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Polytope of Type {10,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 4
Schlafli Type : {10,12,4}
Number of vertices, edges, etc : 10, 120, 48, 8
Order of s0s1s2s3 : 60
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 : {10,12,4}*960b, {10,12,4}*960c, {10,6,4}*960e
   4-fold quotients : {10,12,2}*480, {10,6,4}*480b
   5-fold quotients : {2,12,4}*384b
   8-fold quotients : {10,6,2}*240
   10-fold quotients : {2,12,4}*192b, {2,12,4}*192c, {2,6,4}*192
   12-fold quotients : {10,4,2}*160
   20-fold quotients : {2,12,2}*96, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   24-fold quotients : {10,2,2}*80
   40-fold quotients : {2,3,4}*48, {2,6,2}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {2,4,2}*32
   80-fold quotients : {2,3,2}*24
   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)
(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)
(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156)
(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)(172,176)
(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)(192,196)
(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)(212,216)
(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)(232,236)
(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)
(365,377)(366,378)(367,379)(368,380)(369,373)(370,374)(371,375)(372,376)
(385,397)(386,398)(387,399)(388,400)(389,393)(390,394)(391,395)(392,396)
(405,417)(406,418)(407,419)(408,420)(409,413)(410,414)(411,415)(412,416)
(425,437)(426,438)(427,439)(428,440)(429,433)(430,434)(431,435)(432,436)
(445,457)(446,458)(447,459)(448,460)(449,453)(450,454)(451,455)(452,456)
(465,477)(466,478)(467,479)(468,480)(469,473)(470,474)(471,475)(472,476);;
s1 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9, 17)( 10, 18)( 11, 20)( 12, 19)
( 15, 16)( 21, 45)( 22, 46)( 23, 48)( 24, 47)( 25, 41)( 26, 42)( 27, 44)
( 28, 43)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 53)( 34, 54)( 35, 56)
( 36, 55)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 61, 65)( 62, 66)( 63, 68)
( 64, 67)( 69, 77)( 70, 78)( 71, 80)( 72, 79)( 75, 76)( 81,105)( 82,106)
( 83,108)( 84,107)( 85,101)( 86,102)( 87,104)( 88,103)( 89,117)( 90,118)
( 91,120)( 92,119)( 93,113)( 94,114)( 95,116)( 96,115)( 97,109)( 98,110)
( 99,112)(100,111)(121,185)(122,186)(123,188)(124,187)(125,181)(126,182)
(127,184)(128,183)(129,197)(130,198)(131,200)(132,199)(133,193)(134,194)
(135,196)(136,195)(137,189)(138,190)(139,192)(140,191)(141,225)(142,226)
(143,228)(144,227)(145,221)(146,222)(147,224)(148,223)(149,237)(150,238)
(151,240)(152,239)(153,233)(154,234)(155,236)(156,235)(157,229)(158,230)
(159,232)(160,231)(161,205)(162,206)(163,208)(164,207)(165,201)(166,202)
(167,204)(168,203)(169,217)(170,218)(171,220)(172,219)(173,213)(174,214)
(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(241,245)(242,246)
(243,248)(244,247)(249,257)(250,258)(251,260)(252,259)(255,256)(261,285)
(262,286)(263,288)(264,287)(265,281)(266,282)(267,284)(268,283)(269,297)
(270,298)(271,300)(272,299)(273,293)(274,294)(275,296)(276,295)(277,289)
(278,290)(279,292)(280,291)(301,305)(302,306)(303,308)(304,307)(309,317)
(310,318)(311,320)(312,319)(315,316)(321,345)(322,346)(323,348)(324,347)
(325,341)(326,342)(327,344)(328,343)(329,357)(330,358)(331,360)(332,359)
(333,353)(334,354)(335,356)(336,355)(337,349)(338,350)(339,352)(340,351)
(361,425)(362,426)(363,428)(364,427)(365,421)(366,422)(367,424)(368,423)
(369,437)(370,438)(371,440)(372,439)(373,433)(374,434)(375,436)(376,435)
(377,429)(378,430)(379,432)(380,431)(381,465)(382,466)(383,468)(384,467)
(385,461)(386,462)(387,464)(388,463)(389,477)(390,478)(391,480)(392,479)
(393,473)(394,474)(395,476)(396,475)(397,469)(398,470)(399,472)(400,471)
(401,445)(402,446)(403,448)(404,447)(405,441)(406,442)(407,444)(408,443)
(409,457)(410,458)(411,460)(412,459)(413,453)(414,454)(415,456)(416,455)
(417,449)(418,450)(419,452)(420,451);;
s2 := (  1,141)(  2,144)(  3,143)(  4,142)(  5,145)(  6,148)(  7,147)(  8,146)
(  9,149)( 10,152)( 11,151)( 12,150)( 13,153)( 14,156)( 15,155)( 16,154)
( 17,157)( 18,160)( 19,159)( 20,158)( 21,121)( 22,124)( 23,123)( 24,122)
( 25,125)( 26,128)( 27,127)( 28,126)( 29,129)( 30,132)( 31,131)( 32,130)
( 33,133)( 34,136)( 35,135)( 36,134)( 37,137)( 38,140)( 39,139)( 40,138)
( 41,161)( 42,164)( 43,163)( 44,162)( 45,165)( 46,168)( 47,167)( 48,166)
( 49,169)( 50,172)( 51,171)( 52,170)( 53,173)( 54,176)( 55,175)( 56,174)
( 57,177)( 58,180)( 59,179)( 60,178)( 61,201)( 62,204)( 63,203)( 64,202)
( 65,205)( 66,208)( 67,207)( 68,206)( 69,209)( 70,212)( 71,211)( 72,210)
( 73,213)( 74,216)( 75,215)( 76,214)( 77,217)( 78,220)( 79,219)( 80,218)
( 81,181)( 82,184)( 83,183)( 84,182)( 85,185)( 86,188)( 87,187)( 88,186)
( 89,189)( 90,192)( 91,191)( 92,190)( 93,193)( 94,196)( 95,195)( 96,194)
( 97,197)( 98,200)( 99,199)(100,198)(101,221)(102,224)(103,223)(104,222)
(105,225)(106,228)(107,227)(108,226)(109,229)(110,232)(111,231)(112,230)
(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)(120,238)
(241,381)(242,384)(243,383)(244,382)(245,385)(246,388)(247,387)(248,386)
(249,389)(250,392)(251,391)(252,390)(253,393)(254,396)(255,395)(256,394)
(257,397)(258,400)(259,399)(260,398)(261,361)(262,364)(263,363)(264,362)
(265,365)(266,368)(267,367)(268,366)(269,369)(270,372)(271,371)(272,370)
(273,373)(274,376)(275,375)(276,374)(277,377)(278,380)(279,379)(280,378)
(281,401)(282,404)(283,403)(284,402)(285,405)(286,408)(287,407)(288,406)
(289,409)(290,412)(291,411)(292,410)(293,413)(294,416)(295,415)(296,414)
(297,417)(298,420)(299,419)(300,418)(301,441)(302,444)(303,443)(304,442)
(305,445)(306,448)(307,447)(308,446)(309,449)(310,452)(311,451)(312,450)
(313,453)(314,456)(315,455)(316,454)(317,457)(318,460)(319,459)(320,458)
(321,421)(322,424)(323,423)(324,422)(325,425)(326,428)(327,427)(328,426)
(329,429)(330,432)(331,431)(332,430)(333,433)(334,436)(335,435)(336,434)
(337,437)(338,440)(339,439)(340,438)(341,461)(342,464)(343,463)(344,462)
(345,465)(346,468)(347,467)(348,466)(349,469)(350,472)(351,471)(352,470)
(353,473)(354,476)(355,475)(356,474)(357,477)(358,480)(359,479)(360,478);;
s3 := (  1,242)(  2,241)(  3,244)(  4,243)(  5,246)(  6,245)(  7,248)(  8,247)
(  9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)( 16,255)
( 17,258)( 18,257)( 19,260)( 20,259)( 21,262)( 22,261)( 23,264)( 24,263)
( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)( 32,271)
( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)( 40,279)
( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)( 48,287)
( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)( 56,295)
( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)( 64,303)
( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)( 72,311)
( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)( 80,319)
( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)( 88,327)
( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)( 96,335)
( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)(104,343)
(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)(112,351)
(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)(120,359)
(121,362)(122,361)(123,364)(124,363)(125,366)(126,365)(127,368)(128,367)
(129,370)(130,369)(131,372)(132,371)(133,374)(134,373)(135,376)(136,375)
(137,378)(138,377)(139,380)(140,379)(141,382)(142,381)(143,384)(144,383)
(145,386)(146,385)(147,388)(148,387)(149,390)(150,389)(151,392)(152,391)
(153,394)(154,393)(155,396)(156,395)(157,398)(158,397)(159,400)(160,399)
(161,402)(162,401)(163,404)(164,403)(165,406)(166,405)(167,408)(168,407)
(169,410)(170,409)(171,412)(172,411)(173,414)(174,413)(175,416)(176,415)
(177,418)(178,417)(179,420)(180,419)(181,422)(182,421)(183,424)(184,423)
(185,426)(186,425)(187,428)(188,427)(189,430)(190,429)(191,432)(192,431)
(193,434)(194,433)(195,436)(196,435)(197,438)(198,437)(199,440)(200,439)
(201,442)(202,441)(203,444)(204,443)(205,446)(206,445)(207,448)(208,447)
(209,450)(210,449)(211,452)(212,451)(213,454)(214,453)(215,456)(216,455)
(217,458)(218,457)(219,460)(220,459)(221,462)(222,461)(223,464)(224,463)
(225,466)(226,465)(227,468)(228,467)(229,470)(230,469)(231,472)(232,471)
(233,474)(234,473)(235,476)(236,475)(237,478)(238,477)(239,480)(240,479);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, 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, 
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)!(  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)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)
(132,136)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)
(152,156)(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)
(172,176)(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)
(192,196)(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)
(212,216)(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)
(232,236)(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)(365,377)(366,378)(367,379)(368,380)(369,373)(370,374)(371,375)
(372,376)(385,397)(386,398)(387,399)(388,400)(389,393)(390,394)(391,395)
(392,396)(405,417)(406,418)(407,419)(408,420)(409,413)(410,414)(411,415)
(412,416)(425,437)(426,438)(427,439)(428,440)(429,433)(430,434)(431,435)
(432,436)(445,457)(446,458)(447,459)(448,460)(449,453)(450,454)(451,455)
(452,456)(465,477)(466,478)(467,479)(468,480)(469,473)(470,474)(471,475)
(472,476);
s1 := Sym(480)!(  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9, 17)( 10, 18)( 11, 20)
( 12, 19)( 15, 16)( 21, 45)( 22, 46)( 23, 48)( 24, 47)( 25, 41)( 26, 42)
( 27, 44)( 28, 43)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 53)( 34, 54)
( 35, 56)( 36, 55)( 37, 49)( 38, 50)( 39, 52)( 40, 51)( 61, 65)( 62, 66)
( 63, 68)( 64, 67)( 69, 77)( 70, 78)( 71, 80)( 72, 79)( 75, 76)( 81,105)
( 82,106)( 83,108)( 84,107)( 85,101)( 86,102)( 87,104)( 88,103)( 89,117)
( 90,118)( 91,120)( 92,119)( 93,113)( 94,114)( 95,116)( 96,115)( 97,109)
( 98,110)( 99,112)(100,111)(121,185)(122,186)(123,188)(124,187)(125,181)
(126,182)(127,184)(128,183)(129,197)(130,198)(131,200)(132,199)(133,193)
(134,194)(135,196)(136,195)(137,189)(138,190)(139,192)(140,191)(141,225)
(142,226)(143,228)(144,227)(145,221)(146,222)(147,224)(148,223)(149,237)
(150,238)(151,240)(152,239)(153,233)(154,234)(155,236)(156,235)(157,229)
(158,230)(159,232)(160,231)(161,205)(162,206)(163,208)(164,207)(165,201)
(166,202)(167,204)(168,203)(169,217)(170,218)(171,220)(172,219)(173,213)
(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(241,245)
(242,246)(243,248)(244,247)(249,257)(250,258)(251,260)(252,259)(255,256)
(261,285)(262,286)(263,288)(264,287)(265,281)(266,282)(267,284)(268,283)
(269,297)(270,298)(271,300)(272,299)(273,293)(274,294)(275,296)(276,295)
(277,289)(278,290)(279,292)(280,291)(301,305)(302,306)(303,308)(304,307)
(309,317)(310,318)(311,320)(312,319)(315,316)(321,345)(322,346)(323,348)
(324,347)(325,341)(326,342)(327,344)(328,343)(329,357)(330,358)(331,360)
(332,359)(333,353)(334,354)(335,356)(336,355)(337,349)(338,350)(339,352)
(340,351)(361,425)(362,426)(363,428)(364,427)(365,421)(366,422)(367,424)
(368,423)(369,437)(370,438)(371,440)(372,439)(373,433)(374,434)(375,436)
(376,435)(377,429)(378,430)(379,432)(380,431)(381,465)(382,466)(383,468)
(384,467)(385,461)(386,462)(387,464)(388,463)(389,477)(390,478)(391,480)
(392,479)(393,473)(394,474)(395,476)(396,475)(397,469)(398,470)(399,472)
(400,471)(401,445)(402,446)(403,448)(404,447)(405,441)(406,442)(407,444)
(408,443)(409,457)(410,458)(411,460)(412,459)(413,453)(414,454)(415,456)
(416,455)(417,449)(418,450)(419,452)(420,451);
s2 := Sym(480)!(  1,141)(  2,144)(  3,143)(  4,142)(  5,145)(  6,148)(  7,147)
(  8,146)(  9,149)( 10,152)( 11,151)( 12,150)( 13,153)( 14,156)( 15,155)
( 16,154)( 17,157)( 18,160)( 19,159)( 20,158)( 21,121)( 22,124)( 23,123)
( 24,122)( 25,125)( 26,128)( 27,127)( 28,126)( 29,129)( 30,132)( 31,131)
( 32,130)( 33,133)( 34,136)( 35,135)( 36,134)( 37,137)( 38,140)( 39,139)
( 40,138)( 41,161)( 42,164)( 43,163)( 44,162)( 45,165)( 46,168)( 47,167)
( 48,166)( 49,169)( 50,172)( 51,171)( 52,170)( 53,173)( 54,176)( 55,175)
( 56,174)( 57,177)( 58,180)( 59,179)( 60,178)( 61,201)( 62,204)( 63,203)
( 64,202)( 65,205)( 66,208)( 67,207)( 68,206)( 69,209)( 70,212)( 71,211)
( 72,210)( 73,213)( 74,216)( 75,215)( 76,214)( 77,217)( 78,220)( 79,219)
( 80,218)( 81,181)( 82,184)( 83,183)( 84,182)( 85,185)( 86,188)( 87,187)
( 88,186)( 89,189)( 90,192)( 91,191)( 92,190)( 93,193)( 94,196)( 95,195)
( 96,194)( 97,197)( 98,200)( 99,199)(100,198)(101,221)(102,224)(103,223)
(104,222)(105,225)(106,228)(107,227)(108,226)(109,229)(110,232)(111,231)
(112,230)(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)
(120,238)(241,381)(242,384)(243,383)(244,382)(245,385)(246,388)(247,387)
(248,386)(249,389)(250,392)(251,391)(252,390)(253,393)(254,396)(255,395)
(256,394)(257,397)(258,400)(259,399)(260,398)(261,361)(262,364)(263,363)
(264,362)(265,365)(266,368)(267,367)(268,366)(269,369)(270,372)(271,371)
(272,370)(273,373)(274,376)(275,375)(276,374)(277,377)(278,380)(279,379)
(280,378)(281,401)(282,404)(283,403)(284,402)(285,405)(286,408)(287,407)
(288,406)(289,409)(290,412)(291,411)(292,410)(293,413)(294,416)(295,415)
(296,414)(297,417)(298,420)(299,419)(300,418)(301,441)(302,444)(303,443)
(304,442)(305,445)(306,448)(307,447)(308,446)(309,449)(310,452)(311,451)
(312,450)(313,453)(314,456)(315,455)(316,454)(317,457)(318,460)(319,459)
(320,458)(321,421)(322,424)(323,423)(324,422)(325,425)(326,428)(327,427)
(328,426)(329,429)(330,432)(331,431)(332,430)(333,433)(334,436)(335,435)
(336,434)(337,437)(338,440)(339,439)(340,438)(341,461)(342,464)(343,463)
(344,462)(345,465)(346,468)(347,467)(348,466)(349,469)(350,472)(351,471)
(352,470)(353,473)(354,476)(355,475)(356,474)(357,477)(358,480)(359,479)
(360,478);
s3 := Sym(480)!(  1,242)(  2,241)(  3,244)(  4,243)(  5,246)(  6,245)(  7,248)
(  8,247)(  9,250)( 10,249)( 11,252)( 12,251)( 13,254)( 14,253)( 15,256)
( 16,255)( 17,258)( 18,257)( 19,260)( 20,259)( 21,262)( 22,261)( 23,264)
( 24,263)( 25,266)( 26,265)( 27,268)( 28,267)( 29,270)( 30,269)( 31,272)
( 32,271)( 33,274)( 34,273)( 35,276)( 36,275)( 37,278)( 38,277)( 39,280)
( 40,279)( 41,282)( 42,281)( 43,284)( 44,283)( 45,286)( 46,285)( 47,288)
( 48,287)( 49,290)( 50,289)( 51,292)( 52,291)( 53,294)( 54,293)( 55,296)
( 56,295)( 57,298)( 58,297)( 59,300)( 60,299)( 61,302)( 62,301)( 63,304)
( 64,303)( 65,306)( 66,305)( 67,308)( 68,307)( 69,310)( 70,309)( 71,312)
( 72,311)( 73,314)( 74,313)( 75,316)( 76,315)( 77,318)( 78,317)( 79,320)
( 80,319)( 81,322)( 82,321)( 83,324)( 84,323)( 85,326)( 86,325)( 87,328)
( 88,327)( 89,330)( 90,329)( 91,332)( 92,331)( 93,334)( 94,333)( 95,336)
( 96,335)( 97,338)( 98,337)( 99,340)(100,339)(101,342)(102,341)(103,344)
(104,343)(105,346)(106,345)(107,348)(108,347)(109,350)(110,349)(111,352)
(112,351)(113,354)(114,353)(115,356)(116,355)(117,358)(118,357)(119,360)
(120,359)(121,362)(122,361)(123,364)(124,363)(125,366)(126,365)(127,368)
(128,367)(129,370)(130,369)(131,372)(132,371)(133,374)(134,373)(135,376)
(136,375)(137,378)(138,377)(139,380)(140,379)(141,382)(142,381)(143,384)
(144,383)(145,386)(146,385)(147,388)(148,387)(149,390)(150,389)(151,392)
(152,391)(153,394)(154,393)(155,396)(156,395)(157,398)(158,397)(159,400)
(160,399)(161,402)(162,401)(163,404)(164,403)(165,406)(166,405)(167,408)
(168,407)(169,410)(170,409)(171,412)(172,411)(173,414)(174,413)(175,416)
(176,415)(177,418)(178,417)(179,420)(180,419)(181,422)(182,421)(183,424)
(184,423)(185,426)(186,425)(187,428)(188,427)(189,430)(190,429)(191,432)
(192,431)(193,434)(194,433)(195,436)(196,435)(197,438)(198,437)(199,440)
(200,439)(201,442)(202,441)(203,444)(204,443)(205,446)(206,445)(207,448)
(208,447)(209,450)(210,449)(211,452)(212,451)(213,454)(214,453)(215,456)
(216,455)(217,458)(218,457)(219,460)(220,459)(221,462)(222,461)(223,464)
(224,463)(225,466)(226,465)(227,468)(228,467)(229,470)(230,469)(231,472)
(232,471)(233,474)(234,473)(235,476)(236,475)(237,478)(238,477)(239,480)
(240,479);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
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, 
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