Polytope of Type {20,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,240142)
Rank : 4
Schlafli Type : {20,6,6}
Number of vertices, edges, etc : 20, 80, 24, 8
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {20,6,3}*960, {10,6,6}*960
4-fold quotients : {10,6,3}*480
5-fold quotients : {4,6,6}*384
10-fold quotients : {4,6,3}*192, {2,6,6}*192
12-fold quotients : {20,2,2}*160
20-fold quotients : {2,3,6}*96, {2,6,3}*96
24-fold quotients : {10,2,2}*80
40-fold quotients : {2,3,3}*48
48-fold quotients : {5,2,2}*40
60-fold quotients : {4,2,2}*32
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 17)( 6, 18)( 7, 19)( 8, 20)( 9, 13)( 10, 14)( 11, 15)( 12, 16)
( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)
( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116)
(121,181)(122,182)(123,183)(124,184)(125,197)(126,198)(127,199)(128,200)
(129,193)(130,194)(131,195)(132,196)(133,189)(134,190)(135,191)(136,192)
(137,185)(138,186)(139,187)(140,188)(141,201)(142,202)(143,203)(144,204)
(145,217)(146,218)(147,219)(148,220)(149,213)(150,214)(151,215)(152,216)
(153,209)(154,210)(155,211)(156,212)(157,205)(158,206)(159,207)(160,208)
(161,221)(162,222)(163,223)(164,224)(165,237)(166,238)(167,239)(168,240)
(169,233)(170,234)(171,235)(172,236)(173,229)(174,230)(175,231)(176,232)
(177,225)(178,226)(179,227)(180,228)(245,257)(246,258)(247,259)(248,260)
(249,253)(250,254)(251,255)(252,256)(265,277)(266,278)(267,279)(268,280)
(269,273)(270,274)(271,275)(272,276)(285,297)(286,298)(287,299)(288,300)
(289,293)(290,294)(291,295)(292,296)(305,317)(306,318)(307,319)(308,320)
(309,313)(310,314)(311,315)(312,316)(325,337)(326,338)(327,339)(328,340)
(329,333)(330,334)(331,335)(332,336)(345,357)(346,358)(347,359)(348,360)
(349,353)(350,354)(351,355)(352,356)(361,421)(362,422)(363,423)(364,424)
(365,437)(366,438)(367,439)(368,440)(369,433)(370,434)(371,435)(372,436)
(373,429)(374,430)(375,431)(376,432)(377,425)(378,426)(379,427)(380,428)
(381,441)(382,442)(383,443)(384,444)(385,457)(386,458)(387,459)(388,460)
(389,453)(390,454)(391,455)(392,456)(393,449)(394,450)(395,451)(396,452)
(397,445)(398,446)(399,447)(400,448)(401,461)(402,462)(403,463)(404,464)
(405,477)(406,478)(407,479)(408,480)(409,473)(410,474)(411,475)(412,476)
(413,469)(414,470)(415,471)(416,472)(417,465)(418,466)(419,467)(420,468);;
s1 := ( 1,125)( 2,126)( 3,128)( 4,127)( 5,121)( 6,122)( 7,124)( 8,123)
( 9,137)( 10,138)( 11,140)( 12,139)( 13,133)( 14,134)( 15,136)( 16,135)
( 17,129)( 18,130)( 19,132)( 20,131)( 21,165)( 22,166)( 23,168)( 24,167)
( 25,161)( 26,162)( 27,164)( 28,163)( 29,177)( 30,178)( 31,180)( 32,179)
( 33,173)( 34,174)( 35,176)( 36,175)( 37,169)( 38,170)( 39,172)( 40,171)
( 41,145)( 42,146)( 43,148)( 44,147)( 45,141)( 46,142)( 47,144)( 48,143)
( 49,157)( 50,158)( 51,160)( 52,159)( 53,153)( 54,154)( 55,156)( 56,155)
( 57,149)( 58,150)( 59,152)( 60,151)( 61,185)( 62,186)( 63,188)( 64,187)
( 65,181)( 66,182)( 67,184)( 68,183)( 69,197)( 70,198)( 71,200)( 72,199)
( 73,193)( 74,194)( 75,196)( 76,195)( 77,189)( 78,190)( 79,192)( 80,191)
( 81,225)( 82,226)( 83,228)( 84,227)( 85,221)( 86,222)( 87,224)( 88,223)
( 89,237)( 90,238)( 91,240)( 92,239)( 93,233)( 94,234)( 95,236)( 96,235)
( 97,229)( 98,230)( 99,232)(100,231)(101,205)(102,206)(103,208)(104,207)
(105,201)(106,202)(107,204)(108,203)(109,217)(110,218)(111,220)(112,219)
(113,213)(114,214)(115,216)(116,215)(117,209)(118,210)(119,212)(120,211)
(241,365)(242,366)(243,368)(244,367)(245,361)(246,362)(247,364)(248,363)
(249,377)(250,378)(251,380)(252,379)(253,373)(254,374)(255,376)(256,375)
(257,369)(258,370)(259,372)(260,371)(261,405)(262,406)(263,408)(264,407)
(265,401)(266,402)(267,404)(268,403)(269,417)(270,418)(271,420)(272,419)
(273,413)(274,414)(275,416)(276,415)(277,409)(278,410)(279,412)(280,411)
(281,385)(282,386)(283,388)(284,387)(285,381)(286,382)(287,384)(288,383)
(289,397)(290,398)(291,400)(292,399)(293,393)(294,394)(295,396)(296,395)
(297,389)(298,390)(299,392)(300,391)(301,425)(302,426)(303,428)(304,427)
(305,421)(306,422)(307,424)(308,423)(309,437)(310,438)(311,440)(312,439)
(313,433)(314,434)(315,436)(316,435)(317,429)(318,430)(319,432)(320,431)
(321,465)(322,466)(323,468)(324,467)(325,461)(326,462)(327,464)(328,463)
(329,477)(330,478)(331,480)(332,479)(333,473)(334,474)(335,476)(336,475)
(337,469)(338,470)(339,472)(340,471)(341,445)(342,446)(343,448)(344,447)
(345,441)(346,442)(347,444)(348,443)(349,457)(350,458)(351,460)(352,459)
(353,453)(354,454)(355,456)(356,455)(357,449)(358,450)(359,452)(360,451);;
s2 := ( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)( 8, 26)
( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)
( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)
( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)
( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)
(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)
(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)
(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)
(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)
(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)
(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)
(226,228)(230,232)(234,236)(238,240)(241,261)(242,264)(243,263)(244,262)
(245,265)(246,268)(247,267)(248,266)(249,269)(250,272)(251,271)(252,270)
(253,273)(254,276)(255,275)(256,274)(257,277)(258,280)(259,279)(260,278)
(282,284)(286,288)(290,292)(294,296)(298,300)(301,321)(302,324)(303,323)
(304,322)(305,325)(306,328)(307,327)(308,326)(309,329)(310,332)(311,331)
(312,330)(313,333)(314,336)(315,335)(316,334)(317,337)(318,340)(319,339)
(320,338)(342,344)(346,348)(350,352)(354,356)(358,360)(361,381)(362,384)
(363,383)(364,382)(365,385)(366,388)(367,387)(368,386)(369,389)(370,392)
(371,391)(372,390)(373,393)(374,396)(375,395)(376,394)(377,397)(378,400)
(379,399)(380,398)(402,404)(406,408)(410,412)(414,416)(418,420)(421,441)
(422,444)(423,443)(424,442)(425,445)(426,448)(427,447)(428,446)(429,449)
(430,452)(431,451)(432,450)(433,453)(434,456)(435,455)(436,454)(437,457)
(438,460)(439,459)(440,458)(462,464)(466,468)(470,472)(474,476)(478,480);;
s3 := ( 1,242)( 2,241)( 3,243)( 4,244)( 5,246)( 6,245)( 7,247)( 8,248)
( 9,250)( 10,249)( 11,251)( 12,252)( 13,254)( 14,253)( 15,255)( 16,256)
( 17,258)( 18,257)( 19,259)( 20,260)( 21,282)( 22,281)( 23,283)( 24,284)
( 25,286)( 26,285)( 27,287)( 28,288)( 29,290)( 30,289)( 31,291)( 32,292)
( 33,294)( 34,293)( 35,295)( 36,296)( 37,298)( 38,297)( 39,299)( 40,300)
( 41,262)( 42,261)( 43,263)( 44,264)( 45,266)( 46,265)( 47,267)( 48,268)
( 49,270)( 50,269)( 51,271)( 52,272)( 53,274)( 54,273)( 55,275)( 56,276)
( 57,278)( 58,277)( 59,279)( 60,280)( 61,302)( 62,301)( 63,303)( 64,304)
( 65,306)( 66,305)( 67,307)( 68,308)( 69,310)( 70,309)( 71,311)( 72,312)
( 73,314)( 74,313)( 75,315)( 76,316)( 77,318)( 78,317)( 79,319)( 80,320)
( 81,342)( 82,341)( 83,343)( 84,344)( 85,346)( 86,345)( 87,347)( 88,348)
( 89,350)( 90,349)( 91,351)( 92,352)( 93,354)( 94,353)( 95,355)( 96,356)
( 97,358)( 98,357)( 99,359)(100,360)(101,322)(102,321)(103,323)(104,324)
(105,326)(106,325)(107,327)(108,328)(109,330)(110,329)(111,331)(112,332)
(113,334)(114,333)(115,335)(116,336)(117,338)(118,337)(119,339)(120,340)
(121,362)(122,361)(123,363)(124,364)(125,366)(126,365)(127,367)(128,368)
(129,370)(130,369)(131,371)(132,372)(133,374)(134,373)(135,375)(136,376)
(137,378)(138,377)(139,379)(140,380)(141,402)(142,401)(143,403)(144,404)
(145,406)(146,405)(147,407)(148,408)(149,410)(150,409)(151,411)(152,412)
(153,414)(154,413)(155,415)(156,416)(157,418)(158,417)(159,419)(160,420)
(161,382)(162,381)(163,383)(164,384)(165,386)(166,385)(167,387)(168,388)
(169,390)(170,389)(171,391)(172,392)(173,394)(174,393)(175,395)(176,396)
(177,398)(178,397)(179,399)(180,400)(181,422)(182,421)(183,423)(184,424)
(185,426)(186,425)(187,427)(188,428)(189,430)(190,429)(191,431)(192,432)
(193,434)(194,433)(195,435)(196,436)(197,438)(198,437)(199,439)(200,440)
(201,462)(202,461)(203,463)(204,464)(205,466)(206,465)(207,467)(208,468)
(209,470)(210,469)(211,471)(212,472)(213,474)(214,473)(215,475)(216,476)
(217,478)(218,477)(219,479)(220,480)(221,442)(222,441)(223,443)(224,444)
(225,446)(226,445)(227,447)(228,448)(229,450)(230,449)(231,451)(232,452)
(233,454)(234,453)(235,455)(236,456)(237,458)(238,457)(239,459)(240,460);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 5, 17)( 6, 18)( 7, 19)( 8, 20)( 9, 13)( 10, 14)( 11, 15)
( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)
( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)
( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)
(112,116)(121,181)(122,182)(123,183)(124,184)(125,197)(126,198)(127,199)
(128,200)(129,193)(130,194)(131,195)(132,196)(133,189)(134,190)(135,191)
(136,192)(137,185)(138,186)(139,187)(140,188)(141,201)(142,202)(143,203)
(144,204)(145,217)(146,218)(147,219)(148,220)(149,213)(150,214)(151,215)
(152,216)(153,209)(154,210)(155,211)(156,212)(157,205)(158,206)(159,207)
(160,208)(161,221)(162,222)(163,223)(164,224)(165,237)(166,238)(167,239)
(168,240)(169,233)(170,234)(171,235)(172,236)(173,229)(174,230)(175,231)
(176,232)(177,225)(178,226)(179,227)(180,228)(245,257)(246,258)(247,259)
(248,260)(249,253)(250,254)(251,255)(252,256)(265,277)(266,278)(267,279)
(268,280)(269,273)(270,274)(271,275)(272,276)(285,297)(286,298)(287,299)
(288,300)(289,293)(290,294)(291,295)(292,296)(305,317)(306,318)(307,319)
(308,320)(309,313)(310,314)(311,315)(312,316)(325,337)(326,338)(327,339)
(328,340)(329,333)(330,334)(331,335)(332,336)(345,357)(346,358)(347,359)
(348,360)(349,353)(350,354)(351,355)(352,356)(361,421)(362,422)(363,423)
(364,424)(365,437)(366,438)(367,439)(368,440)(369,433)(370,434)(371,435)
(372,436)(373,429)(374,430)(375,431)(376,432)(377,425)(378,426)(379,427)
(380,428)(381,441)(382,442)(383,443)(384,444)(385,457)(386,458)(387,459)
(388,460)(389,453)(390,454)(391,455)(392,456)(393,449)(394,450)(395,451)
(396,452)(397,445)(398,446)(399,447)(400,448)(401,461)(402,462)(403,463)
(404,464)(405,477)(406,478)(407,479)(408,480)(409,473)(410,474)(411,475)
(412,476)(413,469)(414,470)(415,471)(416,472)(417,465)(418,466)(419,467)
(420,468);
s1 := Sym(480)!( 1,125)( 2,126)( 3,128)( 4,127)( 5,121)( 6,122)( 7,124)
( 8,123)( 9,137)( 10,138)( 11,140)( 12,139)( 13,133)( 14,134)( 15,136)
( 16,135)( 17,129)( 18,130)( 19,132)( 20,131)( 21,165)( 22,166)( 23,168)
( 24,167)( 25,161)( 26,162)( 27,164)( 28,163)( 29,177)( 30,178)( 31,180)
( 32,179)( 33,173)( 34,174)( 35,176)( 36,175)( 37,169)( 38,170)( 39,172)
( 40,171)( 41,145)( 42,146)( 43,148)( 44,147)( 45,141)( 46,142)( 47,144)
( 48,143)( 49,157)( 50,158)( 51,160)( 52,159)( 53,153)( 54,154)( 55,156)
( 56,155)( 57,149)( 58,150)( 59,152)( 60,151)( 61,185)( 62,186)( 63,188)
( 64,187)( 65,181)( 66,182)( 67,184)( 68,183)( 69,197)( 70,198)( 71,200)
( 72,199)( 73,193)( 74,194)( 75,196)( 76,195)( 77,189)( 78,190)( 79,192)
( 80,191)( 81,225)( 82,226)( 83,228)( 84,227)( 85,221)( 86,222)( 87,224)
( 88,223)( 89,237)( 90,238)( 91,240)( 92,239)( 93,233)( 94,234)( 95,236)
( 96,235)( 97,229)( 98,230)( 99,232)(100,231)(101,205)(102,206)(103,208)
(104,207)(105,201)(106,202)(107,204)(108,203)(109,217)(110,218)(111,220)
(112,219)(113,213)(114,214)(115,216)(116,215)(117,209)(118,210)(119,212)
(120,211)(241,365)(242,366)(243,368)(244,367)(245,361)(246,362)(247,364)
(248,363)(249,377)(250,378)(251,380)(252,379)(253,373)(254,374)(255,376)
(256,375)(257,369)(258,370)(259,372)(260,371)(261,405)(262,406)(263,408)
(264,407)(265,401)(266,402)(267,404)(268,403)(269,417)(270,418)(271,420)
(272,419)(273,413)(274,414)(275,416)(276,415)(277,409)(278,410)(279,412)
(280,411)(281,385)(282,386)(283,388)(284,387)(285,381)(286,382)(287,384)
(288,383)(289,397)(290,398)(291,400)(292,399)(293,393)(294,394)(295,396)
(296,395)(297,389)(298,390)(299,392)(300,391)(301,425)(302,426)(303,428)
(304,427)(305,421)(306,422)(307,424)(308,423)(309,437)(310,438)(311,440)
(312,439)(313,433)(314,434)(315,436)(316,435)(317,429)(318,430)(319,432)
(320,431)(321,465)(322,466)(323,468)(324,467)(325,461)(326,462)(327,464)
(328,463)(329,477)(330,478)(331,480)(332,479)(333,473)(334,474)(335,476)
(336,475)(337,469)(338,470)(339,472)(340,471)(341,445)(342,446)(343,448)
(344,447)(345,441)(346,442)(347,444)(348,443)(349,457)(350,458)(351,460)
(352,459)(353,453)(354,454)(355,456)(356,455)(357,449)(358,450)(359,452)
(360,451);
s2 := Sym(480)!( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)
( 8, 26)( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)
( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)
( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)
( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)
(110,112)(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)
(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)
(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)
(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)
(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)
(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)
(222,224)(226,228)(230,232)(234,236)(238,240)(241,261)(242,264)(243,263)
(244,262)(245,265)(246,268)(247,267)(248,266)(249,269)(250,272)(251,271)
(252,270)(253,273)(254,276)(255,275)(256,274)(257,277)(258,280)(259,279)
(260,278)(282,284)(286,288)(290,292)(294,296)(298,300)(301,321)(302,324)
(303,323)(304,322)(305,325)(306,328)(307,327)(308,326)(309,329)(310,332)
(311,331)(312,330)(313,333)(314,336)(315,335)(316,334)(317,337)(318,340)
(319,339)(320,338)(342,344)(346,348)(350,352)(354,356)(358,360)(361,381)
(362,384)(363,383)(364,382)(365,385)(366,388)(367,387)(368,386)(369,389)
(370,392)(371,391)(372,390)(373,393)(374,396)(375,395)(376,394)(377,397)
(378,400)(379,399)(380,398)(402,404)(406,408)(410,412)(414,416)(418,420)
(421,441)(422,444)(423,443)(424,442)(425,445)(426,448)(427,447)(428,446)
(429,449)(430,452)(431,451)(432,450)(433,453)(434,456)(435,455)(436,454)
(437,457)(438,460)(439,459)(440,458)(462,464)(466,468)(470,472)(474,476)
(478,480);
s3 := Sym(480)!( 1,242)( 2,241)( 3,243)( 4,244)( 5,246)( 6,245)( 7,247)
( 8,248)( 9,250)( 10,249)( 11,251)( 12,252)( 13,254)( 14,253)( 15,255)
( 16,256)( 17,258)( 18,257)( 19,259)( 20,260)( 21,282)( 22,281)( 23,283)
( 24,284)( 25,286)( 26,285)( 27,287)( 28,288)( 29,290)( 30,289)( 31,291)
( 32,292)( 33,294)( 34,293)( 35,295)( 36,296)( 37,298)( 38,297)( 39,299)
( 40,300)( 41,262)( 42,261)( 43,263)( 44,264)( 45,266)( 46,265)( 47,267)
( 48,268)( 49,270)( 50,269)( 51,271)( 52,272)( 53,274)( 54,273)( 55,275)
( 56,276)( 57,278)( 58,277)( 59,279)( 60,280)( 61,302)( 62,301)( 63,303)
( 64,304)( 65,306)( 66,305)( 67,307)( 68,308)( 69,310)( 70,309)( 71,311)
( 72,312)( 73,314)( 74,313)( 75,315)( 76,316)( 77,318)( 78,317)( 79,319)
( 80,320)( 81,342)( 82,341)( 83,343)( 84,344)( 85,346)( 86,345)( 87,347)
( 88,348)( 89,350)( 90,349)( 91,351)( 92,352)( 93,354)( 94,353)( 95,355)
( 96,356)( 97,358)( 98,357)( 99,359)(100,360)(101,322)(102,321)(103,323)
(104,324)(105,326)(106,325)(107,327)(108,328)(109,330)(110,329)(111,331)
(112,332)(113,334)(114,333)(115,335)(116,336)(117,338)(118,337)(119,339)
(120,340)(121,362)(122,361)(123,363)(124,364)(125,366)(126,365)(127,367)
(128,368)(129,370)(130,369)(131,371)(132,372)(133,374)(134,373)(135,375)
(136,376)(137,378)(138,377)(139,379)(140,380)(141,402)(142,401)(143,403)
(144,404)(145,406)(146,405)(147,407)(148,408)(149,410)(150,409)(151,411)
(152,412)(153,414)(154,413)(155,415)(156,416)(157,418)(158,417)(159,419)
(160,420)(161,382)(162,381)(163,383)(164,384)(165,386)(166,385)(167,387)
(168,388)(169,390)(170,389)(171,391)(172,392)(173,394)(174,393)(175,395)
(176,396)(177,398)(178,397)(179,399)(180,400)(181,422)(182,421)(183,423)
(184,424)(185,426)(186,425)(187,427)(188,428)(189,430)(190,429)(191,431)
(192,432)(193,434)(194,433)(195,435)(196,436)(197,438)(198,437)(199,439)
(200,440)(201,462)(202,461)(203,463)(204,464)(205,466)(206,465)(207,467)
(208,468)(209,470)(210,469)(211,471)(212,472)(213,474)(214,473)(215,475)
(216,476)(217,478)(218,477)(219,479)(220,480)(221,442)(222,441)(223,443)
(224,444)(225,446)(226,445)(227,447)(228,448)(229,450)(230,449)(231,451)
(232,452)(233,454)(234,453)(235,455)(236,456)(237,458)(238,457)(239,459)
(240,460);
poly := sub<Sym(480)|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,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*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 >;
References : None.
to this polytope