Polytope of Type {20,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240408)
Rank : 4
Schlafli Type : {20,6,4}
Number of vertices, edges, etc : 40, 120, 24, 4
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {20,6,4}*960c
4-fold quotients : {10,6,4}*480b
5-fold quotients : {4,6,4}*384d
10-fold quotients : {4,3,4}*192b, {4,6,4}*192d, {4,6,4}*192f
20-fold quotients : {2,6,4}*96c, {4,3,4}*96
40-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)
( 25, 65)( 26, 66)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 71)( 32, 72)
( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 61)( 38, 62)( 39, 63)( 40, 64)
( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)( 48, 56)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,153)( 98,154)( 99,155)(100,156)(101,157)(102,158)(103,159)(104,160)
(105,145)(106,146)(107,147)(108,148)(109,149)(110,150)(111,151)(112,152)
(113,137)(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)(120,144)
(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,233)(178,234)(179,235)(180,236)(181,237)(182,238)(183,239)(184,240)
(185,225)(186,226)(187,227)(188,228)(189,229)(190,230)(191,231)(192,232)
(193,217)(194,218)(195,219)(196,220)(197,221)(198,222)(199,223)(200,224)
(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,313)(258,314)(259,315)(260,316)(261,317)(262,318)(263,319)(264,320)
(265,305)(266,306)(267,307)(268,308)(269,309)(270,310)(271,311)(272,312)
(273,297)(274,298)(275,299)(276,300)(277,301)(278,302)(279,303)(280,304)
(281,289)(282,290)(283,291)(284,292)(285,293)(286,294)(287,295)(288,296)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,393)(338,394)(339,395)(340,396)(341,397)(342,398)(343,399)(344,400)
(345,385)(346,386)(347,387)(348,388)(349,389)(350,390)(351,391)(352,392)
(353,377)(354,378)(355,379)(356,380)(357,381)(358,382)(359,383)(360,384)
(361,369)(362,370)(363,371)(364,372)(365,373)(366,374)(367,375)(368,376)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)
(417,473)(418,474)(419,475)(420,476)(421,477)(422,478)(423,479)(424,480)
(425,465)(426,466)(427,467)(428,468)(429,469)(430,470)(431,471)(432,472)
(433,457)(434,458)(435,459)(436,460)(437,461)(438,462)(439,463)(440,464)
(441,449)(442,450)(443,451)(444,452)(445,453)(446,454)(447,455)(448,456);;
s1 := ( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 21)( 6, 22)( 7, 24)( 8, 23)
( 9, 29)( 10, 30)( 11, 32)( 12, 31)( 13, 25)( 14, 26)( 15, 28)( 16, 27)
( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 69)( 38, 70)( 39, 72)( 40, 71)
( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)
( 51, 52)( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 81,177)( 82,178)
( 83,180)( 84,179)( 85,181)( 86,182)( 87,184)( 88,183)( 89,189)( 90,190)
( 91,192)( 92,191)( 93,185)( 94,186)( 95,188)( 96,187)( 97,161)( 98,162)
( 99,164)(100,163)(101,165)(102,166)(103,168)(104,167)(105,173)(106,174)
(107,176)(108,175)(109,169)(110,170)(111,172)(112,171)(113,225)(114,226)
(115,228)(116,227)(117,229)(118,230)(119,232)(120,231)(121,237)(122,238)
(123,240)(124,239)(125,233)(126,234)(127,236)(128,235)(129,209)(130,210)
(131,212)(132,211)(133,213)(134,214)(135,216)(136,215)(137,221)(138,222)
(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,193)(146,194)
(147,196)(148,195)(149,197)(150,198)(151,200)(152,199)(153,205)(154,206)
(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(241,257)(242,258)
(243,260)(244,259)(245,261)(246,262)(247,264)(248,263)(249,269)(250,270)
(251,272)(252,271)(253,265)(254,266)(255,268)(256,267)(273,305)(274,306)
(275,308)(276,307)(277,309)(278,310)(279,312)(280,311)(281,317)(282,318)
(283,320)(284,319)(285,313)(286,314)(287,316)(288,315)(291,292)(295,296)
(297,301)(298,302)(299,304)(300,303)(321,417)(322,418)(323,420)(324,419)
(325,421)(326,422)(327,424)(328,423)(329,429)(330,430)(331,432)(332,431)
(333,425)(334,426)(335,428)(336,427)(337,401)(338,402)(339,404)(340,403)
(341,405)(342,406)(343,408)(344,407)(345,413)(346,414)(347,416)(348,415)
(349,409)(350,410)(351,412)(352,411)(353,465)(354,466)(355,468)(356,467)
(357,469)(358,470)(359,472)(360,471)(361,477)(362,478)(363,480)(364,479)
(365,473)(366,474)(367,476)(368,475)(369,449)(370,450)(371,452)(372,451)
(373,453)(374,454)(375,456)(376,455)(377,461)(378,462)(379,464)(380,463)
(381,457)(382,458)(383,460)(384,459)(385,433)(386,434)(387,436)(388,435)
(389,437)(390,438)(391,440)(392,439)(393,445)(394,446)(395,448)(396,447)
(397,441)(398,442)(399,444)(400,443);;
s2 := ( 1,321)( 2,324)( 3,323)( 4,322)( 5,333)( 6,336)( 7,335)( 8,334)
( 9,329)( 10,332)( 11,331)( 12,330)( 13,325)( 14,328)( 15,327)( 16,326)
( 17,337)( 18,340)( 19,339)( 20,338)( 21,349)( 22,352)( 23,351)( 24,350)
( 25,345)( 26,348)( 27,347)( 28,346)( 29,341)( 30,344)( 31,343)( 32,342)
( 33,353)( 34,356)( 35,355)( 36,354)( 37,365)( 38,368)( 39,367)( 40,366)
( 41,361)( 42,364)( 43,363)( 44,362)( 45,357)( 46,360)( 47,359)( 48,358)
( 49,369)( 50,372)( 51,371)( 52,370)( 53,381)( 54,384)( 55,383)( 56,382)
( 57,377)( 58,380)( 59,379)( 60,378)( 61,373)( 62,376)( 63,375)( 64,374)
( 65,385)( 66,388)( 67,387)( 68,386)( 69,397)( 70,400)( 71,399)( 72,398)
( 73,393)( 74,396)( 75,395)( 76,394)( 77,389)( 78,392)( 79,391)( 80,390)
( 81,241)( 82,244)( 83,243)( 84,242)( 85,253)( 86,256)( 87,255)( 88,254)
( 89,249)( 90,252)( 91,251)( 92,250)( 93,245)( 94,248)( 95,247)( 96,246)
( 97,257)( 98,260)( 99,259)(100,258)(101,269)(102,272)(103,271)(104,270)
(105,265)(106,268)(107,267)(108,266)(109,261)(110,264)(111,263)(112,262)
(113,273)(114,276)(115,275)(116,274)(117,285)(118,288)(119,287)(120,286)
(121,281)(122,284)(123,283)(124,282)(125,277)(126,280)(127,279)(128,278)
(129,289)(130,292)(131,291)(132,290)(133,301)(134,304)(135,303)(136,302)
(137,297)(138,300)(139,299)(140,298)(141,293)(142,296)(143,295)(144,294)
(145,305)(146,308)(147,307)(148,306)(149,317)(150,320)(151,319)(152,318)
(153,313)(154,316)(155,315)(156,314)(157,309)(158,312)(159,311)(160,310)
(161,401)(162,404)(163,403)(164,402)(165,413)(166,416)(167,415)(168,414)
(169,409)(170,412)(171,411)(172,410)(173,405)(174,408)(175,407)(176,406)
(177,417)(178,420)(179,419)(180,418)(181,429)(182,432)(183,431)(184,430)
(185,425)(186,428)(187,427)(188,426)(189,421)(190,424)(191,423)(192,422)
(193,433)(194,436)(195,435)(196,434)(197,445)(198,448)(199,447)(200,446)
(201,441)(202,444)(203,443)(204,442)(205,437)(206,440)(207,439)(208,438)
(209,449)(210,452)(211,451)(212,450)(213,461)(214,464)(215,463)(216,462)
(217,457)(218,460)(219,459)(220,458)(221,453)(222,456)(223,455)(224,454)
(225,465)(226,468)(227,467)(228,466)(229,477)(230,480)(231,479)(232,478)
(233,473)(234,476)(235,475)(236,474)(237,469)(238,472)(239,471)(240,470);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)
(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)
( 24, 80)( 25, 65)( 26, 66)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 71)
( 32, 72)( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 61)( 38, 62)( 39, 63)
( 40, 64)( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)
( 48, 56)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,153)( 98,154)( 99,155)(100,156)(101,157)(102,158)(103,159)
(104,160)(105,145)(106,146)(107,147)(108,148)(109,149)(110,150)(111,151)
(112,152)(113,137)(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)
(120,144)(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)
(128,136)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,233)(178,234)(179,235)(180,236)(181,237)(182,238)(183,239)
(184,240)(185,225)(186,226)(187,227)(188,228)(189,229)(190,230)(191,231)
(192,232)(193,217)(194,218)(195,219)(196,220)(197,221)(198,222)(199,223)
(200,224)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)
(208,216)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,313)(258,314)(259,315)(260,316)(261,317)(262,318)(263,319)
(264,320)(265,305)(266,306)(267,307)(268,308)(269,309)(270,310)(271,311)
(272,312)(273,297)(274,298)(275,299)(276,300)(277,301)(278,302)(279,303)
(280,304)(281,289)(282,290)(283,291)(284,292)(285,293)(286,294)(287,295)
(288,296)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)
(328,336)(337,393)(338,394)(339,395)(340,396)(341,397)(342,398)(343,399)
(344,400)(345,385)(346,386)(347,387)(348,388)(349,389)(350,390)(351,391)
(352,392)(353,377)(354,378)(355,379)(356,380)(357,381)(358,382)(359,383)
(360,384)(361,369)(362,370)(363,371)(364,372)(365,373)(366,374)(367,375)
(368,376)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416)(417,473)(418,474)(419,475)(420,476)(421,477)(422,478)(423,479)
(424,480)(425,465)(426,466)(427,467)(428,468)(429,469)(430,470)(431,471)
(432,472)(433,457)(434,458)(435,459)(436,460)(437,461)(438,462)(439,463)
(440,464)(441,449)(442,450)(443,451)(444,452)(445,453)(446,454)(447,455)
(448,456);
s1 := Sym(480)!( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 21)( 6, 22)( 7, 24)
( 8, 23)( 9, 29)( 10, 30)( 11, 32)( 12, 31)( 13, 25)( 14, 26)( 15, 28)
( 16, 27)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 69)( 38, 70)( 39, 72)
( 40, 71)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)
( 48, 75)( 51, 52)( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 81,177)
( 82,178)( 83,180)( 84,179)( 85,181)( 86,182)( 87,184)( 88,183)( 89,189)
( 90,190)( 91,192)( 92,191)( 93,185)( 94,186)( 95,188)( 96,187)( 97,161)
( 98,162)( 99,164)(100,163)(101,165)(102,166)(103,168)(104,167)(105,173)
(106,174)(107,176)(108,175)(109,169)(110,170)(111,172)(112,171)(113,225)
(114,226)(115,228)(116,227)(117,229)(118,230)(119,232)(120,231)(121,237)
(122,238)(123,240)(124,239)(125,233)(126,234)(127,236)(128,235)(129,209)
(130,210)(131,212)(132,211)(133,213)(134,214)(135,216)(136,215)(137,221)
(138,222)(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,193)
(146,194)(147,196)(148,195)(149,197)(150,198)(151,200)(152,199)(153,205)
(154,206)(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(241,257)
(242,258)(243,260)(244,259)(245,261)(246,262)(247,264)(248,263)(249,269)
(250,270)(251,272)(252,271)(253,265)(254,266)(255,268)(256,267)(273,305)
(274,306)(275,308)(276,307)(277,309)(278,310)(279,312)(280,311)(281,317)
(282,318)(283,320)(284,319)(285,313)(286,314)(287,316)(288,315)(291,292)
(295,296)(297,301)(298,302)(299,304)(300,303)(321,417)(322,418)(323,420)
(324,419)(325,421)(326,422)(327,424)(328,423)(329,429)(330,430)(331,432)
(332,431)(333,425)(334,426)(335,428)(336,427)(337,401)(338,402)(339,404)
(340,403)(341,405)(342,406)(343,408)(344,407)(345,413)(346,414)(347,416)
(348,415)(349,409)(350,410)(351,412)(352,411)(353,465)(354,466)(355,468)
(356,467)(357,469)(358,470)(359,472)(360,471)(361,477)(362,478)(363,480)
(364,479)(365,473)(366,474)(367,476)(368,475)(369,449)(370,450)(371,452)
(372,451)(373,453)(374,454)(375,456)(376,455)(377,461)(378,462)(379,464)
(380,463)(381,457)(382,458)(383,460)(384,459)(385,433)(386,434)(387,436)
(388,435)(389,437)(390,438)(391,440)(392,439)(393,445)(394,446)(395,448)
(396,447)(397,441)(398,442)(399,444)(400,443);
s2 := Sym(480)!( 1,321)( 2,324)( 3,323)( 4,322)( 5,333)( 6,336)( 7,335)
( 8,334)( 9,329)( 10,332)( 11,331)( 12,330)( 13,325)( 14,328)( 15,327)
( 16,326)( 17,337)( 18,340)( 19,339)( 20,338)( 21,349)( 22,352)( 23,351)
( 24,350)( 25,345)( 26,348)( 27,347)( 28,346)( 29,341)( 30,344)( 31,343)
( 32,342)( 33,353)( 34,356)( 35,355)( 36,354)( 37,365)( 38,368)( 39,367)
( 40,366)( 41,361)( 42,364)( 43,363)( 44,362)( 45,357)( 46,360)( 47,359)
( 48,358)( 49,369)( 50,372)( 51,371)( 52,370)( 53,381)( 54,384)( 55,383)
( 56,382)( 57,377)( 58,380)( 59,379)( 60,378)( 61,373)( 62,376)( 63,375)
( 64,374)( 65,385)( 66,388)( 67,387)( 68,386)( 69,397)( 70,400)( 71,399)
( 72,398)( 73,393)( 74,396)( 75,395)( 76,394)( 77,389)( 78,392)( 79,391)
( 80,390)( 81,241)( 82,244)( 83,243)( 84,242)( 85,253)( 86,256)( 87,255)
( 88,254)( 89,249)( 90,252)( 91,251)( 92,250)( 93,245)( 94,248)( 95,247)
( 96,246)( 97,257)( 98,260)( 99,259)(100,258)(101,269)(102,272)(103,271)
(104,270)(105,265)(106,268)(107,267)(108,266)(109,261)(110,264)(111,263)
(112,262)(113,273)(114,276)(115,275)(116,274)(117,285)(118,288)(119,287)
(120,286)(121,281)(122,284)(123,283)(124,282)(125,277)(126,280)(127,279)
(128,278)(129,289)(130,292)(131,291)(132,290)(133,301)(134,304)(135,303)
(136,302)(137,297)(138,300)(139,299)(140,298)(141,293)(142,296)(143,295)
(144,294)(145,305)(146,308)(147,307)(148,306)(149,317)(150,320)(151,319)
(152,318)(153,313)(154,316)(155,315)(156,314)(157,309)(158,312)(159,311)
(160,310)(161,401)(162,404)(163,403)(164,402)(165,413)(166,416)(167,415)
(168,414)(169,409)(170,412)(171,411)(172,410)(173,405)(174,408)(175,407)
(176,406)(177,417)(178,420)(179,419)(180,418)(181,429)(182,432)(183,431)
(184,430)(185,425)(186,428)(187,427)(188,426)(189,421)(190,424)(191,423)
(192,422)(193,433)(194,436)(195,435)(196,434)(197,445)(198,448)(199,447)
(200,446)(201,441)(202,444)(203,443)(204,442)(205,437)(206,440)(207,439)
(208,438)(209,449)(210,452)(211,451)(212,450)(213,461)(214,464)(215,463)
(216,462)(217,457)(218,460)(219,459)(220,458)(221,453)(222,456)(223,455)
(224,454)(225,465)(226,468)(227,467)(228,466)(229,477)(230,480)(231,479)
(232,478)(233,473)(234,476)(235,475)(236,474)(237,469)(238,472)(239,471)
(240,470);
s3 := Sym(480)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)
(479,480);
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,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 >;
References : None.
to this polytope