Polytope of Type {30,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240399)
Rank : 3
Schlafli Type : {30,10}
Number of vertices, edges, etc : 96, 480, 32
Order of s0s1s2 : 12
Order of s0s1s2s1 : 10
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 : {15,10}*960
3-fold quotients : {10,10}*640d
6-fold quotients : {5,10}*320b, {10,5}*320b
12-fold quotients : {5,5}*160
80-fold quotients : {6,2}*24
160-fold quotients : {3,2}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 65)( 18, 66)
( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 78)( 26, 77)
( 27, 79)( 28, 80)( 29, 74)( 30, 73)( 31, 75)( 32, 76)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 62)( 42, 61)
( 43, 63)( 44, 64)( 45, 58)( 46, 57)( 47, 59)( 48, 60)( 81,161)( 82,162)
( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,174)( 90,173)
( 91,175)( 92,176)( 93,170)( 94,169)( 95,171)( 96,172)( 97,225)( 98,226)
( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,238)(106,237)
(107,239)(108,240)(109,234)(110,233)(111,235)(112,236)(113,209)(114,210)
(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,222)(122,221)
(123,223)(124,224)(125,218)(126,217)(127,219)(128,220)(129,193)(130,194)
(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,206)(138,205)
(139,207)(140,208)(141,202)(142,201)(143,203)(144,204)(145,177)(146,178)
(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,190)(154,189)
(155,191)(156,192)(157,186)(158,185)(159,187)(160,188)(243,244)(247,248)
(249,254)(250,253)(251,255)(252,256)(257,305)(258,306)(259,308)(260,307)
(261,309)(262,310)(263,312)(264,311)(265,318)(266,317)(267,319)(268,320)
(269,314)(270,313)(271,315)(272,316)(273,289)(274,290)(275,292)(276,291)
(277,293)(278,294)(279,296)(280,295)(281,302)(282,301)(283,303)(284,304)
(285,298)(286,297)(287,299)(288,300)(321,401)(322,402)(323,404)(324,403)
(325,405)(326,406)(327,408)(328,407)(329,414)(330,413)(331,415)(332,416)
(333,410)(334,409)(335,411)(336,412)(337,465)(338,466)(339,468)(340,467)
(341,469)(342,470)(343,472)(344,471)(345,478)(346,477)(347,479)(348,480)
(349,474)(350,473)(351,475)(352,476)(353,449)(354,450)(355,452)(356,451)
(357,453)(358,454)(359,456)(360,455)(361,462)(362,461)(363,463)(364,464)
(365,458)(366,457)(367,459)(368,460)(369,433)(370,434)(371,436)(372,435)
(373,437)(374,438)(375,440)(376,439)(377,446)(378,445)(379,447)(380,448)
(381,442)(382,441)(383,443)(384,444)(385,417)(386,418)(387,420)(388,419)
(389,421)(390,422)(391,424)(392,423)(393,430)(394,429)(395,431)(396,432)
(397,426)(398,425)(399,427)(400,428);;
s1 := ( 1,337)( 2,352)( 3,342)( 4,347)( 5,350)( 6,339)( 7,345)( 8,344)
( 9,343)( 10,346)( 11,340)( 12,349)( 13,348)( 14,341)( 15,351)( 16,338)
( 17,321)( 18,336)( 19,326)( 20,331)( 21,334)( 22,323)( 23,329)( 24,328)
( 25,327)( 26,330)( 27,324)( 28,333)( 29,332)( 30,325)( 31,335)( 32,322)
( 33,385)( 34,400)( 35,390)( 36,395)( 37,398)( 38,387)( 39,393)( 40,392)
( 41,391)( 42,394)( 43,388)( 44,397)( 45,396)( 46,389)( 47,399)( 48,386)
( 49,369)( 50,384)( 51,374)( 52,379)( 53,382)( 54,371)( 55,377)( 56,376)
( 57,375)( 58,378)( 59,372)( 60,381)( 61,380)( 62,373)( 63,383)( 64,370)
( 65,353)( 66,368)( 67,358)( 68,363)( 69,366)( 70,355)( 71,361)( 72,360)
( 73,359)( 74,362)( 75,356)( 76,365)( 77,364)( 78,357)( 79,367)( 80,354)
( 81,257)( 82,272)( 83,262)( 84,267)( 85,270)( 86,259)( 87,265)( 88,264)
( 89,263)( 90,266)( 91,260)( 92,269)( 93,268)( 94,261)( 95,271)( 96,258)
( 97,241)( 98,256)( 99,246)(100,251)(101,254)(102,243)(103,249)(104,248)
(105,247)(106,250)(107,244)(108,253)(109,252)(110,245)(111,255)(112,242)
(113,305)(114,320)(115,310)(116,315)(117,318)(118,307)(119,313)(120,312)
(121,311)(122,314)(123,308)(124,317)(125,316)(126,309)(127,319)(128,306)
(129,289)(130,304)(131,294)(132,299)(133,302)(134,291)(135,297)(136,296)
(137,295)(138,298)(139,292)(140,301)(141,300)(142,293)(143,303)(144,290)
(145,273)(146,288)(147,278)(148,283)(149,286)(150,275)(151,281)(152,280)
(153,279)(154,282)(155,276)(156,285)(157,284)(158,277)(159,287)(160,274)
(161,417)(162,432)(163,422)(164,427)(165,430)(166,419)(167,425)(168,424)
(169,423)(170,426)(171,420)(172,429)(173,428)(174,421)(175,431)(176,418)
(177,401)(178,416)(179,406)(180,411)(181,414)(182,403)(183,409)(184,408)
(185,407)(186,410)(187,404)(188,413)(189,412)(190,405)(191,415)(192,402)
(193,465)(194,480)(195,470)(196,475)(197,478)(198,467)(199,473)(200,472)
(201,471)(202,474)(203,468)(204,477)(205,476)(206,469)(207,479)(208,466)
(209,449)(210,464)(211,454)(212,459)(213,462)(214,451)(215,457)(216,456)
(217,455)(218,458)(219,452)(220,461)(221,460)(222,453)(223,463)(224,450)
(225,433)(226,448)(227,438)(228,443)(229,446)(230,435)(231,441)(232,440)
(233,439)(234,442)(235,436)(236,445)(237,444)(238,437)(239,447)(240,434);;
s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 10)( 13, 14)( 17, 69)( 18, 70)
( 19, 72)( 20, 71)( 21, 65)( 22, 66)( 23, 68)( 24, 67)( 25, 74)( 26, 73)
( 27, 75)( 28, 76)( 29, 78)( 30, 77)( 31, 79)( 32, 80)( 33, 53)( 34, 54)
( 35, 56)( 36, 55)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 41, 58)( 42, 57)
( 43, 59)( 44, 60)( 45, 62)( 46, 61)( 47, 63)( 48, 64)( 81, 85)( 82, 86)
( 83, 88)( 84, 87)( 89, 90)( 93, 94)( 97,149)( 98,150)( 99,152)(100,151)
(101,145)(102,146)(103,148)(104,147)(105,154)(106,153)(107,155)(108,156)
(109,158)(110,157)(111,159)(112,160)(113,133)(114,134)(115,136)(116,135)
(117,129)(118,130)(119,132)(120,131)(121,138)(122,137)(123,139)(124,140)
(125,142)(126,141)(127,143)(128,144)(161,165)(162,166)(163,168)(164,167)
(169,170)(173,174)(177,229)(178,230)(179,232)(180,231)(181,225)(182,226)
(183,228)(184,227)(185,234)(186,233)(187,235)(188,236)(189,238)(190,237)
(191,239)(192,240)(193,213)(194,214)(195,216)(196,215)(197,209)(198,210)
(199,212)(200,211)(201,218)(202,217)(203,219)(204,220)(205,222)(206,221)
(207,223)(208,224)(241,245)(242,246)(243,248)(244,247)(249,250)(253,254)
(257,309)(258,310)(259,312)(260,311)(261,305)(262,306)(263,308)(264,307)
(265,314)(266,313)(267,315)(268,316)(269,318)(270,317)(271,319)(272,320)
(273,293)(274,294)(275,296)(276,295)(277,289)(278,290)(279,292)(280,291)
(281,298)(282,297)(283,299)(284,300)(285,302)(286,301)(287,303)(288,304)
(321,325)(322,326)(323,328)(324,327)(329,330)(333,334)(337,389)(338,390)
(339,392)(340,391)(341,385)(342,386)(343,388)(344,387)(345,394)(346,393)
(347,395)(348,396)(349,398)(350,397)(351,399)(352,400)(353,373)(354,374)
(355,376)(356,375)(357,369)(358,370)(359,372)(360,371)(361,378)(362,377)
(363,379)(364,380)(365,382)(366,381)(367,383)(368,384)(401,405)(402,406)
(403,408)(404,407)(409,410)(413,414)(417,469)(418,470)(419,472)(420,471)
(421,465)(422,466)(423,468)(424,467)(425,474)(426,473)(427,475)(428,476)
(429,478)(430,477)(431,479)(432,480)(433,453)(434,454)(435,456)(436,455)
(437,449)(438,450)(439,452)(440,451)(441,458)(442,457)(443,459)(444,460)
(445,462)(446,461)(447,463)(448,464);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 3, 4)( 7, 8)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 65)
( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 78)
( 26, 77)( 27, 79)( 28, 80)( 29, 74)( 30, 73)( 31, 75)( 32, 76)( 33, 49)
( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 62)
( 42, 61)( 43, 63)( 44, 64)( 45, 58)( 46, 57)( 47, 59)( 48, 60)( 81,161)
( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,174)
( 90,173)( 91,175)( 92,176)( 93,170)( 94,169)( 95,171)( 96,172)( 97,225)
( 98,226)( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,238)
(106,237)(107,239)(108,240)(109,234)(110,233)(111,235)(112,236)(113,209)
(114,210)(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,222)
(122,221)(123,223)(124,224)(125,218)(126,217)(127,219)(128,220)(129,193)
(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,206)
(138,205)(139,207)(140,208)(141,202)(142,201)(143,203)(144,204)(145,177)
(146,178)(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,190)
(154,189)(155,191)(156,192)(157,186)(158,185)(159,187)(160,188)(243,244)
(247,248)(249,254)(250,253)(251,255)(252,256)(257,305)(258,306)(259,308)
(260,307)(261,309)(262,310)(263,312)(264,311)(265,318)(266,317)(267,319)
(268,320)(269,314)(270,313)(271,315)(272,316)(273,289)(274,290)(275,292)
(276,291)(277,293)(278,294)(279,296)(280,295)(281,302)(282,301)(283,303)
(284,304)(285,298)(286,297)(287,299)(288,300)(321,401)(322,402)(323,404)
(324,403)(325,405)(326,406)(327,408)(328,407)(329,414)(330,413)(331,415)
(332,416)(333,410)(334,409)(335,411)(336,412)(337,465)(338,466)(339,468)
(340,467)(341,469)(342,470)(343,472)(344,471)(345,478)(346,477)(347,479)
(348,480)(349,474)(350,473)(351,475)(352,476)(353,449)(354,450)(355,452)
(356,451)(357,453)(358,454)(359,456)(360,455)(361,462)(362,461)(363,463)
(364,464)(365,458)(366,457)(367,459)(368,460)(369,433)(370,434)(371,436)
(372,435)(373,437)(374,438)(375,440)(376,439)(377,446)(378,445)(379,447)
(380,448)(381,442)(382,441)(383,443)(384,444)(385,417)(386,418)(387,420)
(388,419)(389,421)(390,422)(391,424)(392,423)(393,430)(394,429)(395,431)
(396,432)(397,426)(398,425)(399,427)(400,428);
s1 := Sym(480)!( 1,337)( 2,352)( 3,342)( 4,347)( 5,350)( 6,339)( 7,345)
( 8,344)( 9,343)( 10,346)( 11,340)( 12,349)( 13,348)( 14,341)( 15,351)
( 16,338)( 17,321)( 18,336)( 19,326)( 20,331)( 21,334)( 22,323)( 23,329)
( 24,328)( 25,327)( 26,330)( 27,324)( 28,333)( 29,332)( 30,325)( 31,335)
( 32,322)( 33,385)( 34,400)( 35,390)( 36,395)( 37,398)( 38,387)( 39,393)
( 40,392)( 41,391)( 42,394)( 43,388)( 44,397)( 45,396)( 46,389)( 47,399)
( 48,386)( 49,369)( 50,384)( 51,374)( 52,379)( 53,382)( 54,371)( 55,377)
( 56,376)( 57,375)( 58,378)( 59,372)( 60,381)( 61,380)( 62,373)( 63,383)
( 64,370)( 65,353)( 66,368)( 67,358)( 68,363)( 69,366)( 70,355)( 71,361)
( 72,360)( 73,359)( 74,362)( 75,356)( 76,365)( 77,364)( 78,357)( 79,367)
( 80,354)( 81,257)( 82,272)( 83,262)( 84,267)( 85,270)( 86,259)( 87,265)
( 88,264)( 89,263)( 90,266)( 91,260)( 92,269)( 93,268)( 94,261)( 95,271)
( 96,258)( 97,241)( 98,256)( 99,246)(100,251)(101,254)(102,243)(103,249)
(104,248)(105,247)(106,250)(107,244)(108,253)(109,252)(110,245)(111,255)
(112,242)(113,305)(114,320)(115,310)(116,315)(117,318)(118,307)(119,313)
(120,312)(121,311)(122,314)(123,308)(124,317)(125,316)(126,309)(127,319)
(128,306)(129,289)(130,304)(131,294)(132,299)(133,302)(134,291)(135,297)
(136,296)(137,295)(138,298)(139,292)(140,301)(141,300)(142,293)(143,303)
(144,290)(145,273)(146,288)(147,278)(148,283)(149,286)(150,275)(151,281)
(152,280)(153,279)(154,282)(155,276)(156,285)(157,284)(158,277)(159,287)
(160,274)(161,417)(162,432)(163,422)(164,427)(165,430)(166,419)(167,425)
(168,424)(169,423)(170,426)(171,420)(172,429)(173,428)(174,421)(175,431)
(176,418)(177,401)(178,416)(179,406)(180,411)(181,414)(182,403)(183,409)
(184,408)(185,407)(186,410)(187,404)(188,413)(189,412)(190,405)(191,415)
(192,402)(193,465)(194,480)(195,470)(196,475)(197,478)(198,467)(199,473)
(200,472)(201,471)(202,474)(203,468)(204,477)(205,476)(206,469)(207,479)
(208,466)(209,449)(210,464)(211,454)(212,459)(213,462)(214,451)(215,457)
(216,456)(217,455)(218,458)(219,452)(220,461)(221,460)(222,453)(223,463)
(224,450)(225,433)(226,448)(227,438)(228,443)(229,446)(230,435)(231,441)
(232,440)(233,439)(234,442)(235,436)(236,445)(237,444)(238,437)(239,447)
(240,434);
s2 := Sym(480)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9, 10)( 13, 14)( 17, 69)
( 18, 70)( 19, 72)( 20, 71)( 21, 65)( 22, 66)( 23, 68)( 24, 67)( 25, 74)
( 26, 73)( 27, 75)( 28, 76)( 29, 78)( 30, 77)( 31, 79)( 32, 80)( 33, 53)
( 34, 54)( 35, 56)( 36, 55)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 41, 58)
( 42, 57)( 43, 59)( 44, 60)( 45, 62)( 46, 61)( 47, 63)( 48, 64)( 81, 85)
( 82, 86)( 83, 88)( 84, 87)( 89, 90)( 93, 94)( 97,149)( 98,150)( 99,152)
(100,151)(101,145)(102,146)(103,148)(104,147)(105,154)(106,153)(107,155)
(108,156)(109,158)(110,157)(111,159)(112,160)(113,133)(114,134)(115,136)
(116,135)(117,129)(118,130)(119,132)(120,131)(121,138)(122,137)(123,139)
(124,140)(125,142)(126,141)(127,143)(128,144)(161,165)(162,166)(163,168)
(164,167)(169,170)(173,174)(177,229)(178,230)(179,232)(180,231)(181,225)
(182,226)(183,228)(184,227)(185,234)(186,233)(187,235)(188,236)(189,238)
(190,237)(191,239)(192,240)(193,213)(194,214)(195,216)(196,215)(197,209)
(198,210)(199,212)(200,211)(201,218)(202,217)(203,219)(204,220)(205,222)
(206,221)(207,223)(208,224)(241,245)(242,246)(243,248)(244,247)(249,250)
(253,254)(257,309)(258,310)(259,312)(260,311)(261,305)(262,306)(263,308)
(264,307)(265,314)(266,313)(267,315)(268,316)(269,318)(270,317)(271,319)
(272,320)(273,293)(274,294)(275,296)(276,295)(277,289)(278,290)(279,292)
(280,291)(281,298)(282,297)(283,299)(284,300)(285,302)(286,301)(287,303)
(288,304)(321,325)(322,326)(323,328)(324,327)(329,330)(333,334)(337,389)
(338,390)(339,392)(340,391)(341,385)(342,386)(343,388)(344,387)(345,394)
(346,393)(347,395)(348,396)(349,398)(350,397)(351,399)(352,400)(353,373)
(354,374)(355,376)(356,375)(357,369)(358,370)(359,372)(360,371)(361,378)
(362,377)(363,379)(364,380)(365,382)(366,381)(367,383)(368,384)(401,405)
(402,406)(403,408)(404,407)(409,410)(413,414)(417,469)(418,470)(419,472)
(420,471)(421,465)(422,466)(423,468)(424,467)(425,474)(426,473)(427,475)
(428,476)(429,478)(430,477)(431,479)(432,480)(433,453)(434,454)(435,456)
(436,455)(437,449)(438,450)(439,452)(440,451)(441,458)(442,457)(443,459)
(444,460)(445,462)(446,461)(447,463)(448,464);
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, s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1 >;
References : None.
to this polytope