Questions?
See the FAQ
or other info.

# Polytope of Type {6,4,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,5}*1920
Also Known As : {{6,4|2},{4,5|4}}. if this polytope has another name.
Group : SmallGroup(1920,240399)
Rank : 4
Schlafli Type : {6,4,5}
Number of vertices, edges, etc : 6, 96, 80, 40
Order of s0s1s2s3 : 30
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) :
3-fold quotients : {2,4,5}*640
6-fold quotients : {2,4,5}*320
16-fold quotients : {6,2,5}*120
32-fold quotients : {3,2,5}*60
48-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 81,161)( 82,162)( 83,163)( 84,164)( 85,165)( 86,166)( 87,167)( 88,168)
( 89,169)( 90,170)( 91,171)( 92,172)( 93,173)( 94,174)( 95,175)( 96,176)
( 97,177)( 98,178)( 99,179)(100,180)(101,181)(102,182)(103,183)(104,184)
(105,185)(106,186)(107,187)(108,188)(109,189)(110,190)(111,191)(112,192)
(113,193)(114,194)(115,195)(116,196)(117,197)(118,198)(119,199)(120,200)
(121,201)(122,202)(123,203)(124,204)(125,205)(126,206)(127,207)(128,208)
(129,209)(130,210)(131,211)(132,212)(133,213)(134,214)(135,215)(136,216)
(137,217)(138,218)(139,219)(140,220)(141,221)(142,222)(143,223)(144,224)
(145,225)(146,226)(147,227)(148,228)(149,229)(150,230)(151,231)(152,232)
(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)(160,240)
(321,401)(322,402)(323,403)(324,404)(325,405)(326,406)(327,407)(328,408)
(329,409)(330,410)(331,411)(332,412)(333,413)(334,414)(335,415)(336,416)
(337,417)(338,418)(339,419)(340,420)(341,421)(342,422)(343,423)(344,424)
(345,425)(346,426)(347,427)(348,428)(349,429)(350,430)(351,431)(352,432)
(353,433)(354,434)(355,435)(356,436)(357,437)(358,438)(359,439)(360,440)
(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)(368,448)
(369,449)(370,450)(371,451)(372,452)(373,453)(374,454)(375,455)(376,456)
(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)(384,464)
(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,471)(392,472)
(393,473)(394,474)(395,475)(396,476)(397,477)(398,478)(399,479)(400,480);;
s1 := (  1,329)(  2,330)(  3,331)(  4,332)(  5,333)(  6,334)(  7,335)(  8,336)
(  9,321)( 10,322)( 11,323)( 12,324)( 13,325)( 14,326)( 15,327)( 16,328)
( 17,345)( 18,346)( 19,347)( 20,348)( 21,349)( 22,350)( 23,351)( 24,352)
( 25,337)( 26,338)( 27,339)( 28,340)( 29,341)( 30,342)( 31,343)( 32,344)
( 33,361)( 34,362)( 35,363)( 36,364)( 37,365)( 38,366)( 39,367)( 40,368)
( 41,353)( 42,354)( 43,355)( 44,356)( 45,357)( 46,358)( 47,359)( 48,360)
( 49,377)( 50,378)( 51,379)( 52,380)( 53,381)( 54,382)( 55,383)( 56,384)
( 57,369)( 58,370)( 59,371)( 60,372)( 61,373)( 62,374)( 63,375)( 64,376)
( 65,393)( 66,394)( 67,395)( 68,396)( 69,397)( 70,398)( 71,399)( 72,400)
( 73,385)( 74,386)( 75,387)( 76,388)( 77,389)( 78,390)( 79,391)( 80,392)
( 81,249)( 82,250)( 83,251)( 84,252)( 85,253)( 86,254)( 87,255)( 88,256)
( 89,241)( 90,242)( 91,243)( 92,244)( 93,245)( 94,246)( 95,247)( 96,248)
( 97,265)( 98,266)( 99,267)(100,268)(101,269)(102,270)(103,271)(104,272)
(105,257)(106,258)(107,259)(108,260)(109,261)(110,262)(111,263)(112,264)
(113,281)(114,282)(115,283)(116,284)(117,285)(118,286)(119,287)(120,288)
(121,273)(122,274)(123,275)(124,276)(125,277)(126,278)(127,279)(128,280)
(129,297)(130,298)(131,299)(132,300)(133,301)(134,302)(135,303)(136,304)
(137,289)(138,290)(139,291)(140,292)(141,293)(142,294)(143,295)(144,296)
(145,313)(146,314)(147,315)(148,316)(149,317)(150,318)(151,319)(152,320)
(153,305)(154,306)(155,307)(156,308)(157,309)(158,310)(159,311)(160,312)
(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)
(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)
(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)
(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)
(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)
(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)
(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)
(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)
(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)
(233,465)(234,466)(235,467)(236,468)(237,469)(238,470)(239,471)(240,472);;
s2 := (  3,  4)(  7,  8)(  9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 65)( 18, 66)
( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 78)( 26, 77)
( 27, 79)( 28, 80)( 29, 74)( 30, 73)( 31, 75)( 32, 76)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 62)( 42, 61)
( 43, 63)( 44, 64)( 45, 58)( 46, 57)( 47, 59)( 48, 60)( 83, 84)( 87, 88)
( 89, 94)( 90, 93)( 91, 95)( 92, 96)( 97,145)( 98,146)( 99,148)(100,147)
(101,149)(102,150)(103,152)(104,151)(105,158)(106,157)(107,159)(108,160)
(109,154)(110,153)(111,155)(112,156)(113,129)(114,130)(115,132)(116,131)
(117,133)(118,134)(119,136)(120,135)(121,142)(122,141)(123,143)(124,144)
(125,138)(126,137)(127,139)(128,140)(163,164)(167,168)(169,174)(170,173)
(171,175)(172,176)(177,225)(178,226)(179,228)(180,227)(181,229)(182,230)
(183,232)(184,231)(185,238)(186,237)(187,239)(188,240)(189,234)(190,233)
(191,235)(192,236)(193,209)(194,210)(195,212)(196,211)(197,213)(198,214)
(199,216)(200,215)(201,222)(202,221)(203,223)(204,224)(205,218)(206,217)
(207,219)(208,220)(243,244)(247,248)(249,254)(250,253)(251,255)(252,256)
(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)(264,311)
(265,318)(266,317)(267,319)(268,320)(269,314)(270,313)(271,315)(272,316)
(273,289)(274,290)(275,292)(276,291)(277,293)(278,294)(279,296)(280,295)
(281,302)(282,301)(283,303)(284,304)(285,298)(286,297)(287,299)(288,300)
(323,324)(327,328)(329,334)(330,333)(331,335)(332,336)(337,385)(338,386)
(339,388)(340,387)(341,389)(342,390)(343,392)(344,391)(345,398)(346,397)
(347,399)(348,400)(349,394)(350,393)(351,395)(352,396)(353,369)(354,370)
(355,372)(356,371)(357,373)(358,374)(359,376)(360,375)(361,382)(362,381)
(363,383)(364,384)(365,378)(366,377)(367,379)(368,380)(403,404)(407,408)
(409,414)(410,413)(411,415)(412,416)(417,465)(418,466)(419,468)(420,467)
(421,469)(422,470)(423,472)(424,471)(425,478)(426,477)(427,479)(428,480)
(429,474)(430,473)(431,475)(432,476)(433,449)(434,450)(435,452)(436,451)
(437,453)(438,454)(439,456)(440,455)(441,462)(442,461)(443,463)(444,464)
(445,458)(446,457)(447,459)(448,460);;
s3 := (  1, 49)(  2, 58)(  3, 59)(  4, 52)(  5, 56)(  6, 63)(  7, 62)(  8, 53)
(  9, 57)( 10, 50)( 11, 51)( 12, 60)( 13, 64)( 14, 55)( 15, 54)( 16, 61)
( 17, 33)( 18, 42)( 19, 43)( 20, 36)( 21, 40)( 22, 47)( 23, 46)( 24, 37)
( 25, 41)( 26, 34)( 27, 35)( 28, 44)( 29, 48)( 30, 39)( 31, 38)( 32, 45)
( 66, 74)( 67, 75)( 69, 72)( 70, 79)( 71, 78)( 77, 80)( 81,129)( 82,138)
( 83,139)( 84,132)( 85,136)( 86,143)( 87,142)( 88,133)( 89,137)( 90,130)
( 91,131)( 92,140)( 93,144)( 94,135)( 95,134)( 96,141)( 97,113)( 98,122)
( 99,123)(100,116)(101,120)(102,127)(103,126)(104,117)(105,121)(106,114)
(107,115)(108,124)(109,128)(110,119)(111,118)(112,125)(146,154)(147,155)
(149,152)(150,159)(151,158)(157,160)(161,209)(162,218)(163,219)(164,212)
(165,216)(166,223)(167,222)(168,213)(169,217)(170,210)(171,211)(172,220)
(173,224)(174,215)(175,214)(176,221)(177,193)(178,202)(179,203)(180,196)
(181,200)(182,207)(183,206)(184,197)(185,201)(186,194)(187,195)(188,204)
(189,208)(190,199)(191,198)(192,205)(226,234)(227,235)(229,232)(230,239)
(231,238)(237,240)(241,289)(242,298)(243,299)(244,292)(245,296)(246,303)
(247,302)(248,293)(249,297)(250,290)(251,291)(252,300)(253,304)(254,295)
(255,294)(256,301)(257,273)(258,282)(259,283)(260,276)(261,280)(262,287)
(263,286)(264,277)(265,281)(266,274)(267,275)(268,284)(269,288)(270,279)
(271,278)(272,285)(306,314)(307,315)(309,312)(310,319)(311,318)(317,320)
(321,369)(322,378)(323,379)(324,372)(325,376)(326,383)(327,382)(328,373)
(329,377)(330,370)(331,371)(332,380)(333,384)(334,375)(335,374)(336,381)
(337,353)(338,362)(339,363)(340,356)(341,360)(342,367)(343,366)(344,357)
(345,361)(346,354)(347,355)(348,364)(349,368)(350,359)(351,358)(352,365)
(386,394)(387,395)(389,392)(390,399)(391,398)(397,400)(401,449)(402,458)
(403,459)(404,452)(405,456)(406,463)(407,462)(408,453)(409,457)(410,450)
(411,451)(412,460)(413,464)(414,455)(415,454)(416,461)(417,433)(418,442)
(419,443)(420,436)(421,440)(422,447)(423,446)(424,437)(425,441)(426,434)
(427,435)(428,444)(429,448)(430,439)(431,438)(432,445)(466,474)(467,475)
(469,472)(470,479)(471,478)(477,480);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope