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Polytope of Type {30,6}

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