Polytope of Type {8,30}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30}*960b
if this polytope has a name.
Group : SmallGroup(960,11101)
Rank : 3
Schlafli Type : {8,30}
Number of vertices, edges, etc : 16, 240, 60
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,30,2} of size 1920
Vertex Figure Of :
{2,8,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,15}*480, {4,30}*480
4-fold quotients : {4,15}*240, {4,30}*240b, {4,30}*240c
5-fold quotients : {8,6}*192b
8-fold quotients : {4,15}*120, {2,30}*120
10-fold quotients : {8,3}*96, {4,6}*96
16-fold quotients : {2,15}*60
20-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
24-fold quotients : {2,10}*40
40-fold quotients : {4,3}*24, {2,6}*24
48-fold quotients : {2,5}*20
80-fold quotients : {2,3}*12
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,60}*1920e, {8,30}*1920f, {8,60}*1920h
Permutation Representation (GAP) :
s0 := ( 1,125)( 2,126)( 3,128)( 4,127)( 5,122)( 6,121)( 7,123)( 8,124)
( 9,133)( 10,134)( 11,136)( 12,135)( 13,130)( 14,129)( 15,131)( 16,132)
( 17,141)( 18,142)( 19,144)( 20,143)( 21,138)( 22,137)( 23,139)( 24,140)
( 25,149)( 26,150)( 27,152)( 28,151)( 29,146)( 30,145)( 31,147)( 32,148)
( 33,157)( 34,158)( 35,160)( 36,159)( 37,154)( 38,153)( 39,155)( 40,156)
( 41,165)( 42,166)( 43,168)( 44,167)( 45,162)( 46,161)( 47,163)( 48,164)
( 49,173)( 50,174)( 51,176)( 52,175)( 53,170)( 54,169)( 55,171)( 56,172)
( 57,181)( 58,182)( 59,184)( 60,183)( 61,178)( 62,177)( 63,179)( 64,180)
( 65,189)( 66,190)( 67,192)( 68,191)( 69,186)( 70,185)( 71,187)( 72,188)
( 73,197)( 74,198)( 75,200)( 76,199)( 77,194)( 78,193)( 79,195)( 80,196)
( 81,205)( 82,206)( 83,208)( 84,207)( 85,202)( 86,201)( 87,203)( 88,204)
( 89,213)( 90,214)( 91,216)( 92,215)( 93,210)( 94,209)( 95,211)( 96,212)
( 97,221)( 98,222)( 99,224)(100,223)(101,218)(102,217)(103,219)(104,220)
(105,229)(106,230)(107,232)(108,231)(109,226)(110,225)(111,227)(112,228)
(113,237)(114,238)(115,240)(116,239)(117,234)(118,233)(119,235)(120,236)
(241,365)(242,366)(243,368)(244,367)(245,362)(246,361)(247,363)(248,364)
(249,373)(250,374)(251,376)(252,375)(253,370)(254,369)(255,371)(256,372)
(257,381)(258,382)(259,384)(260,383)(261,378)(262,377)(263,379)(264,380)
(265,389)(266,390)(267,392)(268,391)(269,386)(270,385)(271,387)(272,388)
(273,397)(274,398)(275,400)(276,399)(277,394)(278,393)(279,395)(280,396)
(281,405)(282,406)(283,408)(284,407)(285,402)(286,401)(287,403)(288,404)
(289,413)(290,414)(291,416)(292,415)(293,410)(294,409)(295,411)(296,412)
(297,421)(298,422)(299,424)(300,423)(301,418)(302,417)(303,419)(304,420)
(305,429)(306,430)(307,432)(308,431)(309,426)(310,425)(311,427)(312,428)
(313,437)(314,438)(315,440)(316,439)(317,434)(318,433)(319,435)(320,436)
(321,445)(322,446)(323,448)(324,447)(325,442)(326,441)(327,443)(328,444)
(329,453)(330,454)(331,456)(332,455)(333,450)(334,449)(335,451)(336,452)
(337,461)(338,462)(339,464)(340,463)(341,458)(342,457)(343,459)(344,460)
(345,469)(346,470)(347,472)(348,471)(349,466)(350,465)(351,467)(352,468)
(353,477)(354,478)(355,480)(356,479)(357,474)(358,473)(359,475)(360,476);;
s1 := ( 3, 6)( 4, 5)( 7, 8)( 9, 33)( 10, 34)( 11, 38)( 12, 37)( 13, 36)
( 14, 35)( 15, 40)( 16, 39)( 17, 25)( 18, 26)( 19, 30)( 20, 29)( 21, 28)
( 22, 27)( 23, 32)( 24, 31)( 41, 81)( 42, 82)( 43, 86)( 44, 85)( 45, 84)
( 46, 83)( 47, 88)( 48, 87)( 49,113)( 50,114)( 51,118)( 52,117)( 53,116)
( 54,115)( 55,120)( 56,119)( 57,105)( 58,106)( 59,110)( 60,109)( 61,108)
( 62,107)( 63,112)( 64,111)( 65, 97)( 66, 98)( 67,102)( 68,101)( 69,100)
( 70, 99)( 71,104)( 72,103)( 73, 89)( 74, 90)( 75, 94)( 76, 93)( 77, 92)
( 78, 91)( 79, 96)( 80, 95)(121,122)(123,125)(124,126)(129,154)(130,153)
(131,157)(132,158)(133,155)(134,156)(135,159)(136,160)(137,146)(138,145)
(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(161,202)(162,201)
(163,205)(164,206)(165,203)(166,204)(167,207)(168,208)(169,234)(170,233)
(171,237)(172,238)(173,235)(174,236)(175,239)(176,240)(177,226)(178,225)
(179,229)(180,230)(181,227)(182,228)(183,231)(184,232)(185,218)(186,217)
(187,221)(188,222)(189,219)(190,220)(191,223)(192,224)(193,210)(194,209)
(195,213)(196,214)(197,211)(198,212)(199,215)(200,216)(243,246)(244,245)
(247,248)(249,273)(250,274)(251,278)(252,277)(253,276)(254,275)(255,280)
(256,279)(257,265)(258,266)(259,270)(260,269)(261,268)(262,267)(263,272)
(264,271)(281,321)(282,322)(283,326)(284,325)(285,324)(286,323)(287,328)
(288,327)(289,353)(290,354)(291,358)(292,357)(293,356)(294,355)(295,360)
(296,359)(297,345)(298,346)(299,350)(300,349)(301,348)(302,347)(303,352)
(304,351)(305,337)(306,338)(307,342)(308,341)(309,340)(310,339)(311,344)
(312,343)(313,329)(314,330)(315,334)(316,333)(317,332)(318,331)(319,336)
(320,335)(361,362)(363,365)(364,366)(369,394)(370,393)(371,397)(372,398)
(373,395)(374,396)(375,399)(376,400)(377,386)(378,385)(379,389)(380,390)
(381,387)(382,388)(383,391)(384,392)(401,442)(402,441)(403,445)(404,446)
(405,443)(406,444)(407,447)(408,448)(409,474)(410,473)(411,477)(412,478)
(413,475)(414,476)(415,479)(416,480)(417,466)(418,465)(419,469)(420,470)
(421,467)(422,468)(423,471)(424,472)(425,458)(426,457)(427,461)(428,462)
(429,459)(430,460)(431,463)(432,464)(433,450)(434,449)(435,453)(436,454)
(437,451)(438,452)(439,455)(440,456);;
s2 := ( 1,329)( 2,330)( 3,335)( 4,336)( 5,334)( 6,333)( 7,331)( 8,332)
( 9,321)( 10,322)( 11,327)( 12,328)( 13,326)( 14,325)( 15,323)( 16,324)
( 17,353)( 18,354)( 19,359)( 20,360)( 21,358)( 22,357)( 23,355)( 24,356)
( 25,345)( 26,346)( 27,351)( 28,352)( 29,350)( 30,349)( 31,347)( 32,348)
( 33,337)( 34,338)( 35,343)( 36,344)( 37,342)( 38,341)( 39,339)( 40,340)
( 41,289)( 42,290)( 43,295)( 44,296)( 45,294)( 46,293)( 47,291)( 48,292)
( 49,281)( 50,282)( 51,287)( 52,288)( 53,286)( 54,285)( 55,283)( 56,284)
( 57,313)( 58,314)( 59,319)( 60,320)( 61,318)( 62,317)( 63,315)( 64,316)
( 65,305)( 66,306)( 67,311)( 68,312)( 69,310)( 70,309)( 71,307)( 72,308)
( 73,297)( 74,298)( 75,303)( 76,304)( 77,302)( 78,301)( 79,299)( 80,300)
( 81,249)( 82,250)( 83,255)( 84,256)( 85,254)( 86,253)( 87,251)( 88,252)
( 89,241)( 90,242)( 91,247)( 92,248)( 93,246)( 94,245)( 95,243)( 96,244)
( 97,273)( 98,274)( 99,279)(100,280)(101,278)(102,277)(103,275)(104,276)
(105,265)(106,266)(107,271)(108,272)(109,270)(110,269)(111,267)(112,268)
(113,257)(114,258)(115,263)(116,264)(117,262)(118,261)(119,259)(120,260)
(121,450)(122,449)(123,456)(124,455)(125,453)(126,454)(127,452)(128,451)
(129,442)(130,441)(131,448)(132,447)(133,445)(134,446)(135,444)(136,443)
(137,474)(138,473)(139,480)(140,479)(141,477)(142,478)(143,476)(144,475)
(145,466)(146,465)(147,472)(148,471)(149,469)(150,470)(151,468)(152,467)
(153,458)(154,457)(155,464)(156,463)(157,461)(158,462)(159,460)(160,459)
(161,410)(162,409)(163,416)(164,415)(165,413)(166,414)(167,412)(168,411)
(169,402)(170,401)(171,408)(172,407)(173,405)(174,406)(175,404)(176,403)
(177,434)(178,433)(179,440)(180,439)(181,437)(182,438)(183,436)(184,435)
(185,426)(186,425)(187,432)(188,431)(189,429)(190,430)(191,428)(192,427)
(193,418)(194,417)(195,424)(196,423)(197,421)(198,422)(199,420)(200,419)
(201,370)(202,369)(203,376)(204,375)(205,373)(206,374)(207,372)(208,371)
(209,362)(210,361)(211,368)(212,367)(213,365)(214,366)(215,364)(216,363)
(217,394)(218,393)(219,400)(220,399)(221,397)(222,398)(223,396)(224,395)
(225,386)(226,385)(227,392)(228,391)(229,389)(230,390)(231,388)(232,387)
(233,378)(234,377)(235,384)(236,383)(237,381)(238,382)(239,380)(240,379);;
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*s2*s1*s0*s1*s2*s1*s2*s1,
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,
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)!( 1,125)( 2,126)( 3,128)( 4,127)( 5,122)( 6,121)( 7,123)
( 8,124)( 9,133)( 10,134)( 11,136)( 12,135)( 13,130)( 14,129)( 15,131)
( 16,132)( 17,141)( 18,142)( 19,144)( 20,143)( 21,138)( 22,137)( 23,139)
( 24,140)( 25,149)( 26,150)( 27,152)( 28,151)( 29,146)( 30,145)( 31,147)
( 32,148)( 33,157)( 34,158)( 35,160)( 36,159)( 37,154)( 38,153)( 39,155)
( 40,156)( 41,165)( 42,166)( 43,168)( 44,167)( 45,162)( 46,161)( 47,163)
( 48,164)( 49,173)( 50,174)( 51,176)( 52,175)( 53,170)( 54,169)( 55,171)
( 56,172)( 57,181)( 58,182)( 59,184)( 60,183)( 61,178)( 62,177)( 63,179)
( 64,180)( 65,189)( 66,190)( 67,192)( 68,191)( 69,186)( 70,185)( 71,187)
( 72,188)( 73,197)( 74,198)( 75,200)( 76,199)( 77,194)( 78,193)( 79,195)
( 80,196)( 81,205)( 82,206)( 83,208)( 84,207)( 85,202)( 86,201)( 87,203)
( 88,204)( 89,213)( 90,214)( 91,216)( 92,215)( 93,210)( 94,209)( 95,211)
( 96,212)( 97,221)( 98,222)( 99,224)(100,223)(101,218)(102,217)(103,219)
(104,220)(105,229)(106,230)(107,232)(108,231)(109,226)(110,225)(111,227)
(112,228)(113,237)(114,238)(115,240)(116,239)(117,234)(118,233)(119,235)
(120,236)(241,365)(242,366)(243,368)(244,367)(245,362)(246,361)(247,363)
(248,364)(249,373)(250,374)(251,376)(252,375)(253,370)(254,369)(255,371)
(256,372)(257,381)(258,382)(259,384)(260,383)(261,378)(262,377)(263,379)
(264,380)(265,389)(266,390)(267,392)(268,391)(269,386)(270,385)(271,387)
(272,388)(273,397)(274,398)(275,400)(276,399)(277,394)(278,393)(279,395)
(280,396)(281,405)(282,406)(283,408)(284,407)(285,402)(286,401)(287,403)
(288,404)(289,413)(290,414)(291,416)(292,415)(293,410)(294,409)(295,411)
(296,412)(297,421)(298,422)(299,424)(300,423)(301,418)(302,417)(303,419)
(304,420)(305,429)(306,430)(307,432)(308,431)(309,426)(310,425)(311,427)
(312,428)(313,437)(314,438)(315,440)(316,439)(317,434)(318,433)(319,435)
(320,436)(321,445)(322,446)(323,448)(324,447)(325,442)(326,441)(327,443)
(328,444)(329,453)(330,454)(331,456)(332,455)(333,450)(334,449)(335,451)
(336,452)(337,461)(338,462)(339,464)(340,463)(341,458)(342,457)(343,459)
(344,460)(345,469)(346,470)(347,472)(348,471)(349,466)(350,465)(351,467)
(352,468)(353,477)(354,478)(355,480)(356,479)(357,474)(358,473)(359,475)
(360,476);
s1 := Sym(480)!( 3, 6)( 4, 5)( 7, 8)( 9, 33)( 10, 34)( 11, 38)( 12, 37)
( 13, 36)( 14, 35)( 15, 40)( 16, 39)( 17, 25)( 18, 26)( 19, 30)( 20, 29)
( 21, 28)( 22, 27)( 23, 32)( 24, 31)( 41, 81)( 42, 82)( 43, 86)( 44, 85)
( 45, 84)( 46, 83)( 47, 88)( 48, 87)( 49,113)( 50,114)( 51,118)( 52,117)
( 53,116)( 54,115)( 55,120)( 56,119)( 57,105)( 58,106)( 59,110)( 60,109)
( 61,108)( 62,107)( 63,112)( 64,111)( 65, 97)( 66, 98)( 67,102)( 68,101)
( 69,100)( 70, 99)( 71,104)( 72,103)( 73, 89)( 74, 90)( 75, 94)( 76, 93)
( 77, 92)( 78, 91)( 79, 96)( 80, 95)(121,122)(123,125)(124,126)(129,154)
(130,153)(131,157)(132,158)(133,155)(134,156)(135,159)(136,160)(137,146)
(138,145)(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(161,202)
(162,201)(163,205)(164,206)(165,203)(166,204)(167,207)(168,208)(169,234)
(170,233)(171,237)(172,238)(173,235)(174,236)(175,239)(176,240)(177,226)
(178,225)(179,229)(180,230)(181,227)(182,228)(183,231)(184,232)(185,218)
(186,217)(187,221)(188,222)(189,219)(190,220)(191,223)(192,224)(193,210)
(194,209)(195,213)(196,214)(197,211)(198,212)(199,215)(200,216)(243,246)
(244,245)(247,248)(249,273)(250,274)(251,278)(252,277)(253,276)(254,275)
(255,280)(256,279)(257,265)(258,266)(259,270)(260,269)(261,268)(262,267)
(263,272)(264,271)(281,321)(282,322)(283,326)(284,325)(285,324)(286,323)
(287,328)(288,327)(289,353)(290,354)(291,358)(292,357)(293,356)(294,355)
(295,360)(296,359)(297,345)(298,346)(299,350)(300,349)(301,348)(302,347)
(303,352)(304,351)(305,337)(306,338)(307,342)(308,341)(309,340)(310,339)
(311,344)(312,343)(313,329)(314,330)(315,334)(316,333)(317,332)(318,331)
(319,336)(320,335)(361,362)(363,365)(364,366)(369,394)(370,393)(371,397)
(372,398)(373,395)(374,396)(375,399)(376,400)(377,386)(378,385)(379,389)
(380,390)(381,387)(382,388)(383,391)(384,392)(401,442)(402,441)(403,445)
(404,446)(405,443)(406,444)(407,447)(408,448)(409,474)(410,473)(411,477)
(412,478)(413,475)(414,476)(415,479)(416,480)(417,466)(418,465)(419,469)
(420,470)(421,467)(422,468)(423,471)(424,472)(425,458)(426,457)(427,461)
(428,462)(429,459)(430,460)(431,463)(432,464)(433,450)(434,449)(435,453)
(436,454)(437,451)(438,452)(439,455)(440,456);
s2 := Sym(480)!( 1,329)( 2,330)( 3,335)( 4,336)( 5,334)( 6,333)( 7,331)
( 8,332)( 9,321)( 10,322)( 11,327)( 12,328)( 13,326)( 14,325)( 15,323)
( 16,324)( 17,353)( 18,354)( 19,359)( 20,360)( 21,358)( 22,357)( 23,355)
( 24,356)( 25,345)( 26,346)( 27,351)( 28,352)( 29,350)( 30,349)( 31,347)
( 32,348)( 33,337)( 34,338)( 35,343)( 36,344)( 37,342)( 38,341)( 39,339)
( 40,340)( 41,289)( 42,290)( 43,295)( 44,296)( 45,294)( 46,293)( 47,291)
( 48,292)( 49,281)( 50,282)( 51,287)( 52,288)( 53,286)( 54,285)( 55,283)
( 56,284)( 57,313)( 58,314)( 59,319)( 60,320)( 61,318)( 62,317)( 63,315)
( 64,316)( 65,305)( 66,306)( 67,311)( 68,312)( 69,310)( 70,309)( 71,307)
( 72,308)( 73,297)( 74,298)( 75,303)( 76,304)( 77,302)( 78,301)( 79,299)
( 80,300)( 81,249)( 82,250)( 83,255)( 84,256)( 85,254)( 86,253)( 87,251)
( 88,252)( 89,241)( 90,242)( 91,247)( 92,248)( 93,246)( 94,245)( 95,243)
( 96,244)( 97,273)( 98,274)( 99,279)(100,280)(101,278)(102,277)(103,275)
(104,276)(105,265)(106,266)(107,271)(108,272)(109,270)(110,269)(111,267)
(112,268)(113,257)(114,258)(115,263)(116,264)(117,262)(118,261)(119,259)
(120,260)(121,450)(122,449)(123,456)(124,455)(125,453)(126,454)(127,452)
(128,451)(129,442)(130,441)(131,448)(132,447)(133,445)(134,446)(135,444)
(136,443)(137,474)(138,473)(139,480)(140,479)(141,477)(142,478)(143,476)
(144,475)(145,466)(146,465)(147,472)(148,471)(149,469)(150,470)(151,468)
(152,467)(153,458)(154,457)(155,464)(156,463)(157,461)(158,462)(159,460)
(160,459)(161,410)(162,409)(163,416)(164,415)(165,413)(166,414)(167,412)
(168,411)(169,402)(170,401)(171,408)(172,407)(173,405)(174,406)(175,404)
(176,403)(177,434)(178,433)(179,440)(180,439)(181,437)(182,438)(183,436)
(184,435)(185,426)(186,425)(187,432)(188,431)(189,429)(190,430)(191,428)
(192,427)(193,418)(194,417)(195,424)(196,423)(197,421)(198,422)(199,420)
(200,419)(201,370)(202,369)(203,376)(204,375)(205,373)(206,374)(207,372)
(208,371)(209,362)(210,361)(211,368)(212,367)(213,365)(214,366)(215,364)
(216,363)(217,394)(218,393)(219,400)(220,399)(221,397)(222,398)(223,396)
(224,395)(225,386)(226,385)(227,392)(228,391)(229,389)(230,390)(231,388)
(232,387)(233,378)(234,377)(235,384)(236,383)(237,381)(238,382)(239,380)
(240,379);
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*s2*s1*s0*s1*s2*s1*s2*s1,
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,
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