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Polytope of Type {26,30}

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