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Polytope of Type {12,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 4
Schlafli Type : {12,4,10}
Number of vertices, edges, etc : 24, 48, 40, 10
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 : {6,4,10}*960
   4-fold quotients : {12,2,10}*480, {3,4,10}*480
   5-fold quotients : {12,4,2}*384b
   8-fold quotients : {12,2,5}*240, {6,2,10}*240
   10-fold quotients : {12,4,2}*192b, {12,4,2}*192c, {6,4,2}*192
   12-fold quotients : {4,2,10}*160
   16-fold quotients : {3,2,10}*120, {6,2,5}*120
   20-fold quotients : {12,2,2}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   32-fold quotients : {3,2,5}*60
   40-fold quotients : {3,4,2}*48, {6,2,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {4,2,2}*32
   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,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)( 23, 44)
( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)( 31, 52)
( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)( 39, 60)
( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)( 90,110)
( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)( 98,118)
( 99,120)(100,119)(121,181)(122,182)(123,184)(124,183)(125,185)(126,186)
(127,188)(128,187)(129,189)(130,190)(131,192)(132,191)(133,193)(134,194)
(135,196)(136,195)(137,197)(138,198)(139,200)(140,199)(141,221)(142,222)
(143,224)(144,223)(145,225)(146,226)(147,228)(148,227)(149,229)(150,230)
(151,232)(152,231)(153,233)(154,234)(155,236)(156,235)(157,237)(158,238)
(159,240)(160,239)(161,201)(162,202)(163,204)(164,203)(165,205)(166,206)
(167,208)(168,207)(169,209)(170,210)(171,212)(172,211)(173,213)(174,214)
(175,216)(176,215)(177,217)(178,218)(179,220)(180,219)(243,244)(247,248)
(251,252)(255,256)(259,260)(261,281)(262,282)(263,284)(264,283)(265,285)
(266,286)(267,288)(268,287)(269,289)(270,290)(271,292)(272,291)(273,293)
(274,294)(275,296)(276,295)(277,297)(278,298)(279,300)(280,299)(303,304)
(307,308)(311,312)(315,316)(319,320)(321,341)(322,342)(323,344)(324,343)
(325,345)(326,346)(327,348)(328,347)(329,349)(330,350)(331,352)(332,351)
(333,353)(334,354)(335,356)(336,355)(337,357)(338,358)(339,360)(340,359)
(361,421)(362,422)(363,424)(364,423)(365,425)(366,426)(367,428)(368,427)
(369,429)(370,430)(371,432)(372,431)(373,433)(374,434)(375,436)(376,435)
(377,437)(378,438)(379,440)(380,439)(381,461)(382,462)(383,464)(384,463)
(385,465)(386,466)(387,468)(388,467)(389,469)(390,470)(391,472)(392,471)
(393,473)(394,474)(395,476)(396,475)(397,477)(398,478)(399,480)(400,479)
(401,441)(402,442)(403,444)(404,443)(405,445)(406,446)(407,448)(408,447)
(409,449)(410,450)(411,452)(412,451)(413,453)(414,454)(415,456)(416,455)
(417,457)(418,458)(419,460)(420,459);;
s1 := (  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);;
s2 := (  1,  2)(  3,  4)(  5, 18)(  6, 17)(  7, 20)(  8, 19)(  9, 14)( 10, 13)
( 11, 16)( 12, 15)( 21, 22)( 23, 24)( 25, 38)( 26, 37)( 27, 40)( 28, 39)
( 29, 34)( 30, 33)( 31, 36)( 32, 35)( 41, 42)( 43, 44)( 45, 58)( 46, 57)
( 47, 60)( 48, 59)( 49, 54)( 50, 53)( 51, 56)( 52, 55)( 61, 62)( 63, 64)
( 65, 78)( 66, 77)( 67, 80)( 68, 79)( 69, 74)( 70, 73)( 71, 76)( 72, 75)
( 81, 82)( 83, 84)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89, 94)( 90, 93)
( 91, 96)( 92, 95)(101,102)(103,104)(105,118)(106,117)(107,120)(108,119)
(109,114)(110,113)(111,116)(112,115)(121,122)(123,124)(125,138)(126,137)
(127,140)(128,139)(129,134)(130,133)(131,136)(132,135)(141,142)(143,144)
(145,158)(146,157)(147,160)(148,159)(149,154)(150,153)(151,156)(152,155)
(161,162)(163,164)(165,178)(166,177)(167,180)(168,179)(169,174)(170,173)
(171,176)(172,175)(181,182)(183,184)(185,198)(186,197)(187,200)(188,199)
(189,194)(190,193)(191,196)(192,195)(201,202)(203,204)(205,218)(206,217)
(207,220)(208,219)(209,214)(210,213)(211,216)(212,215)(221,222)(223,224)
(225,238)(226,237)(227,240)(228,239)(229,234)(230,233)(231,236)(232,235)
(241,242)(243,244)(245,258)(246,257)(247,260)(248,259)(249,254)(250,253)
(251,256)(252,255)(261,262)(263,264)(265,278)(266,277)(267,280)(268,279)
(269,274)(270,273)(271,276)(272,275)(281,282)(283,284)(285,298)(286,297)
(287,300)(288,299)(289,294)(290,293)(291,296)(292,295)(301,302)(303,304)
(305,318)(306,317)(307,320)(308,319)(309,314)(310,313)(311,316)(312,315)
(321,322)(323,324)(325,338)(326,337)(327,340)(328,339)(329,334)(330,333)
(331,336)(332,335)(341,342)(343,344)(345,358)(346,357)(347,360)(348,359)
(349,354)(350,353)(351,356)(352,355)(361,362)(363,364)(365,378)(366,377)
(367,380)(368,379)(369,374)(370,373)(371,376)(372,375)(381,382)(383,384)
(385,398)(386,397)(387,400)(388,399)(389,394)(390,393)(391,396)(392,395)
(401,402)(403,404)(405,418)(406,417)(407,420)(408,419)(409,414)(410,413)
(411,416)(412,415)(421,422)(423,424)(425,438)(426,437)(427,440)(428,439)
(429,434)(430,433)(431,436)(432,435)(441,442)(443,444)(445,458)(446,457)
(447,460)(448,459)(449,454)(450,453)(451,456)(452,455)(461,462)(463,464)
(465,478)(466,477)(467,480)(468,479)(469,474)(470,473)(471,476)(472,475);;
s3 := (  1,245)(  2,246)(  3,247)(  4,248)(  5,241)(  6,242)(  7,243)(  8,244)
(  9,257)( 10,258)( 11,259)( 12,260)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,249)( 18,250)( 19,251)( 20,252)( 21,265)( 22,266)( 23,267)( 24,268)
( 25,261)( 26,262)( 27,263)( 28,264)( 29,277)( 30,278)( 31,279)( 32,280)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,269)( 38,270)( 39,271)( 40,272)
( 41,285)( 42,286)( 43,287)( 44,288)( 45,281)( 46,282)( 47,283)( 48,284)
( 49,297)( 50,298)( 51,299)( 52,300)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,289)( 58,290)( 59,291)( 60,292)( 61,305)( 62,306)( 63,307)( 64,308)
( 65,301)( 66,302)( 67,303)( 68,304)( 69,317)( 70,318)( 71,319)( 72,320)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,309)( 78,310)( 79,311)( 80,312)
( 81,325)( 82,326)( 83,327)( 84,328)( 85,321)( 86,322)( 87,323)( 88,324)
( 89,337)( 90,338)( 91,339)( 92,340)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,329)( 98,330)( 99,331)(100,332)(101,345)(102,346)(103,347)(104,348)
(105,341)(106,342)(107,343)(108,344)(109,357)(110,358)(111,359)(112,360)
(113,353)(114,354)(115,355)(116,356)(117,349)(118,350)(119,351)(120,352)
(121,365)(122,366)(123,367)(124,368)(125,361)(126,362)(127,363)(128,364)
(129,377)(130,378)(131,379)(132,380)(133,373)(134,374)(135,375)(136,376)
(137,369)(138,370)(139,371)(140,372)(141,385)(142,386)(143,387)(144,388)
(145,381)(146,382)(147,383)(148,384)(149,397)(150,398)(151,399)(152,400)
(153,393)(154,394)(155,395)(156,396)(157,389)(158,390)(159,391)(160,392)
(161,405)(162,406)(163,407)(164,408)(165,401)(166,402)(167,403)(168,404)
(169,417)(170,418)(171,419)(172,420)(173,413)(174,414)(175,415)(176,416)
(177,409)(178,410)(179,411)(180,412)(181,425)(182,426)(183,427)(184,428)
(185,421)(186,422)(187,423)(188,424)(189,437)(190,438)(191,439)(192,440)
(193,433)(194,434)(195,435)(196,436)(197,429)(198,430)(199,431)(200,432)
(201,445)(202,446)(203,447)(204,448)(205,441)(206,442)(207,443)(208,444)
(209,457)(210,458)(211,459)(212,460)(213,453)(214,454)(215,455)(216,456)
(217,449)(218,450)(219,451)(220,452)(221,465)(222,466)(223,467)(224,468)
(225,461)(226,462)(227,463)(228,464)(229,477)(230,478)(231,479)(232,480)
(233,473)(234,474)(235,475)(236,476)(237,469)(238,470)(239,471)(240,472);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)!(  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)
( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)
( 31, 52)( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)
( 39, 60)( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)
( 90,110)( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)
( 98,118)( 99,120)(100,119)(121,181)(122,182)(123,184)(124,183)(125,185)
(126,186)(127,188)(128,187)(129,189)(130,190)(131,192)(132,191)(133,193)
(134,194)(135,196)(136,195)(137,197)(138,198)(139,200)(140,199)(141,221)
(142,222)(143,224)(144,223)(145,225)(146,226)(147,228)(148,227)(149,229)
(150,230)(151,232)(152,231)(153,233)(154,234)(155,236)(156,235)(157,237)
(158,238)(159,240)(160,239)(161,201)(162,202)(163,204)(164,203)(165,205)
(166,206)(167,208)(168,207)(169,209)(170,210)(171,212)(172,211)(173,213)
(174,214)(175,216)(176,215)(177,217)(178,218)(179,220)(180,219)(243,244)
(247,248)(251,252)(255,256)(259,260)(261,281)(262,282)(263,284)(264,283)
(265,285)(266,286)(267,288)(268,287)(269,289)(270,290)(271,292)(272,291)
(273,293)(274,294)(275,296)(276,295)(277,297)(278,298)(279,300)(280,299)
(303,304)(307,308)(311,312)(315,316)(319,320)(321,341)(322,342)(323,344)
(324,343)(325,345)(326,346)(327,348)(328,347)(329,349)(330,350)(331,352)
(332,351)(333,353)(334,354)(335,356)(336,355)(337,357)(338,358)(339,360)
(340,359)(361,421)(362,422)(363,424)(364,423)(365,425)(366,426)(367,428)
(368,427)(369,429)(370,430)(371,432)(372,431)(373,433)(374,434)(375,436)
(376,435)(377,437)(378,438)(379,440)(380,439)(381,461)(382,462)(383,464)
(384,463)(385,465)(386,466)(387,468)(388,467)(389,469)(390,470)(391,472)
(392,471)(393,473)(394,474)(395,476)(396,475)(397,477)(398,478)(399,480)
(400,479)(401,441)(402,442)(403,444)(404,443)(405,445)(406,446)(407,448)
(408,447)(409,449)(410,450)(411,452)(412,451)(413,453)(414,454)(415,456)
(416,455)(417,457)(418,458)(419,460)(420,459);
s1 := 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);
s2 := Sym(480)!(  1,  2)(  3,  4)(  5, 18)(  6, 17)(  7, 20)(  8, 19)(  9, 14)
( 10, 13)( 11, 16)( 12, 15)( 21, 22)( 23, 24)( 25, 38)( 26, 37)( 27, 40)
( 28, 39)( 29, 34)( 30, 33)( 31, 36)( 32, 35)( 41, 42)( 43, 44)( 45, 58)
( 46, 57)( 47, 60)( 48, 59)( 49, 54)( 50, 53)( 51, 56)( 52, 55)( 61, 62)
( 63, 64)( 65, 78)( 66, 77)( 67, 80)( 68, 79)( 69, 74)( 70, 73)( 71, 76)
( 72, 75)( 81, 82)( 83, 84)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89, 94)
( 90, 93)( 91, 96)( 92, 95)(101,102)(103,104)(105,118)(106,117)(107,120)
(108,119)(109,114)(110,113)(111,116)(112,115)(121,122)(123,124)(125,138)
(126,137)(127,140)(128,139)(129,134)(130,133)(131,136)(132,135)(141,142)
(143,144)(145,158)(146,157)(147,160)(148,159)(149,154)(150,153)(151,156)
(152,155)(161,162)(163,164)(165,178)(166,177)(167,180)(168,179)(169,174)
(170,173)(171,176)(172,175)(181,182)(183,184)(185,198)(186,197)(187,200)
(188,199)(189,194)(190,193)(191,196)(192,195)(201,202)(203,204)(205,218)
(206,217)(207,220)(208,219)(209,214)(210,213)(211,216)(212,215)(221,222)
(223,224)(225,238)(226,237)(227,240)(228,239)(229,234)(230,233)(231,236)
(232,235)(241,242)(243,244)(245,258)(246,257)(247,260)(248,259)(249,254)
(250,253)(251,256)(252,255)(261,262)(263,264)(265,278)(266,277)(267,280)
(268,279)(269,274)(270,273)(271,276)(272,275)(281,282)(283,284)(285,298)
(286,297)(287,300)(288,299)(289,294)(290,293)(291,296)(292,295)(301,302)
(303,304)(305,318)(306,317)(307,320)(308,319)(309,314)(310,313)(311,316)
(312,315)(321,322)(323,324)(325,338)(326,337)(327,340)(328,339)(329,334)
(330,333)(331,336)(332,335)(341,342)(343,344)(345,358)(346,357)(347,360)
(348,359)(349,354)(350,353)(351,356)(352,355)(361,362)(363,364)(365,378)
(366,377)(367,380)(368,379)(369,374)(370,373)(371,376)(372,375)(381,382)
(383,384)(385,398)(386,397)(387,400)(388,399)(389,394)(390,393)(391,396)
(392,395)(401,402)(403,404)(405,418)(406,417)(407,420)(408,419)(409,414)
(410,413)(411,416)(412,415)(421,422)(423,424)(425,438)(426,437)(427,440)
(428,439)(429,434)(430,433)(431,436)(432,435)(441,442)(443,444)(445,458)
(446,457)(447,460)(448,459)(449,454)(450,453)(451,456)(452,455)(461,462)
(463,464)(465,478)(466,477)(467,480)(468,479)(469,474)(470,473)(471,476)
(472,475);
s3 := Sym(480)!(  1,245)(  2,246)(  3,247)(  4,248)(  5,241)(  6,242)(  7,243)
(  8,244)(  9,257)( 10,258)( 11,259)( 12,260)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,249)( 18,250)( 19,251)( 20,252)( 21,265)( 22,266)( 23,267)
( 24,268)( 25,261)( 26,262)( 27,263)( 28,264)( 29,277)( 30,278)( 31,279)
( 32,280)( 33,273)( 34,274)( 35,275)( 36,276)( 37,269)( 38,270)( 39,271)
( 40,272)( 41,285)( 42,286)( 43,287)( 44,288)( 45,281)( 46,282)( 47,283)
( 48,284)( 49,297)( 50,298)( 51,299)( 52,300)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,289)( 58,290)( 59,291)( 60,292)( 61,305)( 62,306)( 63,307)
( 64,308)( 65,301)( 66,302)( 67,303)( 68,304)( 69,317)( 70,318)( 71,319)
( 72,320)( 73,313)( 74,314)( 75,315)( 76,316)( 77,309)( 78,310)( 79,311)
( 80,312)( 81,325)( 82,326)( 83,327)( 84,328)( 85,321)( 86,322)( 87,323)
( 88,324)( 89,337)( 90,338)( 91,339)( 92,340)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,329)( 98,330)( 99,331)(100,332)(101,345)(102,346)(103,347)
(104,348)(105,341)(106,342)(107,343)(108,344)(109,357)(110,358)(111,359)
(112,360)(113,353)(114,354)(115,355)(116,356)(117,349)(118,350)(119,351)
(120,352)(121,365)(122,366)(123,367)(124,368)(125,361)(126,362)(127,363)
(128,364)(129,377)(130,378)(131,379)(132,380)(133,373)(134,374)(135,375)
(136,376)(137,369)(138,370)(139,371)(140,372)(141,385)(142,386)(143,387)
(144,388)(145,381)(146,382)(147,383)(148,384)(149,397)(150,398)(151,399)
(152,400)(153,393)(154,394)(155,395)(156,396)(157,389)(158,390)(159,391)
(160,392)(161,405)(162,406)(163,407)(164,408)(165,401)(166,402)(167,403)
(168,404)(169,417)(170,418)(171,419)(172,420)(173,413)(174,414)(175,415)
(176,416)(177,409)(178,410)(179,411)(180,412)(181,425)(182,426)(183,427)
(184,428)(185,421)(186,422)(187,423)(188,424)(189,437)(190,438)(191,439)
(192,440)(193,433)(194,434)(195,435)(196,436)(197,429)(198,430)(199,431)
(200,432)(201,445)(202,446)(203,447)(204,448)(205,441)(206,442)(207,443)
(208,444)(209,457)(210,458)(211,459)(212,460)(213,453)(214,454)(215,455)
(216,456)(217,449)(218,450)(219,451)(220,452)(221,465)(222,466)(223,467)
(224,468)(225,461)(226,462)(227,463)(228,464)(229,477)(230,478)(231,479)
(232,480)(233,473)(234,474)(235,475)(236,476)(237,469)(238,470)(239,471)
(240,472);
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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