Polytope of Type {8,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30}*1920g
if this polytope has a name.
Group : SmallGroup(1920,239556)
Rank : 3
Schlafli Type : {8,30}
Number of vertices, edges, etc : 32, 480, 120
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
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 : {4,30}*960b
   4-fold quotients : {8,30}*480, {4,30}*480
   5-fold quotients : {8,6}*384g
   8-fold quotients : {4,30}*240a, {4,15}*240, {4,30}*240b, {4,30}*240c
   10-fold quotients : {4,6}*192b
   12-fold quotients : {8,10}*160
   16-fold quotients : {4,15}*120, {2,30}*120
   20-fold quotients : {8,6}*96, {4,6}*96
   24-fold quotients : {4,10}*80
   32-fold quotients : {2,15}*60
   40-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {2,10}*40
   60-fold quotients : {8,2}*32
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {4,2}*16
   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 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,183)(122,184)(123,181)(124,182)
(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)(132,190)
(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)(140,198)
(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)(148,206)
(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)(156,214)
(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)(164,222)
(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)(172,230)
(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)(180,238)
(241,363)(242,364)(243,361)(244,362)(245,367)(246,368)(247,365)(248,366)
(249,371)(250,372)(251,369)(252,370)(253,375)(254,376)(255,373)(256,374)
(257,379)(258,380)(259,377)(260,378)(261,383)(262,384)(263,381)(264,382)
(265,387)(266,388)(267,385)(268,386)(269,391)(270,392)(271,389)(272,390)
(273,395)(274,396)(275,393)(276,394)(277,399)(278,400)(279,397)(280,398)
(281,403)(282,404)(283,401)(284,402)(285,407)(286,408)(287,405)(288,406)
(289,411)(290,412)(291,409)(292,410)(293,415)(294,416)(295,413)(296,414)
(297,419)(298,420)(299,417)(300,418)(301,423)(302,424)(303,421)(304,422)
(305,427)(306,428)(307,425)(308,426)(309,431)(310,432)(311,429)(312,430)
(313,435)(314,436)(315,433)(316,434)(317,439)(318,440)(319,437)(320,438)
(321,443)(322,444)(323,441)(324,442)(325,447)(326,448)(327,445)(328,446)
(329,451)(330,452)(331,449)(332,450)(333,455)(334,456)(335,453)(336,454)
(337,459)(338,460)(339,457)(340,458)(341,463)(342,464)(343,461)(344,462)
(345,467)(346,468)(347,465)(348,466)(349,471)(350,472)(351,469)(352,470)
(353,475)(354,476)(355,473)(356,474)(357,479)(358,480)(359,477)(360,478);;
s1 := (  1,241)(  2,242)(  3,244)(  4,243)(  5,257)(  6,258)(  7,260)(  8,259)
(  9,253)( 10,254)( 11,256)( 12,255)( 13,249)( 14,250)( 15,252)( 16,251)
( 17,245)( 18,246)( 19,248)( 20,247)( 21,281)( 22,282)( 23,284)( 24,283)
( 25,297)( 26,298)( 27,300)( 28,299)( 29,293)( 30,294)( 31,296)( 32,295)
( 33,289)( 34,290)( 35,292)( 36,291)( 37,285)( 38,286)( 39,288)( 40,287)
( 41,261)( 42,262)( 43,264)( 44,263)( 45,277)( 46,278)( 47,280)( 48,279)
( 49,273)( 50,274)( 51,276)( 52,275)( 53,269)( 54,270)( 55,272)( 56,271)
( 57,265)( 58,266)( 59,268)( 60,267)( 61,301)( 62,302)( 63,304)( 64,303)
( 65,317)( 66,318)( 67,320)( 68,319)( 69,313)( 70,314)( 71,316)( 72,315)
( 73,309)( 74,310)( 75,312)( 76,311)( 77,305)( 78,306)( 79,308)( 80,307)
( 81,341)( 82,342)( 83,344)( 84,343)( 85,357)( 86,358)( 87,360)( 88,359)
( 89,353)( 90,354)( 91,356)( 92,355)( 93,349)( 94,350)( 95,352)( 96,351)
( 97,345)( 98,346)( 99,348)(100,347)(101,321)(102,322)(103,324)(104,323)
(105,337)(106,338)(107,340)(108,339)(109,333)(110,334)(111,336)(112,335)
(113,329)(114,330)(115,332)(116,331)(117,325)(118,326)(119,328)(120,327)
(121,421)(122,422)(123,424)(124,423)(125,437)(126,438)(127,440)(128,439)
(129,433)(130,434)(131,436)(132,435)(133,429)(134,430)(135,432)(136,431)
(137,425)(138,426)(139,428)(140,427)(141,461)(142,462)(143,464)(144,463)
(145,477)(146,478)(147,480)(148,479)(149,473)(150,474)(151,476)(152,475)
(153,469)(154,470)(155,472)(156,471)(157,465)(158,466)(159,468)(160,467)
(161,441)(162,442)(163,444)(164,443)(165,457)(166,458)(167,460)(168,459)
(169,453)(170,454)(171,456)(172,455)(173,449)(174,450)(175,452)(176,451)
(177,445)(178,446)(179,448)(180,447)(181,361)(182,362)(183,364)(184,363)
(185,377)(186,378)(187,380)(188,379)(189,373)(190,374)(191,376)(192,375)
(193,369)(194,370)(195,372)(196,371)(197,365)(198,366)(199,368)(200,367)
(201,401)(202,402)(203,404)(204,403)(205,417)(206,418)(207,420)(208,419)
(209,413)(210,414)(211,416)(212,415)(213,409)(214,410)(215,412)(216,411)
(217,405)(218,406)(219,408)(220,407)(221,381)(222,382)(223,384)(224,383)
(225,397)(226,398)(227,400)(228,399)(229,393)(230,394)(231,396)(232,395)
(233,389)(234,390)(235,392)(236,391)(237,385)(238,386)(239,388)(240,387);;
s2 := (  1, 25)(  2, 28)(  3, 27)(  4, 26)(  5, 21)(  6, 24)(  7, 23)(  8, 22)
(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)
( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)
( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)
( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)
( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)
(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)(126,144)
(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)(134,156)
(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)(162,168)
(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)(181,205)
(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)(189,217)
(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)(197,209)
(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)(229,237)
(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)(244,266)
(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)(252,278)
(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)(260,270)
(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)(292,298)
(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)(307,323)
(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)(315,335)
(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)(343,347)
(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)(362,388)
(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)(370,400)
(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)(378,392)
(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)(410,420)
(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)(425,441)
(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)(433,453)
(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)(461,465)
(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)(474,476);;
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*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(480)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,183)(122,184)(123,181)
(124,182)(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)
(132,190)(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)
(140,198)(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)
(148,206)(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)
(156,214)(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)
(164,222)(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)
(172,230)(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)
(180,238)(241,363)(242,364)(243,361)(244,362)(245,367)(246,368)(247,365)
(248,366)(249,371)(250,372)(251,369)(252,370)(253,375)(254,376)(255,373)
(256,374)(257,379)(258,380)(259,377)(260,378)(261,383)(262,384)(263,381)
(264,382)(265,387)(266,388)(267,385)(268,386)(269,391)(270,392)(271,389)
(272,390)(273,395)(274,396)(275,393)(276,394)(277,399)(278,400)(279,397)
(280,398)(281,403)(282,404)(283,401)(284,402)(285,407)(286,408)(287,405)
(288,406)(289,411)(290,412)(291,409)(292,410)(293,415)(294,416)(295,413)
(296,414)(297,419)(298,420)(299,417)(300,418)(301,423)(302,424)(303,421)
(304,422)(305,427)(306,428)(307,425)(308,426)(309,431)(310,432)(311,429)
(312,430)(313,435)(314,436)(315,433)(316,434)(317,439)(318,440)(319,437)
(320,438)(321,443)(322,444)(323,441)(324,442)(325,447)(326,448)(327,445)
(328,446)(329,451)(330,452)(331,449)(332,450)(333,455)(334,456)(335,453)
(336,454)(337,459)(338,460)(339,457)(340,458)(341,463)(342,464)(343,461)
(344,462)(345,467)(346,468)(347,465)(348,466)(349,471)(350,472)(351,469)
(352,470)(353,475)(354,476)(355,473)(356,474)(357,479)(358,480)(359,477)
(360,478);
s1 := Sym(480)!(  1,241)(  2,242)(  3,244)(  4,243)(  5,257)(  6,258)(  7,260)
(  8,259)(  9,253)( 10,254)( 11,256)( 12,255)( 13,249)( 14,250)( 15,252)
( 16,251)( 17,245)( 18,246)( 19,248)( 20,247)( 21,281)( 22,282)( 23,284)
( 24,283)( 25,297)( 26,298)( 27,300)( 28,299)( 29,293)( 30,294)( 31,296)
( 32,295)( 33,289)( 34,290)( 35,292)( 36,291)( 37,285)( 38,286)( 39,288)
( 40,287)( 41,261)( 42,262)( 43,264)( 44,263)( 45,277)( 46,278)( 47,280)
( 48,279)( 49,273)( 50,274)( 51,276)( 52,275)( 53,269)( 54,270)( 55,272)
( 56,271)( 57,265)( 58,266)( 59,268)( 60,267)( 61,301)( 62,302)( 63,304)
( 64,303)( 65,317)( 66,318)( 67,320)( 68,319)( 69,313)( 70,314)( 71,316)
( 72,315)( 73,309)( 74,310)( 75,312)( 76,311)( 77,305)( 78,306)( 79,308)
( 80,307)( 81,341)( 82,342)( 83,344)( 84,343)( 85,357)( 86,358)( 87,360)
( 88,359)( 89,353)( 90,354)( 91,356)( 92,355)( 93,349)( 94,350)( 95,352)
( 96,351)( 97,345)( 98,346)( 99,348)(100,347)(101,321)(102,322)(103,324)
(104,323)(105,337)(106,338)(107,340)(108,339)(109,333)(110,334)(111,336)
(112,335)(113,329)(114,330)(115,332)(116,331)(117,325)(118,326)(119,328)
(120,327)(121,421)(122,422)(123,424)(124,423)(125,437)(126,438)(127,440)
(128,439)(129,433)(130,434)(131,436)(132,435)(133,429)(134,430)(135,432)
(136,431)(137,425)(138,426)(139,428)(140,427)(141,461)(142,462)(143,464)
(144,463)(145,477)(146,478)(147,480)(148,479)(149,473)(150,474)(151,476)
(152,475)(153,469)(154,470)(155,472)(156,471)(157,465)(158,466)(159,468)
(160,467)(161,441)(162,442)(163,444)(164,443)(165,457)(166,458)(167,460)
(168,459)(169,453)(170,454)(171,456)(172,455)(173,449)(174,450)(175,452)
(176,451)(177,445)(178,446)(179,448)(180,447)(181,361)(182,362)(183,364)
(184,363)(185,377)(186,378)(187,380)(188,379)(189,373)(190,374)(191,376)
(192,375)(193,369)(194,370)(195,372)(196,371)(197,365)(198,366)(199,368)
(200,367)(201,401)(202,402)(203,404)(204,403)(205,417)(206,418)(207,420)
(208,419)(209,413)(210,414)(211,416)(212,415)(213,409)(214,410)(215,412)
(216,411)(217,405)(218,406)(219,408)(220,407)(221,381)(222,382)(223,384)
(224,383)(225,397)(226,398)(227,400)(228,399)(229,393)(230,394)(231,396)
(232,395)(233,389)(234,390)(235,392)(236,391)(237,385)(238,386)(239,388)
(240,387);
s2 := Sym(480)!(  1, 25)(  2, 28)(  3, 27)(  4, 26)(  5, 21)(  6, 24)(  7, 23)
(  8, 22)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)
( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)
( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)
( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)
( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)
(111,119)(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)
(126,144)(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)
(134,156)(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)
(162,168)(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)
(181,205)(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)
(189,217)(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)
(197,209)(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)
(229,237)(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)
(244,266)(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)
(252,278)(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)
(260,270)(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)
(292,298)(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)
(307,323)(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)
(315,335)(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)
(343,347)(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)
(362,388)(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)
(370,400)(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)
(378,392)(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)
(410,420)(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)
(425,441)(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)
(433,453)(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)
(461,465)(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)
(474,476);
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*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope