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Polytope of Type {130,6}

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