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Polytope of Type {30,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,8,2}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240302)
Rank : 4
Schlafli Type : {30,8,2}
Number of vertices, edges, etc : 60, 240, 16, 2
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
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 : {15,8,2}*960, {30,4,2}*960
   4-fold quotients : {15,4,2}*480, {30,4,2}*480b, {30,4,2}*480c
   5-fold quotients : {6,8,2}*384b
   8-fold quotients : {15,4,2}*240, {30,2,2}*240
   10-fold quotients : {3,8,2}*192, {6,4,2}*192
   16-fold quotients : {15,2,2}*120
   20-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   24-fold quotients : {10,2,2}*80
   40-fold quotients : {3,4,2}*48, {6,2,2}*48
   48-fold quotients : {5,2,2}*40
   80-fold quotients : {3,2,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  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);;
s1 := (  1,289)(  2,290)(  3,292)(  4,291)(  5,295)(  6,296)(  7,293)(  8,294)
(  9,281)( 10,282)( 11,284)( 12,283)( 13,287)( 14,288)( 15,285)( 16,286)
( 17,313)( 18,314)( 19,316)( 20,315)( 21,319)( 22,320)( 23,317)( 24,318)
( 25,305)( 26,306)( 27,308)( 28,307)( 29,311)( 30,312)( 31,309)( 32,310)
( 33,297)( 34,298)( 35,300)( 36,299)( 37,303)( 38,304)( 39,301)( 40,302)
( 41,249)( 42,250)( 43,252)( 44,251)( 45,255)( 46,256)( 47,253)( 48,254)
( 49,241)( 50,242)( 51,244)( 52,243)( 53,247)( 54,248)( 55,245)( 56,246)
( 57,273)( 58,274)( 59,276)( 60,275)( 61,279)( 62,280)( 63,277)( 64,278)
( 65,265)( 66,266)( 67,268)( 68,267)( 69,271)( 70,272)( 71,269)( 72,270)
( 73,257)( 74,258)( 75,260)( 76,259)( 77,263)( 78,264)( 79,261)( 80,262)
( 81,329)( 82,330)( 83,332)( 84,331)( 85,335)( 86,336)( 87,333)( 88,334)
( 89,321)( 90,322)( 91,324)( 92,323)( 93,327)( 94,328)( 95,325)( 96,326)
( 97,353)( 98,354)( 99,356)(100,355)(101,359)(102,360)(103,357)(104,358)
(105,345)(106,346)(107,348)(108,347)(109,351)(110,352)(111,349)(112,350)
(113,337)(114,338)(115,340)(116,339)(117,343)(118,344)(119,341)(120,342)
(121,410)(122,409)(123,411)(124,412)(125,416)(126,415)(127,414)(128,413)
(129,402)(130,401)(131,403)(132,404)(133,408)(134,407)(135,406)(136,405)
(137,434)(138,433)(139,435)(140,436)(141,440)(142,439)(143,438)(144,437)
(145,426)(146,425)(147,427)(148,428)(149,432)(150,431)(151,430)(152,429)
(153,418)(154,417)(155,419)(156,420)(157,424)(158,423)(159,422)(160,421)
(161,370)(162,369)(163,371)(164,372)(165,376)(166,375)(167,374)(168,373)
(169,362)(170,361)(171,363)(172,364)(173,368)(174,367)(175,366)(176,365)
(177,394)(178,393)(179,395)(180,396)(181,400)(182,399)(183,398)(184,397)
(185,386)(186,385)(187,387)(188,388)(189,392)(190,391)(191,390)(192,389)
(193,378)(194,377)(195,379)(196,380)(197,384)(198,383)(199,382)(200,381)
(201,450)(202,449)(203,451)(204,452)(205,456)(206,455)(207,454)(208,453)
(209,442)(210,441)(211,443)(212,444)(213,448)(214,447)(215,446)(216,445)
(217,474)(218,473)(219,475)(220,476)(221,480)(222,479)(223,478)(224,477)
(225,466)(226,465)(227,467)(228,468)(229,472)(230,471)(231,470)(232,469)
(233,458)(234,457)(235,459)(236,460)(237,464)(238,463)(239,462)(240,461);;
s2 := (  1,127)(  2,128)(  3,125)(  4,126)(  5,124)(  6,123)(  7,122)(  8,121)
(  9,135)( 10,136)( 11,133)( 12,134)( 13,132)( 14,131)( 15,130)( 16,129)
( 17,143)( 18,144)( 19,141)( 20,142)( 21,140)( 22,139)( 23,138)( 24,137)
( 25,151)( 26,152)( 27,149)( 28,150)( 29,148)( 30,147)( 31,146)( 32,145)
( 33,159)( 34,160)( 35,157)( 36,158)( 37,156)( 38,155)( 39,154)( 40,153)
( 41,167)( 42,168)( 43,165)( 44,166)( 45,164)( 46,163)( 47,162)( 48,161)
( 49,175)( 50,176)( 51,173)( 52,174)( 53,172)( 54,171)( 55,170)( 56,169)
( 57,183)( 58,184)( 59,181)( 60,182)( 61,180)( 62,179)( 63,178)( 64,177)
( 65,191)( 66,192)( 67,189)( 68,190)( 69,188)( 70,187)( 71,186)( 72,185)
( 73,199)( 74,200)( 75,197)( 76,198)( 77,196)( 78,195)( 79,194)( 80,193)
( 81,207)( 82,208)( 83,205)( 84,206)( 85,204)( 86,203)( 87,202)( 88,201)
( 89,215)( 90,216)( 91,213)( 92,214)( 93,212)( 94,211)( 95,210)( 96,209)
( 97,223)( 98,224)( 99,221)(100,222)(101,220)(102,219)(103,218)(104,217)
(105,231)(106,232)(107,229)(108,230)(109,228)(110,227)(111,226)(112,225)
(113,239)(114,240)(115,237)(116,238)(117,236)(118,235)(119,234)(120,233)
(241,367)(242,368)(243,365)(244,366)(245,364)(246,363)(247,362)(248,361)
(249,375)(250,376)(251,373)(252,374)(253,372)(254,371)(255,370)(256,369)
(257,383)(258,384)(259,381)(260,382)(261,380)(262,379)(263,378)(264,377)
(265,391)(266,392)(267,389)(268,390)(269,388)(270,387)(271,386)(272,385)
(273,399)(274,400)(275,397)(276,398)(277,396)(278,395)(279,394)(280,393)
(281,407)(282,408)(283,405)(284,406)(285,404)(286,403)(287,402)(288,401)
(289,415)(290,416)(291,413)(292,414)(293,412)(294,411)(295,410)(296,409)
(297,423)(298,424)(299,421)(300,422)(301,420)(302,419)(303,418)(304,417)
(305,431)(306,432)(307,429)(308,430)(309,428)(310,427)(311,426)(312,425)
(313,439)(314,440)(315,437)(316,438)(317,436)(318,435)(319,434)(320,433)
(321,447)(322,448)(323,445)(324,446)(325,444)(326,443)(327,442)(328,441)
(329,455)(330,456)(331,453)(332,454)(333,452)(334,451)(335,450)(336,449)
(337,463)(338,464)(339,461)(340,462)(341,460)(342,459)(343,458)(344,457)
(345,471)(346,472)(347,469)(348,470)(349,468)(350,467)(351,466)(352,465)
(353,479)(354,480)(355,477)(356,478)(357,476)(358,475)(359,474)(360,473);;
s3 := (481,482);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(482)!(  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);
s1 := Sym(482)!(  1,289)(  2,290)(  3,292)(  4,291)(  5,295)(  6,296)(  7,293)
(  8,294)(  9,281)( 10,282)( 11,284)( 12,283)( 13,287)( 14,288)( 15,285)
( 16,286)( 17,313)( 18,314)( 19,316)( 20,315)( 21,319)( 22,320)( 23,317)
( 24,318)( 25,305)( 26,306)( 27,308)( 28,307)( 29,311)( 30,312)( 31,309)
( 32,310)( 33,297)( 34,298)( 35,300)( 36,299)( 37,303)( 38,304)( 39,301)
( 40,302)( 41,249)( 42,250)( 43,252)( 44,251)( 45,255)( 46,256)( 47,253)
( 48,254)( 49,241)( 50,242)( 51,244)( 52,243)( 53,247)( 54,248)( 55,245)
( 56,246)( 57,273)( 58,274)( 59,276)( 60,275)( 61,279)( 62,280)( 63,277)
( 64,278)( 65,265)( 66,266)( 67,268)( 68,267)( 69,271)( 70,272)( 71,269)
( 72,270)( 73,257)( 74,258)( 75,260)( 76,259)( 77,263)( 78,264)( 79,261)
( 80,262)( 81,329)( 82,330)( 83,332)( 84,331)( 85,335)( 86,336)( 87,333)
( 88,334)( 89,321)( 90,322)( 91,324)( 92,323)( 93,327)( 94,328)( 95,325)
( 96,326)( 97,353)( 98,354)( 99,356)(100,355)(101,359)(102,360)(103,357)
(104,358)(105,345)(106,346)(107,348)(108,347)(109,351)(110,352)(111,349)
(112,350)(113,337)(114,338)(115,340)(116,339)(117,343)(118,344)(119,341)
(120,342)(121,410)(122,409)(123,411)(124,412)(125,416)(126,415)(127,414)
(128,413)(129,402)(130,401)(131,403)(132,404)(133,408)(134,407)(135,406)
(136,405)(137,434)(138,433)(139,435)(140,436)(141,440)(142,439)(143,438)
(144,437)(145,426)(146,425)(147,427)(148,428)(149,432)(150,431)(151,430)
(152,429)(153,418)(154,417)(155,419)(156,420)(157,424)(158,423)(159,422)
(160,421)(161,370)(162,369)(163,371)(164,372)(165,376)(166,375)(167,374)
(168,373)(169,362)(170,361)(171,363)(172,364)(173,368)(174,367)(175,366)
(176,365)(177,394)(178,393)(179,395)(180,396)(181,400)(182,399)(183,398)
(184,397)(185,386)(186,385)(187,387)(188,388)(189,392)(190,391)(191,390)
(192,389)(193,378)(194,377)(195,379)(196,380)(197,384)(198,383)(199,382)
(200,381)(201,450)(202,449)(203,451)(204,452)(205,456)(206,455)(207,454)
(208,453)(209,442)(210,441)(211,443)(212,444)(213,448)(214,447)(215,446)
(216,445)(217,474)(218,473)(219,475)(220,476)(221,480)(222,479)(223,478)
(224,477)(225,466)(226,465)(227,467)(228,468)(229,472)(230,471)(231,470)
(232,469)(233,458)(234,457)(235,459)(236,460)(237,464)(238,463)(239,462)
(240,461);
s2 := Sym(482)!(  1,127)(  2,128)(  3,125)(  4,126)(  5,124)(  6,123)(  7,122)
(  8,121)(  9,135)( 10,136)( 11,133)( 12,134)( 13,132)( 14,131)( 15,130)
( 16,129)( 17,143)( 18,144)( 19,141)( 20,142)( 21,140)( 22,139)( 23,138)
( 24,137)( 25,151)( 26,152)( 27,149)( 28,150)( 29,148)( 30,147)( 31,146)
( 32,145)( 33,159)( 34,160)( 35,157)( 36,158)( 37,156)( 38,155)( 39,154)
( 40,153)( 41,167)( 42,168)( 43,165)( 44,166)( 45,164)( 46,163)( 47,162)
( 48,161)( 49,175)( 50,176)( 51,173)( 52,174)( 53,172)( 54,171)( 55,170)
( 56,169)( 57,183)( 58,184)( 59,181)( 60,182)( 61,180)( 62,179)( 63,178)
( 64,177)( 65,191)( 66,192)( 67,189)( 68,190)( 69,188)( 70,187)( 71,186)
( 72,185)( 73,199)( 74,200)( 75,197)( 76,198)( 77,196)( 78,195)( 79,194)
( 80,193)( 81,207)( 82,208)( 83,205)( 84,206)( 85,204)( 86,203)( 87,202)
( 88,201)( 89,215)( 90,216)( 91,213)( 92,214)( 93,212)( 94,211)( 95,210)
( 96,209)( 97,223)( 98,224)( 99,221)(100,222)(101,220)(102,219)(103,218)
(104,217)(105,231)(106,232)(107,229)(108,230)(109,228)(110,227)(111,226)
(112,225)(113,239)(114,240)(115,237)(116,238)(117,236)(118,235)(119,234)
(120,233)(241,367)(242,368)(243,365)(244,366)(245,364)(246,363)(247,362)
(248,361)(249,375)(250,376)(251,373)(252,374)(253,372)(254,371)(255,370)
(256,369)(257,383)(258,384)(259,381)(260,382)(261,380)(262,379)(263,378)
(264,377)(265,391)(266,392)(267,389)(268,390)(269,388)(270,387)(271,386)
(272,385)(273,399)(274,400)(275,397)(276,398)(277,396)(278,395)(279,394)
(280,393)(281,407)(282,408)(283,405)(284,406)(285,404)(286,403)(287,402)
(288,401)(289,415)(290,416)(291,413)(292,414)(293,412)(294,411)(295,410)
(296,409)(297,423)(298,424)(299,421)(300,422)(301,420)(302,419)(303,418)
(304,417)(305,431)(306,432)(307,429)(308,430)(309,428)(310,427)(311,426)
(312,425)(313,439)(314,440)(315,437)(316,438)(317,436)(318,435)(319,434)
(320,433)(321,447)(322,448)(323,445)(324,446)(325,444)(326,443)(327,442)
(328,441)(329,455)(330,456)(331,453)(332,454)(333,452)(334,451)(335,450)
(336,449)(337,463)(338,464)(339,461)(340,462)(341,460)(342,459)(343,458)
(344,457)(345,471)(346,472)(347,469)(348,470)(349,468)(350,467)(351,466)
(352,465)(353,479)(354,480)(355,477)(356,478)(357,476)(358,475)(359,474)
(360,473);
s3 := Sym(482)!(481,482);
poly := sub<Sym(482)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

to this polytope