Polytope of Type {10,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,12}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 4
Schlafli Type : {10,4,12}
Number of vertices, edges, etc : 10, 40, 48, 24
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 : {10,4,6}*960
   4-fold quotients : {10,2,12}*480, {10,4,3}*480
   5-fold quotients : {2,4,12}*384b
   8-fold quotients : {5,2,12}*240, {10,2,6}*240
   10-fold quotients : {2,4,12}*192b, {2,4,12}*192c, {2,4,6}*192
   12-fold quotients : {10,2,4}*160
   16-fold quotients : {5,2,6}*120, {10,2,3}*120
   20-fold quotients : {2,2,12}*96, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   24-fold quotients : {5,2,4}*80, {10,2,2}*80
   32-fold quotients : {5,2,3}*60
   40-fold quotients : {2,4,3}*48, {2,2,6}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {2,2,4}*32
   80-fold quotients : {2,2,3}*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 := (  1,247)(  2,248)(  3,245)(  4,246)(  5,243)(  6,244)(  7,241)(  8,242)
(  9,259)( 10,260)( 11,257)( 12,258)( 13,255)( 14,256)( 15,253)( 16,254)
( 17,251)( 18,252)( 19,249)( 20,250)( 21,267)( 22,268)( 23,265)( 24,266)
( 25,263)( 26,264)( 27,261)( 28,262)( 29,279)( 30,280)( 31,277)( 32,278)
( 33,275)( 34,276)( 35,273)( 36,274)( 37,271)( 38,272)( 39,269)( 40,270)
( 41,287)( 42,288)( 43,285)( 44,286)( 45,283)( 46,284)( 47,281)( 48,282)
( 49,299)( 50,300)( 51,297)( 52,298)( 53,295)( 54,296)( 55,293)( 56,294)
( 57,291)( 58,292)( 59,289)( 60,290)( 61,307)( 62,308)( 63,305)( 64,306)
( 65,303)( 66,304)( 67,301)( 68,302)( 69,319)( 70,320)( 71,317)( 72,318)
( 73,315)( 74,316)( 75,313)( 76,314)( 77,311)( 78,312)( 79,309)( 80,310)
( 81,327)( 82,328)( 83,325)( 84,326)( 85,323)( 86,324)( 87,321)( 88,322)
( 89,339)( 90,340)( 91,337)( 92,338)( 93,335)( 94,336)( 95,333)( 96,334)
( 97,331)( 98,332)( 99,329)(100,330)(101,347)(102,348)(103,345)(104,346)
(105,343)(106,344)(107,341)(108,342)(109,359)(110,360)(111,357)(112,358)
(113,355)(114,356)(115,353)(116,354)(117,351)(118,352)(119,349)(120,350)
(121,367)(122,368)(123,365)(124,366)(125,363)(126,364)(127,361)(128,362)
(129,379)(130,380)(131,377)(132,378)(133,375)(134,376)(135,373)(136,374)
(137,371)(138,372)(139,369)(140,370)(141,387)(142,388)(143,385)(144,386)
(145,383)(146,384)(147,381)(148,382)(149,399)(150,400)(151,397)(152,398)
(153,395)(154,396)(155,393)(156,394)(157,391)(158,392)(159,389)(160,390)
(161,407)(162,408)(163,405)(164,406)(165,403)(166,404)(167,401)(168,402)
(169,419)(170,420)(171,417)(172,418)(173,415)(174,416)(175,413)(176,414)
(177,411)(178,412)(179,409)(180,410)(181,427)(182,428)(183,425)(184,426)
(185,423)(186,424)(187,421)(188,422)(189,439)(190,440)(191,437)(192,438)
(193,435)(194,436)(195,433)(196,434)(197,431)(198,432)(199,429)(200,430)
(201,447)(202,448)(203,445)(204,446)(205,443)(206,444)(207,441)(208,442)
(209,459)(210,460)(211,457)(212,458)(213,455)(214,456)(215,453)(216,454)
(217,451)(218,452)(219,449)(220,450)(221,467)(222,468)(223,465)(224,466)
(225,463)(226,464)(227,461)(228,462)(229,479)(230,480)(231,477)(232,478)
(233,475)(234,476)(235,473)(236,474)(237,471)(238,472)(239,469)(240,470);;
s2 := (  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);;
s3 := (  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);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!(  1,247)(  2,248)(  3,245)(  4,246)(  5,243)(  6,244)(  7,241)
(  8,242)(  9,259)( 10,260)( 11,257)( 12,258)( 13,255)( 14,256)( 15,253)
( 16,254)( 17,251)( 18,252)( 19,249)( 20,250)( 21,267)( 22,268)( 23,265)
( 24,266)( 25,263)( 26,264)( 27,261)( 28,262)( 29,279)( 30,280)( 31,277)
( 32,278)( 33,275)( 34,276)( 35,273)( 36,274)( 37,271)( 38,272)( 39,269)
( 40,270)( 41,287)( 42,288)( 43,285)( 44,286)( 45,283)( 46,284)( 47,281)
( 48,282)( 49,299)( 50,300)( 51,297)( 52,298)( 53,295)( 54,296)( 55,293)
( 56,294)( 57,291)( 58,292)( 59,289)( 60,290)( 61,307)( 62,308)( 63,305)
( 64,306)( 65,303)( 66,304)( 67,301)( 68,302)( 69,319)( 70,320)( 71,317)
( 72,318)( 73,315)( 74,316)( 75,313)( 76,314)( 77,311)( 78,312)( 79,309)
( 80,310)( 81,327)( 82,328)( 83,325)( 84,326)( 85,323)( 86,324)( 87,321)
( 88,322)( 89,339)( 90,340)( 91,337)( 92,338)( 93,335)( 94,336)( 95,333)
( 96,334)( 97,331)( 98,332)( 99,329)(100,330)(101,347)(102,348)(103,345)
(104,346)(105,343)(106,344)(107,341)(108,342)(109,359)(110,360)(111,357)
(112,358)(113,355)(114,356)(115,353)(116,354)(117,351)(118,352)(119,349)
(120,350)(121,367)(122,368)(123,365)(124,366)(125,363)(126,364)(127,361)
(128,362)(129,379)(130,380)(131,377)(132,378)(133,375)(134,376)(135,373)
(136,374)(137,371)(138,372)(139,369)(140,370)(141,387)(142,388)(143,385)
(144,386)(145,383)(146,384)(147,381)(148,382)(149,399)(150,400)(151,397)
(152,398)(153,395)(154,396)(155,393)(156,394)(157,391)(158,392)(159,389)
(160,390)(161,407)(162,408)(163,405)(164,406)(165,403)(166,404)(167,401)
(168,402)(169,419)(170,420)(171,417)(172,418)(173,415)(174,416)(175,413)
(176,414)(177,411)(178,412)(179,409)(180,410)(181,427)(182,428)(183,425)
(184,426)(185,423)(186,424)(187,421)(188,422)(189,439)(190,440)(191,437)
(192,438)(193,435)(194,436)(195,433)(196,434)(197,431)(198,432)(199,429)
(200,430)(201,447)(202,448)(203,445)(204,446)(205,443)(206,444)(207,441)
(208,442)(209,459)(210,460)(211,457)(212,458)(213,455)(214,456)(215,453)
(216,454)(217,451)(218,452)(219,449)(220,450)(221,467)(222,468)(223,465)
(224,466)(225,463)(226,464)(227,461)(228,462)(229,479)(230,480)(231,477)
(232,478)(233,475)(234,476)(235,473)(236,474)(237,471)(238,472)(239,469)
(240,470);
s2 := 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);
s3 := 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);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope