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Polytope of Type {6,134}

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