Polytope of Type {30,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,26}*1560
Also Known As : {30,26|2}. if this polytope has another name.
Group : SmallGroup(1560,206)
Rank : 3
Schlafli Type : {30,26}
Number of vertices, edges, etc : 30, 390, 26
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 : {10,26}*520
   5-fold quotients : {6,26}*312
   13-fold quotients : {30,2}*120
   15-fold quotients : {2,26}*104
   26-fold quotients : {15,2}*60
   30-fold quotients : {2,13}*52
   39-fold quotients : {10,2}*40
   65-fold quotients : {6,2}*24
   78-fold quotients : {5,2}*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 := ( 14, 53)( 15, 54)( 16, 55)( 17, 56)( 18, 57)( 19, 58)( 20, 59)( 21, 60)
( 22, 61)( 23, 62)( 24, 63)( 25, 64)( 26, 65)( 27, 40)( 28, 41)( 29, 42)
( 30, 43)( 31, 44)( 32, 45)( 33, 46)( 34, 47)( 35, 48)( 36, 49)( 37, 50)
( 38, 51)( 39, 52)( 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)( 79,183)
( 80,184)( 81,185)( 82,186)( 83,187)( 84,188)( 85,189)( 86,190)( 87,191)
( 88,192)( 89,193)( 90,194)( 91,195)( 92,170)( 93,171)( 94,172)( 95,173)
( 96,174)( 97,175)( 98,176)( 99,177)(100,178)(101,179)(102,180)(103,181)
(104,182)(105,157)(106,158)(107,159)(108,160)(109,161)(110,162)(111,163)
(112,164)(113,165)(114,166)(115,167)(116,168)(117,169)(118,144)(119,145)
(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)
(128,154)(129,155)(130,156)(209,248)(210,249)(211,250)(212,251)(213,252)
(214,253)(215,254)(216,255)(217,256)(218,257)(219,258)(220,259)(221,260)
(222,235)(223,236)(224,237)(225,238)(226,239)(227,240)(228,241)(229,242)
(230,243)(231,244)(232,245)(233,246)(234,247)(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)(274,378)(275,379)(276,380)(277,381)(278,382)(279,383)
(280,384)(281,385)(282,386)(283,387)(284,388)(285,389)(286,390)(287,365)
(288,366)(289,367)(290,368)(291,369)(292,370)(293,371)(294,372)(295,373)
(296,374)(297,375)(298,376)(299,377)(300,352)(301,353)(302,354)(303,355)
(304,356)(305,357)(306,358)(307,359)(308,360)(309,361)(310,362)(311,363)
(312,364)(313,339)(314,340)(315,341)(316,342)(317,343)(318,344)(319,345)
(320,346)(321,347)(322,348)(323,349)(324,350)(325,351);;
s1 := (  1, 79)(  2, 91)(  3, 90)(  4, 89)(  5, 88)(  6, 87)(  7, 86)(  8, 85)
(  9, 84)( 10, 83)( 11, 82)( 12, 81)( 13, 80)( 14, 66)( 15, 78)( 16, 77)
( 17, 76)( 18, 75)( 19, 74)( 20, 73)( 21, 72)( 22, 71)( 23, 70)( 24, 69)
( 25, 68)( 26, 67)( 27,118)( 28,130)( 29,129)( 30,128)( 31,127)( 32,126)
( 33,125)( 34,124)( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)( 40,105)
( 41,117)( 42,116)( 43,115)( 44,114)( 45,113)( 46,112)( 47,111)( 48,110)
( 49,109)( 50,108)( 51,107)( 52,106)( 53, 92)( 54,104)( 55,103)( 56,102)
( 57,101)( 58,100)( 59, 99)( 60, 98)( 61, 97)( 62, 96)( 63, 95)( 64, 94)
( 65, 93)(131,144)(132,156)(133,155)(134,154)(135,153)(136,152)(137,151)
(138,150)(139,149)(140,148)(141,147)(142,146)(143,145)(157,183)(158,195)
(159,194)(160,193)(161,192)(162,191)(163,190)(164,189)(165,188)(166,187)
(167,186)(168,185)(169,184)(171,182)(172,181)(173,180)(174,179)(175,178)
(176,177)(196,274)(197,286)(198,285)(199,284)(200,283)(201,282)(202,281)
(203,280)(204,279)(205,278)(206,277)(207,276)(208,275)(209,261)(210,273)
(211,272)(212,271)(213,270)(214,269)(215,268)(216,267)(217,266)(218,265)
(219,264)(220,263)(221,262)(222,313)(223,325)(224,324)(225,323)(226,322)
(227,321)(228,320)(229,319)(230,318)(231,317)(232,316)(233,315)(234,314)
(235,300)(236,312)(237,311)(238,310)(239,309)(240,308)(241,307)(242,306)
(243,305)(244,304)(245,303)(246,302)(247,301)(248,287)(249,299)(250,298)
(251,297)(252,296)(253,295)(254,294)(255,293)(256,292)(257,291)(258,290)
(259,289)(260,288)(326,339)(327,351)(328,350)(329,349)(330,348)(331,347)
(332,346)(333,345)(334,344)(335,343)(336,342)(337,341)(338,340)(352,378)
(353,390)(354,389)(355,388)(356,387)(357,386)(358,385)(359,384)(360,383)
(361,382)(362,381)(363,380)(364,379)(366,377)(367,376)(368,375)(369,374)
(370,373)(371,372);;
s2 := (  1,197)(  2,196)(  3,208)(  4,207)(  5,206)(  6,205)(  7,204)(  8,203)
(  9,202)( 10,201)( 11,200)( 12,199)( 13,198)( 14,210)( 15,209)( 16,221)
( 17,220)( 18,219)( 19,218)( 20,217)( 21,216)( 22,215)( 23,214)( 24,213)
( 25,212)( 26,211)( 27,223)( 28,222)( 29,234)( 30,233)( 31,232)( 32,231)
( 33,230)( 34,229)( 35,228)( 36,227)( 37,226)( 38,225)( 39,224)( 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)( 53,249)( 54,248)( 55,260)( 56,259)
( 57,258)( 58,257)( 59,256)( 60,255)( 61,254)( 62,253)( 63,252)( 64,251)
( 65,250)( 66,262)( 67,261)( 68,273)( 69,272)( 70,271)( 71,270)( 72,269)
( 73,268)( 74,267)( 75,266)( 76,265)( 77,264)( 78,263)( 79,275)( 80,274)
( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)( 88,279)
( 89,278)( 90,277)( 91,276)( 92,288)( 93,287)( 94,299)( 95,298)( 96,297)
( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,290)(104,289)
(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)(118,314)(119,313)(120,325)
(121,324)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)(128,317)
(129,316)(130,315)(131,327)(132,326)(133,338)(134,337)(135,336)(136,335)
(137,334)(138,333)(139,332)(140,331)(141,330)(142,329)(143,328)(144,340)
(145,339)(146,351)(147,350)(148,349)(149,348)(150,347)(151,346)(152,345)
(153,344)(154,343)(155,342)(156,341)(157,353)(158,352)(159,364)(160,363)
(161,362)(162,361)(163,360)(164,359)(165,358)(166,357)(167,356)(168,355)
(169,354)(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)(183,379)(184,378)
(185,390)(186,389)(187,388)(188,387)(189,386)(190,385)(191,384)(192,383)
(193,382)(194,381)(195,380);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(390)!( 14, 53)( 15, 54)( 16, 55)( 17, 56)( 18, 57)( 19, 58)( 20, 59)
( 21, 60)( 22, 61)( 23, 62)( 24, 63)( 25, 64)( 26, 65)( 27, 40)( 28, 41)
( 29, 42)( 30, 43)( 31, 44)( 32, 45)( 33, 46)( 34, 47)( 35, 48)( 36, 49)
( 37, 50)( 38, 51)( 39, 52)( 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)
( 79,183)( 80,184)( 81,185)( 82,186)( 83,187)( 84,188)( 85,189)( 86,190)
( 87,191)( 88,192)( 89,193)( 90,194)( 91,195)( 92,170)( 93,171)( 94,172)
( 95,173)( 96,174)( 97,175)( 98,176)( 99,177)(100,178)(101,179)(102,180)
(103,181)(104,182)(105,157)(106,158)(107,159)(108,160)(109,161)(110,162)
(111,163)(112,164)(113,165)(114,166)(115,167)(116,168)(117,169)(118,144)
(119,145)(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)
(127,153)(128,154)(129,155)(130,156)(209,248)(210,249)(211,250)(212,251)
(213,252)(214,253)(215,254)(216,255)(217,256)(218,257)(219,258)(220,259)
(221,260)(222,235)(223,236)(224,237)(225,238)(226,239)(227,240)(228,241)
(229,242)(230,243)(231,244)(232,245)(233,246)(234,247)(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)(274,378)(275,379)(276,380)(277,381)(278,382)
(279,383)(280,384)(281,385)(282,386)(283,387)(284,388)(285,389)(286,390)
(287,365)(288,366)(289,367)(290,368)(291,369)(292,370)(293,371)(294,372)
(295,373)(296,374)(297,375)(298,376)(299,377)(300,352)(301,353)(302,354)
(303,355)(304,356)(305,357)(306,358)(307,359)(308,360)(309,361)(310,362)
(311,363)(312,364)(313,339)(314,340)(315,341)(316,342)(317,343)(318,344)
(319,345)(320,346)(321,347)(322,348)(323,349)(324,350)(325,351);
s1 := Sym(390)!(  1, 79)(  2, 91)(  3, 90)(  4, 89)(  5, 88)(  6, 87)(  7, 86)
(  8, 85)(  9, 84)( 10, 83)( 11, 82)( 12, 81)( 13, 80)( 14, 66)( 15, 78)
( 16, 77)( 17, 76)( 18, 75)( 19, 74)( 20, 73)( 21, 72)( 22, 71)( 23, 70)
( 24, 69)( 25, 68)( 26, 67)( 27,118)( 28,130)( 29,129)( 30,128)( 31,127)
( 32,126)( 33,125)( 34,124)( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)
( 40,105)( 41,117)( 42,116)( 43,115)( 44,114)( 45,113)( 46,112)( 47,111)
( 48,110)( 49,109)( 50,108)( 51,107)( 52,106)( 53, 92)( 54,104)( 55,103)
( 56,102)( 57,101)( 58,100)( 59, 99)( 60, 98)( 61, 97)( 62, 96)( 63, 95)
( 64, 94)( 65, 93)(131,144)(132,156)(133,155)(134,154)(135,153)(136,152)
(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)(143,145)(157,183)
(158,195)(159,194)(160,193)(161,192)(162,191)(163,190)(164,189)(165,188)
(166,187)(167,186)(168,185)(169,184)(171,182)(172,181)(173,180)(174,179)
(175,178)(176,177)(196,274)(197,286)(198,285)(199,284)(200,283)(201,282)
(202,281)(203,280)(204,279)(205,278)(206,277)(207,276)(208,275)(209,261)
(210,273)(211,272)(212,271)(213,270)(214,269)(215,268)(216,267)(217,266)
(218,265)(219,264)(220,263)(221,262)(222,313)(223,325)(224,324)(225,323)
(226,322)(227,321)(228,320)(229,319)(230,318)(231,317)(232,316)(233,315)
(234,314)(235,300)(236,312)(237,311)(238,310)(239,309)(240,308)(241,307)
(242,306)(243,305)(244,304)(245,303)(246,302)(247,301)(248,287)(249,299)
(250,298)(251,297)(252,296)(253,295)(254,294)(255,293)(256,292)(257,291)
(258,290)(259,289)(260,288)(326,339)(327,351)(328,350)(329,349)(330,348)
(331,347)(332,346)(333,345)(334,344)(335,343)(336,342)(337,341)(338,340)
(352,378)(353,390)(354,389)(355,388)(356,387)(357,386)(358,385)(359,384)
(360,383)(361,382)(362,381)(363,380)(364,379)(366,377)(367,376)(368,375)
(369,374)(370,373)(371,372);
s2 := Sym(390)!(  1,197)(  2,196)(  3,208)(  4,207)(  5,206)(  6,205)(  7,204)
(  8,203)(  9,202)( 10,201)( 11,200)( 12,199)( 13,198)( 14,210)( 15,209)
( 16,221)( 17,220)( 18,219)( 19,218)( 20,217)( 21,216)( 22,215)( 23,214)
( 24,213)( 25,212)( 26,211)( 27,223)( 28,222)( 29,234)( 30,233)( 31,232)
( 32,231)( 33,230)( 34,229)( 35,228)( 36,227)( 37,226)( 38,225)( 39,224)
( 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)( 53,249)( 54,248)( 55,260)
( 56,259)( 57,258)( 58,257)( 59,256)( 60,255)( 61,254)( 62,253)( 63,252)
( 64,251)( 65,250)( 66,262)( 67,261)( 68,273)( 69,272)( 70,271)( 71,270)
( 72,269)( 73,268)( 74,267)( 75,266)( 76,265)( 77,264)( 78,263)( 79,275)
( 80,274)( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)
( 88,279)( 89,278)( 90,277)( 91,276)( 92,288)( 93,287)( 94,299)( 95,298)
( 96,297)( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,290)
(104,289)(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)(118,314)(119,313)
(120,325)(121,324)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)
(128,317)(129,316)(130,315)(131,327)(132,326)(133,338)(134,337)(135,336)
(136,335)(137,334)(138,333)(139,332)(140,331)(141,330)(142,329)(143,328)
(144,340)(145,339)(146,351)(147,350)(148,349)(149,348)(150,347)(151,346)
(152,345)(153,344)(154,343)(155,342)(156,341)(157,353)(158,352)(159,364)
(160,363)(161,362)(162,361)(163,360)(164,359)(165,358)(166,357)(167,356)
(168,355)(169,354)(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)(183,379)
(184,378)(185,390)(186,389)(187,388)(188,387)(189,386)(190,385)(191,384)
(192,383)(193,382)(194,381)(195,380);
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;

References : None.
to this polytope