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Polytope of Type {10,30}

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