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Polytope of Type {4,12,10}

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