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# Polytope of Type {6,4,20}

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