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Polytope of Type {6,130}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,130}*1560
Also Known As : {6,130|2}. if this polytope has another name.
Group : SmallGroup(1560,209)
Rank : 3
Schlafli Type : {6,130}
Number of vertices, edges, etc : 6, 390, 130
Order of s0s1s2 : 390
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 : {2,130}*520
   5-fold quotients : {6,26}*312
   6-fold quotients : {2,65}*260
   13-fold quotients : {6,10}*120
   15-fold quotients : {2,26}*104
   30-fold quotients : {2,13}*52
   39-fold quotients : {2,10}*40
   65-fold quotients : {6,2}*24
   78-fold quotients : {2,5}*20
   130-fold quotients : {3,2}*12
   195-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 66,131)( 67,132)( 68,133)( 69,134)( 70,135)( 71,136)( 72,137)( 73,138)
( 74,139)( 75,140)( 76,141)( 77,142)( 78,143)( 79,144)( 80,145)( 81,146)
( 82,147)( 83,148)( 84,149)( 85,150)( 86,151)( 87,152)( 88,153)( 89,154)
( 90,155)( 91,156)( 92,157)( 93,158)( 94,159)( 95,160)( 96,161)( 97,162)
( 98,163)( 99,164)(100,165)(101,166)(102,167)(103,168)(104,169)(105,170)
(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)
(114,179)(115,180)(116,181)(117,182)(118,183)(119,184)(120,185)(121,186)
(122,187)(123,188)(124,189)(125,190)(126,191)(127,192)(128,193)(129,194)
(130,195)(261,326)(262,327)(263,328)(264,329)(265,330)(266,331)(267,332)
(268,333)(269,334)(270,335)(271,336)(272,337)(273,338)(274,339)(275,340)
(276,341)(277,342)(278,343)(279,344)(280,345)(281,346)(282,347)(283,348)
(284,349)(285,350)(286,351)(287,352)(288,353)(289,354)(290,355)(291,356)
(292,357)(293,358)(294,359)(295,360)(296,361)(297,362)(298,363)(299,364)
(300,365)(301,366)(302,367)(303,368)(304,369)(305,370)(306,371)(307,372)
(308,373)(309,374)(310,375)(311,376)(312,377)(313,378)(314,379)(315,380)
(316,381)(317,382)(318,383)(319,384)(320,385)(321,386)(322,387)(323,388)
(324,389)(325,390);;
s1 := (  1, 66)(  2, 78)(  3, 77)(  4, 76)(  5, 75)(  6, 74)(  7, 73)(  8, 72)
(  9, 71)( 10, 70)( 11, 69)( 12, 68)( 13, 67)( 14,118)( 15,130)( 16,129)
( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)
( 25,120)( 26,119)( 27,105)( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)
( 33,112)( 34,111)( 35,110)( 36,109)( 37,108)( 38,107)( 39,106)( 40, 92)
( 41,104)( 42,103)( 43,102)( 44,101)( 45,100)( 46, 99)( 47, 98)( 48, 97)
( 49, 96)( 50, 95)( 51, 94)( 52, 93)( 53, 79)( 54, 91)( 55, 90)( 56, 89)
( 57, 88)( 58, 87)( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 82)( 64, 81)
( 65, 80)(132,143)(133,142)(134,141)(135,140)(136,139)(137,138)(144,183)
(145,195)(146,194)(147,193)(148,192)(149,191)(150,190)(151,189)(152,188)
(153,187)(154,186)(155,185)(156,184)(157,170)(158,182)(159,181)(160,180)
(161,179)(162,178)(163,177)(164,176)(165,175)(166,174)(167,173)(168,172)
(169,171)(196,261)(197,273)(198,272)(199,271)(200,270)(201,269)(202,268)
(203,267)(204,266)(205,265)(206,264)(207,263)(208,262)(209,313)(210,325)
(211,324)(212,323)(213,322)(214,321)(215,320)(216,319)(217,318)(218,317)
(219,316)(220,315)(221,314)(222,300)(223,312)(224,311)(225,310)(226,309)
(227,308)(228,307)(229,306)(230,305)(231,304)(232,303)(233,302)(234,301)
(235,287)(236,299)(237,298)(238,297)(239,296)(240,295)(241,294)(242,293)
(243,292)(244,291)(245,290)(246,289)(247,288)(248,274)(249,286)(250,285)
(251,284)(252,283)(253,282)(254,281)(255,280)(256,279)(257,278)(258,277)
(259,276)(260,275)(327,338)(328,337)(329,336)(330,335)(331,334)(332,333)
(339,378)(340,390)(341,389)(342,388)(343,387)(344,386)(345,385)(346,384)
(347,383)(348,382)(349,381)(350,380)(351,379)(352,365)(353,377)(354,376)
(355,375)(356,374)(357,373)(358,372)(359,371)(360,370)(361,369)(362,368)
(363,367)(364,366);;
s2 := (  1,210)(  2,209)(  3,221)(  4,220)(  5,219)(  6,218)(  7,217)(  8,216)
(  9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,197)( 15,196)( 16,208)
( 17,207)( 18,206)( 19,205)( 20,204)( 21,203)( 22,202)( 23,201)( 24,200)
( 25,199)( 26,198)( 27,249)( 28,248)( 29,260)( 30,259)( 31,258)( 32,257)
( 33,256)( 34,255)( 35,254)( 36,253)( 37,252)( 38,251)( 39,250)( 40,236)
( 41,235)( 42,247)( 43,246)( 44,245)( 45,244)( 46,243)( 47,242)( 48,241)
( 49,240)( 50,239)( 51,238)( 52,237)( 53,223)( 54,222)( 55,234)( 56,233)
( 57,232)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)( 64,225)
( 65,224)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)( 72,282)
( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,262)( 80,261)
( 81,273)( 82,272)( 83,271)( 84,270)( 85,269)( 86,268)( 87,267)( 88,266)
( 89,265)( 90,264)( 91,263)( 92,314)( 93,313)( 94,325)( 95,324)( 96,323)
( 97,322)( 98,321)( 99,320)(100,319)(101,318)(102,317)(103,316)(104,315)
(105,301)(106,300)(107,312)(108,311)(109,310)(110,309)(111,308)(112,307)
(113,306)(114,305)(115,304)(116,303)(117,302)(118,288)(119,287)(120,299)
(121,298)(122,297)(123,296)(124,295)(125,294)(126,293)(127,292)(128,291)
(129,290)(130,289)(131,340)(132,339)(133,351)(134,350)(135,349)(136,348)
(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)(144,327)
(145,326)(146,338)(147,337)(148,336)(149,335)(150,334)(151,333)(152,332)
(153,331)(154,330)(155,329)(156,328)(157,379)(158,378)(159,390)(160,389)
(161,388)(162,387)(163,386)(164,385)(165,384)(166,383)(167,382)(168,381)
(169,380)(170,366)(171,365)(172,377)(173,376)(174,375)(175,374)(176,373)
(177,372)(178,371)(179,370)(180,369)(181,368)(182,367)(183,353)(184,352)
(185,364)(186,363)(187,362)(188,361)(189,360)(190,359)(191,358)(192,357)
(193,356)(194,355)(195,354);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(390)!( 66,131)( 67,132)( 68,133)( 69,134)( 70,135)( 71,136)( 72,137)
( 73,138)( 74,139)( 75,140)( 76,141)( 77,142)( 78,143)( 79,144)( 80,145)
( 81,146)( 82,147)( 83,148)( 84,149)( 85,150)( 86,151)( 87,152)( 88,153)
( 89,154)( 90,155)( 91,156)( 92,157)( 93,158)( 94,159)( 95,160)( 96,161)
( 97,162)( 98,163)( 99,164)(100,165)(101,166)(102,167)(103,168)(104,169)
(105,170)(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)
(113,178)(114,179)(115,180)(116,181)(117,182)(118,183)(119,184)(120,185)
(121,186)(122,187)(123,188)(124,189)(125,190)(126,191)(127,192)(128,193)
(129,194)(130,195)(261,326)(262,327)(263,328)(264,329)(265,330)(266,331)
(267,332)(268,333)(269,334)(270,335)(271,336)(272,337)(273,338)(274,339)
(275,340)(276,341)(277,342)(278,343)(279,344)(280,345)(281,346)(282,347)
(283,348)(284,349)(285,350)(286,351)(287,352)(288,353)(289,354)(290,355)
(291,356)(292,357)(293,358)(294,359)(295,360)(296,361)(297,362)(298,363)
(299,364)(300,365)(301,366)(302,367)(303,368)(304,369)(305,370)(306,371)
(307,372)(308,373)(309,374)(310,375)(311,376)(312,377)(313,378)(314,379)
(315,380)(316,381)(317,382)(318,383)(319,384)(320,385)(321,386)(322,387)
(323,388)(324,389)(325,390);
s1 := Sym(390)!(  1, 66)(  2, 78)(  3, 77)(  4, 76)(  5, 75)(  6, 74)(  7, 73)
(  8, 72)(  9, 71)( 10, 70)( 11, 69)( 12, 68)( 13, 67)( 14,118)( 15,130)
( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)
( 24,121)( 25,120)( 26,119)( 27,105)( 28,117)( 29,116)( 30,115)( 31,114)
( 32,113)( 33,112)( 34,111)( 35,110)( 36,109)( 37,108)( 38,107)( 39,106)
( 40, 92)( 41,104)( 42,103)( 43,102)( 44,101)( 45,100)( 46, 99)( 47, 98)
( 48, 97)( 49, 96)( 50, 95)( 51, 94)( 52, 93)( 53, 79)( 54, 91)( 55, 90)
( 56, 89)( 57, 88)( 58, 87)( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 82)
( 64, 81)( 65, 80)(132,143)(133,142)(134,141)(135,140)(136,139)(137,138)
(144,183)(145,195)(146,194)(147,193)(148,192)(149,191)(150,190)(151,189)
(152,188)(153,187)(154,186)(155,185)(156,184)(157,170)(158,182)(159,181)
(160,180)(161,179)(162,178)(163,177)(164,176)(165,175)(166,174)(167,173)
(168,172)(169,171)(196,261)(197,273)(198,272)(199,271)(200,270)(201,269)
(202,268)(203,267)(204,266)(205,265)(206,264)(207,263)(208,262)(209,313)
(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)(216,319)(217,318)
(218,317)(219,316)(220,315)(221,314)(222,300)(223,312)(224,311)(225,310)
(226,309)(227,308)(228,307)(229,306)(230,305)(231,304)(232,303)(233,302)
(234,301)(235,287)(236,299)(237,298)(238,297)(239,296)(240,295)(241,294)
(242,293)(243,292)(244,291)(245,290)(246,289)(247,288)(248,274)(249,286)
(250,285)(251,284)(252,283)(253,282)(254,281)(255,280)(256,279)(257,278)
(258,277)(259,276)(260,275)(327,338)(328,337)(329,336)(330,335)(331,334)
(332,333)(339,378)(340,390)(341,389)(342,388)(343,387)(344,386)(345,385)
(346,384)(347,383)(348,382)(349,381)(350,380)(351,379)(352,365)(353,377)
(354,376)(355,375)(356,374)(357,373)(358,372)(359,371)(360,370)(361,369)
(362,368)(363,367)(364,366);
s2 := Sym(390)!(  1,210)(  2,209)(  3,221)(  4,220)(  5,219)(  6,218)(  7,217)
(  8,216)(  9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,197)( 15,196)
( 16,208)( 17,207)( 18,206)( 19,205)( 20,204)( 21,203)( 22,202)( 23,201)
( 24,200)( 25,199)( 26,198)( 27,249)( 28,248)( 29,260)( 30,259)( 31,258)
( 32,257)( 33,256)( 34,255)( 35,254)( 36,253)( 37,252)( 38,251)( 39,250)
( 40,236)( 41,235)( 42,247)( 43,246)( 44,245)( 45,244)( 46,243)( 47,242)
( 48,241)( 49,240)( 50,239)( 51,238)( 52,237)( 53,223)( 54,222)( 55,234)
( 56,233)( 57,232)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)
( 64,225)( 65,224)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)
( 72,282)( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,262)
( 80,261)( 81,273)( 82,272)( 83,271)( 84,270)( 85,269)( 86,268)( 87,267)
( 88,266)( 89,265)( 90,264)( 91,263)( 92,314)( 93,313)( 94,325)( 95,324)
( 96,323)( 97,322)( 98,321)( 99,320)(100,319)(101,318)(102,317)(103,316)
(104,315)(105,301)(106,300)(107,312)(108,311)(109,310)(110,309)(111,308)
(112,307)(113,306)(114,305)(115,304)(116,303)(117,302)(118,288)(119,287)
(120,299)(121,298)(122,297)(123,296)(124,295)(125,294)(126,293)(127,292)
(128,291)(129,290)(130,289)(131,340)(132,339)(133,351)(134,350)(135,349)
(136,348)(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)
(144,327)(145,326)(146,338)(147,337)(148,336)(149,335)(150,334)(151,333)
(152,332)(153,331)(154,330)(155,329)(156,328)(157,379)(158,378)(159,390)
(160,389)(161,388)(162,387)(163,386)(164,385)(165,384)(166,383)(167,382)
(168,381)(169,380)(170,366)(171,365)(172,377)(173,376)(174,375)(175,374)
(176,373)(177,372)(178,371)(179,370)(180,369)(181,368)(182,367)(183,353)
(184,352)(185,364)(186,363)(187,362)(188,361)(189,360)(190,359)(191,358)
(192,357)(193,356)(194,355)(195,354);
poly := sub<Sym(390)|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 >; 
 
References : None.
to this polytope