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Polytope of Type {6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,30}*1920a
if this polytope has a name.
Group : SmallGroup(1920,238293)
Rank : 3
Schlafli Type : {6,30}
Number of vertices, edges, etc : 32, 480, 160
Order of s0s1s2 : 40
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,15}*960
   4-fold quotients : {6,30}*480
   5-fold quotients : {6,6}*384d
   8-fold quotients : {6,15}*240
   10-fold quotients : {6,3}*192
   20-fold quotients : {6,6}*96
   40-fold quotients : {3,6}*48, {6,3}*48
   48-fold quotients : {2,10}*40
   80-fold quotients : {3,3}*24
   96-fold quotients : {2,5}*20
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  3,  4)(  5,  6)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)( 21, 22)
( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 37, 38)( 41, 45)( 42, 46)
( 43, 48)( 44, 47)( 51, 52)( 53, 54)( 57, 61)( 58, 62)( 59, 64)( 60, 63)
( 67, 68)( 69, 70)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 81,161)( 82,162)
( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)( 88,168)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,177)( 98,178)
( 99,180)(100,179)(101,182)(102,181)(103,183)(104,184)(105,189)(106,190)
(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,193)(114,194)
(115,196)(116,195)(117,198)(118,197)(119,199)(120,200)(121,205)(122,206)
(123,208)(124,207)(125,201)(126,202)(127,204)(128,203)(129,209)(130,210)
(131,212)(132,211)(133,214)(134,213)(135,215)(136,216)(137,221)(138,222)
(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,225)(146,226)
(147,228)(148,227)(149,230)(150,229)(151,231)(152,232)(153,237)(154,238)
(155,240)(156,239)(157,233)(158,234)(159,236)(160,235)(243,244)(245,246)
(249,253)(250,254)(251,256)(252,255)(259,260)(261,262)(265,269)(266,270)
(267,272)(268,271)(275,276)(277,278)(281,285)(282,286)(283,288)(284,287)
(291,292)(293,294)(297,301)(298,302)(299,304)(300,303)(307,308)(309,310)
(313,317)(314,318)(315,320)(316,319)(321,401)(322,402)(323,404)(324,403)
(325,406)(326,405)(327,407)(328,408)(329,413)(330,414)(331,416)(332,415)
(333,409)(334,410)(335,412)(336,411)(337,417)(338,418)(339,420)(340,419)
(341,422)(342,421)(343,423)(344,424)(345,429)(346,430)(347,432)(348,431)
(349,425)(350,426)(351,428)(352,427)(353,433)(354,434)(355,436)(356,435)
(357,438)(358,437)(359,439)(360,440)(361,445)(362,446)(363,448)(364,447)
(365,441)(366,442)(367,444)(368,443)(369,449)(370,450)(371,452)(372,451)
(373,454)(374,453)(375,455)(376,456)(377,461)(378,462)(379,464)(380,463)
(381,457)(382,458)(383,460)(384,459)(385,465)(386,466)(387,468)(388,467)
(389,470)(390,469)(391,471)(392,472)(393,477)(394,478)(395,480)(396,479)
(397,473)(398,474)(399,476)(400,475);;
s1 := (  1, 81)(  2, 84)(  3, 83)(  4, 82)(  5, 95)(  6, 94)(  7, 93)(  8, 96)
(  9, 91)( 10, 90)( 11, 89)( 12, 92)( 13, 87)( 14, 86)( 15, 85)( 16, 88)
( 17,145)( 18,148)( 19,147)( 20,146)( 21,159)( 22,158)( 23,157)( 24,160)
( 25,155)( 26,154)( 27,153)( 28,156)( 29,151)( 30,150)( 31,149)( 32,152)
( 33,129)( 34,132)( 35,131)( 36,130)( 37,143)( 38,142)( 39,141)( 40,144)
( 41,139)( 42,138)( 43,137)( 44,140)( 45,135)( 46,134)( 47,133)( 48,136)
( 49,113)( 50,116)( 51,115)( 52,114)( 53,127)( 54,126)( 55,125)( 56,128)
( 57,123)( 58,122)( 59,121)( 60,124)( 61,119)( 62,118)( 63,117)( 64,120)
( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,111)( 70,110)( 71,109)( 72,112)
( 73,107)( 74,106)( 75,105)( 76,108)( 77,103)( 78,102)( 79,101)( 80,104)
(162,164)(165,175)(166,174)(167,173)(168,176)(169,171)(177,225)(178,228)
(179,227)(180,226)(181,239)(182,238)(183,237)(184,240)(185,235)(186,234)
(187,233)(188,236)(189,231)(190,230)(191,229)(192,232)(193,209)(194,212)
(195,211)(196,210)(197,223)(198,222)(199,221)(200,224)(201,219)(202,218)
(203,217)(204,220)(205,215)(206,214)(207,213)(208,216)(241,321)(242,324)
(243,323)(244,322)(245,335)(246,334)(247,333)(248,336)(249,331)(250,330)
(251,329)(252,332)(253,327)(254,326)(255,325)(256,328)(257,385)(258,388)
(259,387)(260,386)(261,399)(262,398)(263,397)(264,400)(265,395)(266,394)
(267,393)(268,396)(269,391)(270,390)(271,389)(272,392)(273,369)(274,372)
(275,371)(276,370)(277,383)(278,382)(279,381)(280,384)(281,379)(282,378)
(283,377)(284,380)(285,375)(286,374)(287,373)(288,376)(289,353)(290,356)
(291,355)(292,354)(293,367)(294,366)(295,365)(296,368)(297,363)(298,362)
(299,361)(300,364)(301,359)(302,358)(303,357)(304,360)(305,337)(306,340)
(307,339)(308,338)(309,351)(310,350)(311,349)(312,352)(313,347)(314,346)
(315,345)(316,348)(317,343)(318,342)(319,341)(320,344)(402,404)(405,415)
(406,414)(407,413)(408,416)(409,411)(417,465)(418,468)(419,467)(420,466)
(421,479)(422,478)(423,477)(424,480)(425,475)(426,474)(427,473)(428,476)
(429,471)(430,470)(431,469)(432,472)(433,449)(434,452)(435,451)(436,450)
(437,463)(438,462)(439,461)(440,464)(441,459)(442,458)(443,457)(444,460)
(445,455)(446,454)(447,453)(448,456);;
s2 := (  1,263)(  2,264)(  3,262)(  4,261)(  5,260)(  6,259)(  7,257)(  8,258)
(  9,265)( 10,266)( 11,268)( 12,267)( 13,269)( 14,270)( 15,272)( 16,271)
( 17,247)( 18,248)( 19,246)( 20,245)( 21,244)( 22,243)( 23,241)( 24,242)
( 25,249)( 26,250)( 27,252)( 28,251)( 29,253)( 30,254)( 31,256)( 32,255)
( 33,311)( 34,312)( 35,310)( 36,309)( 37,308)( 38,307)( 39,305)( 40,306)
( 41,313)( 42,314)( 43,316)( 44,315)( 45,317)( 46,318)( 47,320)( 48,319)
( 49,295)( 50,296)( 51,294)( 52,293)( 53,292)( 54,291)( 55,289)( 56,290)
( 57,297)( 58,298)( 59,300)( 60,299)( 61,301)( 62,302)( 63,304)( 64,303)
( 65,279)( 66,280)( 67,278)( 68,277)( 69,276)( 70,275)( 71,273)( 72,274)
( 73,281)( 74,282)( 75,284)( 76,283)( 77,285)( 78,286)( 79,288)( 80,287)
( 81,423)( 82,424)( 83,422)( 84,421)( 85,420)( 86,419)( 87,417)( 88,418)
( 89,425)( 90,426)( 91,428)( 92,427)( 93,429)( 94,430)( 95,432)( 96,431)
( 97,407)( 98,408)( 99,406)(100,405)(101,404)(102,403)(103,401)(104,402)
(105,409)(106,410)(107,412)(108,411)(109,413)(110,414)(111,416)(112,415)
(113,471)(114,472)(115,470)(116,469)(117,468)(118,467)(119,465)(120,466)
(121,473)(122,474)(123,476)(124,475)(125,477)(126,478)(127,480)(128,479)
(129,455)(130,456)(131,454)(132,453)(133,452)(134,451)(135,449)(136,450)
(137,457)(138,458)(139,460)(140,459)(141,461)(142,462)(143,464)(144,463)
(145,439)(146,440)(147,438)(148,437)(149,436)(150,435)(151,433)(152,434)
(153,441)(154,442)(155,444)(156,443)(157,445)(158,446)(159,448)(160,447)
(161,343)(162,344)(163,342)(164,341)(165,340)(166,339)(167,337)(168,338)
(169,345)(170,346)(171,348)(172,347)(173,349)(174,350)(175,352)(176,351)
(177,327)(178,328)(179,326)(180,325)(181,324)(182,323)(183,321)(184,322)
(185,329)(186,330)(187,332)(188,331)(189,333)(190,334)(191,336)(192,335)
(193,391)(194,392)(195,390)(196,389)(197,388)(198,387)(199,385)(200,386)
(201,393)(202,394)(203,396)(204,395)(205,397)(206,398)(207,400)(208,399)
(209,375)(210,376)(211,374)(212,373)(213,372)(214,371)(215,369)(216,370)
(217,377)(218,378)(219,380)(220,379)(221,381)(222,382)(223,384)(224,383)
(225,359)(226,360)(227,358)(228,357)(229,356)(230,355)(231,353)(232,354)
(233,361)(234,362)(235,364)(236,363)(237,365)(238,366)(239,368)(240,367);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(480)!(  3,  4)(  5,  6)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)
( 21, 22)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 37, 38)( 41, 45)
( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 54)( 57, 61)( 58, 62)( 59, 64)
( 60, 63)( 67, 68)( 69, 70)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 81,161)
( 82,162)( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)( 88,168)( 89,173)
( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,177)
( 98,178)( 99,180)(100,179)(101,182)(102,181)(103,183)(104,184)(105,189)
(106,190)(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,193)
(114,194)(115,196)(116,195)(117,198)(118,197)(119,199)(120,200)(121,205)
(122,206)(123,208)(124,207)(125,201)(126,202)(127,204)(128,203)(129,209)
(130,210)(131,212)(132,211)(133,214)(134,213)(135,215)(136,216)(137,221)
(138,222)(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,225)
(146,226)(147,228)(148,227)(149,230)(150,229)(151,231)(152,232)(153,237)
(154,238)(155,240)(156,239)(157,233)(158,234)(159,236)(160,235)(243,244)
(245,246)(249,253)(250,254)(251,256)(252,255)(259,260)(261,262)(265,269)
(266,270)(267,272)(268,271)(275,276)(277,278)(281,285)(282,286)(283,288)
(284,287)(291,292)(293,294)(297,301)(298,302)(299,304)(300,303)(307,308)
(309,310)(313,317)(314,318)(315,320)(316,319)(321,401)(322,402)(323,404)
(324,403)(325,406)(326,405)(327,407)(328,408)(329,413)(330,414)(331,416)
(332,415)(333,409)(334,410)(335,412)(336,411)(337,417)(338,418)(339,420)
(340,419)(341,422)(342,421)(343,423)(344,424)(345,429)(346,430)(347,432)
(348,431)(349,425)(350,426)(351,428)(352,427)(353,433)(354,434)(355,436)
(356,435)(357,438)(358,437)(359,439)(360,440)(361,445)(362,446)(363,448)
(364,447)(365,441)(366,442)(367,444)(368,443)(369,449)(370,450)(371,452)
(372,451)(373,454)(374,453)(375,455)(376,456)(377,461)(378,462)(379,464)
(380,463)(381,457)(382,458)(383,460)(384,459)(385,465)(386,466)(387,468)
(388,467)(389,470)(390,469)(391,471)(392,472)(393,477)(394,478)(395,480)
(396,479)(397,473)(398,474)(399,476)(400,475);
s1 := Sym(480)!(  1, 81)(  2, 84)(  3, 83)(  4, 82)(  5, 95)(  6, 94)(  7, 93)
(  8, 96)(  9, 91)( 10, 90)( 11, 89)( 12, 92)( 13, 87)( 14, 86)( 15, 85)
( 16, 88)( 17,145)( 18,148)( 19,147)( 20,146)( 21,159)( 22,158)( 23,157)
( 24,160)( 25,155)( 26,154)( 27,153)( 28,156)( 29,151)( 30,150)( 31,149)
( 32,152)( 33,129)( 34,132)( 35,131)( 36,130)( 37,143)( 38,142)( 39,141)
( 40,144)( 41,139)( 42,138)( 43,137)( 44,140)( 45,135)( 46,134)( 47,133)
( 48,136)( 49,113)( 50,116)( 51,115)( 52,114)( 53,127)( 54,126)( 55,125)
( 56,128)( 57,123)( 58,122)( 59,121)( 60,124)( 61,119)( 62,118)( 63,117)
( 64,120)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,111)( 70,110)( 71,109)
( 72,112)( 73,107)( 74,106)( 75,105)( 76,108)( 77,103)( 78,102)( 79,101)
( 80,104)(162,164)(165,175)(166,174)(167,173)(168,176)(169,171)(177,225)
(178,228)(179,227)(180,226)(181,239)(182,238)(183,237)(184,240)(185,235)
(186,234)(187,233)(188,236)(189,231)(190,230)(191,229)(192,232)(193,209)
(194,212)(195,211)(196,210)(197,223)(198,222)(199,221)(200,224)(201,219)
(202,218)(203,217)(204,220)(205,215)(206,214)(207,213)(208,216)(241,321)
(242,324)(243,323)(244,322)(245,335)(246,334)(247,333)(248,336)(249,331)
(250,330)(251,329)(252,332)(253,327)(254,326)(255,325)(256,328)(257,385)
(258,388)(259,387)(260,386)(261,399)(262,398)(263,397)(264,400)(265,395)
(266,394)(267,393)(268,396)(269,391)(270,390)(271,389)(272,392)(273,369)
(274,372)(275,371)(276,370)(277,383)(278,382)(279,381)(280,384)(281,379)
(282,378)(283,377)(284,380)(285,375)(286,374)(287,373)(288,376)(289,353)
(290,356)(291,355)(292,354)(293,367)(294,366)(295,365)(296,368)(297,363)
(298,362)(299,361)(300,364)(301,359)(302,358)(303,357)(304,360)(305,337)
(306,340)(307,339)(308,338)(309,351)(310,350)(311,349)(312,352)(313,347)
(314,346)(315,345)(316,348)(317,343)(318,342)(319,341)(320,344)(402,404)
(405,415)(406,414)(407,413)(408,416)(409,411)(417,465)(418,468)(419,467)
(420,466)(421,479)(422,478)(423,477)(424,480)(425,475)(426,474)(427,473)
(428,476)(429,471)(430,470)(431,469)(432,472)(433,449)(434,452)(435,451)
(436,450)(437,463)(438,462)(439,461)(440,464)(441,459)(442,458)(443,457)
(444,460)(445,455)(446,454)(447,453)(448,456);
s2 := Sym(480)!(  1,263)(  2,264)(  3,262)(  4,261)(  5,260)(  6,259)(  7,257)
(  8,258)(  9,265)( 10,266)( 11,268)( 12,267)( 13,269)( 14,270)( 15,272)
( 16,271)( 17,247)( 18,248)( 19,246)( 20,245)( 21,244)( 22,243)( 23,241)
( 24,242)( 25,249)( 26,250)( 27,252)( 28,251)( 29,253)( 30,254)( 31,256)
( 32,255)( 33,311)( 34,312)( 35,310)( 36,309)( 37,308)( 38,307)( 39,305)
( 40,306)( 41,313)( 42,314)( 43,316)( 44,315)( 45,317)( 46,318)( 47,320)
( 48,319)( 49,295)( 50,296)( 51,294)( 52,293)( 53,292)( 54,291)( 55,289)
( 56,290)( 57,297)( 58,298)( 59,300)( 60,299)( 61,301)( 62,302)( 63,304)
( 64,303)( 65,279)( 66,280)( 67,278)( 68,277)( 69,276)( 70,275)( 71,273)
( 72,274)( 73,281)( 74,282)( 75,284)( 76,283)( 77,285)( 78,286)( 79,288)
( 80,287)( 81,423)( 82,424)( 83,422)( 84,421)( 85,420)( 86,419)( 87,417)
( 88,418)( 89,425)( 90,426)( 91,428)( 92,427)( 93,429)( 94,430)( 95,432)
( 96,431)( 97,407)( 98,408)( 99,406)(100,405)(101,404)(102,403)(103,401)
(104,402)(105,409)(106,410)(107,412)(108,411)(109,413)(110,414)(111,416)
(112,415)(113,471)(114,472)(115,470)(116,469)(117,468)(118,467)(119,465)
(120,466)(121,473)(122,474)(123,476)(124,475)(125,477)(126,478)(127,480)
(128,479)(129,455)(130,456)(131,454)(132,453)(133,452)(134,451)(135,449)
(136,450)(137,457)(138,458)(139,460)(140,459)(141,461)(142,462)(143,464)
(144,463)(145,439)(146,440)(147,438)(148,437)(149,436)(150,435)(151,433)
(152,434)(153,441)(154,442)(155,444)(156,443)(157,445)(158,446)(159,448)
(160,447)(161,343)(162,344)(163,342)(164,341)(165,340)(166,339)(167,337)
(168,338)(169,345)(170,346)(171,348)(172,347)(173,349)(174,350)(175,352)
(176,351)(177,327)(178,328)(179,326)(180,325)(181,324)(182,323)(183,321)
(184,322)(185,329)(186,330)(187,332)(188,331)(189,333)(190,334)(191,336)
(192,335)(193,391)(194,392)(195,390)(196,389)(197,388)(198,387)(199,385)
(200,386)(201,393)(202,394)(203,396)(204,395)(205,397)(206,398)(207,400)
(208,399)(209,375)(210,376)(211,374)(212,373)(213,372)(214,371)(215,369)
(216,370)(217,377)(218,378)(219,380)(220,379)(221,381)(222,382)(223,384)
(224,383)(225,359)(226,360)(227,358)(228,357)(229,356)(230,355)(231,353)
(232,354)(233,361)(234,362)(235,364)(236,363)(237,365)(238,366)(239,368)
(240,367);
poly := sub<Sym(480)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >; 
 
References : None.
to this polytope