,349)(325,348)(326,347)(327,346)
(328,345)(329,344)(330,343)(331,342)(332,341)(333,340)(334,339)(335,338);;
s2 := (  1,269)(  2,270)(  3,271)(  4,272)(  5,273)(  6,274)(  7,275)(  8,276)
(  9,277)( 10,278)( 11,279)( 12,280)( 13,281)( 14,282)( 15,283)( 16,284)
( 17,285)( 18,286)( 19,287)( 20,288)( 21,289)( 22,290)( 23,291)( 24,292)
( 25,293)( 26,294)( 27,295)( 28,296)( 29,297)( 30,298)( 31,299)( 32,300)
( 33,301)( 34,302)( 35,303)( 36,304)( 37,305)( 38,306)( 39,307)( 40,308)
( 41,309)( 42,310)( 43,311)( 44,312)( 45,313)( 46,314)( 47,315)( 48,316)
( 49,317)( 50,318)( 51,319)( 52,320)( 53,321)( 54,322)( 55,323)( 56,324)
( 57,325)( 58,326)( 59,327)( 60,328)( 61,329)( 62,330)( 63,331)( 64,332)
( 65,333)( 66,334)( 67,335)( 68,202)( 69,203)( 70,204)( 71,205)( 72,206)
( 73,207)( 74,208)( 75,209)( 76,210)( 77,211)( 78,212)( 79,213)( 80,214)
( 81,215)( 82,216)( 83,217)( 84,218)( 85,219)( 86,220)( 87,221)( 88,222)
( 89,223)( 90,224)( 91,225)( 92,226)( 93,227)( 94,228)( 95,229)( 96,230)
( 97,231)( 98,232)( 99,233)(100,234)(101,235)(102,236)(103,237)(104,238)
(105,239)(106,240)(107,241)(108,242)(109,243)(110,244)(111,245)(112,246)
(113,247)(114,248)(115,249)(116,250)(117,251)(118,252)(119,253)(120,254)
(121,255)(122,256)(123,257)(124,258)(125,259)(126,260)(127,261)(128,262)
(129,263)(130,264)(131,265)(132,266)(133,267)(134,268)(135,336)(136,337)
(137,338)(138,339)(139,340)(140,341)(141,342)(142,343)(143,344)(144,345)
(145,346)(146,347)(147,348)(148,349)(149,350)(150,351)(151,352)(152,353)
(153,354)(154,355)(155,356)(156,357)(157,358)(158,359)(159,360)(160,361)
(161,362)(162,363)(163,364)(164,365)(165,366)(166,367)(167,368)(168,369)
(169,370)(170,371)(171,372)(172,373)(173,374)(174,375)(175,376)(176,377)
(177,378)(178,379)(179,380)(180,381)(181,382)(182,383)(183,384)(184,385)
(185,386)(186,387)(187,388)(188,389)(189,390)(190,391)(191,392)(192,393)
(193,394)(194,395)(195,396)(196,397)(197,398)(198,399)(199,400)(200,401)
(201,402);;
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, 
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*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*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*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(402)!(  2, 67)(  3, 66)(  4, 65)(  5, 64)(  6, 63)(  7, 62)(  8, 61)
(  9, 60)( 10, 59)( 11, 58)( 12, 57)( 13, 56)( 14, 55)( 15, 54)( 16, 53)
( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 46)( 24, 45)
( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)
( 33, 36)( 34, 35)( 69,134)( 70,133)( 71,132)( 72,131)( 73,130)( 74,129)
( 75,128)( 76,127)( 77,126)( 78,125)( 79,124)( 80,123)( 81,122)( 82,121)
( 83,120)( 84,119)( 85,118)( 86,117)( 87,116)( 88,115)( 89,114)( 90,113)
( 91,112)( 92,111)( 93,110)( 94,109)( 95,108)( 96,107)( 97,106)( 98,105)
( 99,104)(100,103)(101,102)(136,201)(137,200)(138,199)(139,198)(140,197)
(141,196)(142,195)(143,194)(144,193)(145,192)(146,191)(147,190)(148,189)
(149,188)(150,187)(151,186)(152,185)(153,184)(154,183)(155,182)(156,181)
(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)(163,174)(164,173)
(165,172)(166,171)(167,170)(168,169)(203,268)(204,267)(205,266)(206,265)
(207,264)(208,263)(209,262)(210,261)(211,260)(212,259)(213,258)(214,257)
(215,256)(216,255)(217,254)(218,253)(219,252)(220,251)(221,250)(222,249)
(223,248)(224,247)(225,246)(226,245)(227,244)(228,243)(229,242)(230,241)
(231,240)(232,239)(233,238)(234,237)(235,236)(270,335)(271,334)(272,333)
(273,332)(274,331)(275,330)(276,329)(277,328)(278,327)(279,326)(280,325)
(281,324)(282,323)(283,322)(284,321)(285,320)(286,319)(287,318)(288,317)
(289,316)(290,315)(291,314)(292,313)(293,312)(294,311)(295,310)(296,309)
(297,308)(298,307)(299,306)(300,305)(301,304)(302,303)(337,402)(338,401)
(339,400)(340,399)(341,398)(342,397)(343,396)(344,395)(345,394)(346,393)
(347,392)(348,391)(349,390)(350,389)(351,388)(352,387)(353,386)(354,385)
(355,384)(356,383)(357,382)(358,381)(359,380)(360,379)(361,378)(362,377)
(363,376)(364,375)(365,374)(366,373)(367,372)(368,371)(369,370);
s1 := Sym(402)!(  1,  2)(  3, 67)(  4, 66)(  5, 65)(  6, 64)(  7, 63)(  8, 62)
(  9, 61)( 10, 60)( 11, 59)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)
( 17, 53)( 18, 52)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)
( 25, 45)( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)
( 33, 37)( 34, 36)( 68,136)( 69,135)( 70,201)( 71,200)( 72,199)( 73,198)
( 74,197)( 75,196)( 76,195)( 77,194)( 78,193)( 79,192)( 80,191)( 81,190)
( 82,189)( 83,188)( 84,187)( 85,186)( 86,185)( 87,184)( 88,183)( 89,182)
( 90,181)( 91,180)( 92,179)( 93,178)( 94,177)( 95,176)( 96,175)( 97,174)
( 98,173)( 99,172)(100,171)(101,170)(102,169)(103,168)(104,167)(105,166)
(106,165)(107,164)(108,163)(109,162)(110,161)(111,160)(112,159)(113,158)
(114,157)(115,156)(116,155)(117,154)(118,153)(119,152)(120,151)(121,150)
(122,149)(123,148)(124,147)(125,146)(126,145)(127,144)(128,143)(129,142)
(130,141)(131,140)(132,139)(133,138)(134,137)(202,203)(204,268)(205,267)
(206,266)(207,265)(208,264)(209,263)(210,262)(211,261)(212,260)(213,259)
(214,258)(215,257)(216,256)(217,255)(218,254)(219,253)(220,252)(221,251)
(222,250)(223,249)(224,248)(225,247)(226,246)(227,245)(228,244)(229,243)
(230,242)(231,241)(232,240)(233,239)(234,238)(235,237)(269,337)(270,336)
(271,402)(272,401)(273,400)(274,399)(275,398)(276,397)(277,396)(278,395)
(279,394)(280,393)(281,392)(282,391)(283,390)(284,389)(285,388)(286,387)
(287,386)(288,385)(289,384)(290,383)(291,382)(292,381)(293,380)(294,379)
(295,378)(296,377)(297,376)(298,375)(299,374)(300,373)(301,372)(302,371)
(303,370)(304,369)(305,368)(306,367)(307,366)(308,365)(309,364)(310,363)
(311,362)(312,361)(313,360)(314,359)(315,358)(316,357)(317,356)(318,355)
(319,354)(320,353)(321,352)(322,351)(323,350)(324,349)(325,348)(326,347)
(327,346)(328,345)(329,344)(330,343)(331,342)(332,341)(333,340)(334,339)
(335,338);
s2 := Sym(402)!(  1,269)(  2,270)(  3,271)(  4,272)(  5,273)(  6,274)(  7,275)
(  8,276)(  9,277)( 10,278)( 11,279)( 12,280)( 13,281)( 14,282)( 15,283)
( 16,284)( 17,285)( 18,286)( 19,287)( 20,288)( 21,289)( 22,290)( 23,291)
( 24,292)( 25,293)( 26,294)( 27,295)( 28,296)( 29,297)( 30,298)( 31,299)
( 32,300)( 33,301)( 34,302)( 35,303)( 36,304)( 37,305)( 38,306)( 39,307)
( 40,308)( 41,309)( 42,310)( 43,311)( 44,312)( 45,313)( 46,314)( 47,315)
( 48,316)( 49,317)( 50,318)( 51,319)( 52,320)( 53,321)( 54,322)( 55,323)
( 56,324)( 57,325)( 58,326)( 59,327)( 60,328)( 61,329)( 62,330)( 63,331)
( 64,332)( 65,333)( 66,334)( 67,335)( 68,202)( 69,203)( 70,204)( 71,205)
( 72,206)( 73,207)( 74,208)( 75,209)( 76,210)( 77,211)( 78,212)( 79,213)
( 80,214)( 81,215)( 82,216)( 83,217)( 84,218)( 85,219)( 86,220)( 87,221)
( 88,222)( 89,223)( 90,224)( 91,225)( 92,226)( 93,227)( 94,228)( 95,229)
( 96,230)( 97,231)( 98,232)( 99,233)(100,234)(101,235)(102,236)(103,237)
(104,238)(105,239)(106,240)(107,241)(108,242)(109,243)(110,244)(111,245)
(112,246)(113,247)(114,248)(115,249)(116,250)(117,251)(118,252)(119,253)
(120,254)(121,255)(122,256)(123,257)(124,258)(125,259)(126,260)(127,261)
(128,262)(129,263)(130,264)(131,265)(132,266)(133,267)(134,268)(135,336)
(136,337)(137,338)(138,339)(139,340)(140,341)(141,342)(142,343)(143,344)
(144,345)(145,346)(146,347)(147,348)(148,349)(149,350)(150,351)(151,352)
(152,353)(153,354)(154,355)(155,356)(156,357)(157,358)(158,359)(159,360)
(160,361)(161,362)(162,363)(163,364)(164,365)(165,366)(166,367)(167,368)
(168,369)(169,370)(170,371)(171,372)(172,373)(173,374)(174,375)(175,376)
(176,377)(177,378)(178,379)(179,380)(180,381)(181,382)(182,383)(183,384)
(184,385)(185,386)(186,387)(187,388)(188,389)(189,390)(190,391)(191,392)
(192,393)(193,394)(194,395)(195,396)(196,397)(197,398)(198,399)(199,400)
(200,401)(201,402);
poly := sub<Sym(402)|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, 
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope