Polytope of Type {10,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 4
Schlafli Type : {10,12,6}
Number of vertices, edges, etc : 10, 80, 48, 8
Order of s0s1s2s3 : 40
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 : {10,12,3}*960, {10,6,6}*960
4-fold quotients : {10,6,3}*480
5-fold quotients : {2,12,6}*384b
10-fold quotients : {2,12,3}*192, {2,6,6}*192
20-fold quotients : {2,3,6}*96, {2,6,3}*96
24-fold quotients : {10,2,2}*80
40-fold quotients : {2,3,3}*48
48-fold quotients : {5,2,2}*40
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 9, 33)( 10, 34)( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 49, 73)( 50, 74)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 89,113)( 90,114)( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)( 96,120)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)
(137,145)(138,146)(139,147)(140,148)(141,149)(142,150)(143,151)(144,152)
(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(209,233)(210,234)(211,235)(212,236)(213,237)(214,238)(215,239)(216,240)
(217,225)(218,226)(219,227)(220,228)(221,229)(222,230)(223,231)(224,232)
(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)(256,280)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(289,313)(290,314)(291,315)(292,316)(293,317)(294,318)(295,319)(296,320)
(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)(304,312)
(329,353)(330,354)(331,355)(332,356)(333,357)(334,358)(335,359)(336,360)
(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)
(369,393)(370,394)(371,395)(372,396)(373,397)(374,398)(375,399)(376,400)
(377,385)(378,386)(379,387)(380,388)(381,389)(382,390)(383,391)(384,392)
(409,433)(410,434)(411,435)(412,436)(413,437)(414,438)(415,439)(416,440)
(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)
(449,473)(450,474)(451,475)(452,476)(453,477)(454,478)(455,479)(456,480)
(457,465)(458,466)(459,467)(460,468)(461,469)(462,470)(463,471)(464,472);;
s1 := ( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)( 8, 14)
( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)( 24, 38)
( 27, 28)( 29, 31)( 30, 32)( 41, 89)( 42, 90)( 43, 92)( 44, 91)( 45, 95)
( 46, 96)( 47, 93)( 48, 94)( 49, 81)( 50, 82)( 51, 84)( 52, 83)( 53, 87)
( 54, 88)( 55, 85)( 56, 86)( 57,113)( 58,114)( 59,116)( 60,115)( 61,119)
( 62,120)( 63,117)( 64,118)( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)
( 70,112)( 71,109)( 72,110)( 73, 97)( 74, 98)( 75,100)( 76, 99)( 77,103)
( 78,104)( 79,101)( 80,102)(121,130)(122,129)(123,131)(124,132)(125,136)
(126,135)(127,134)(128,133)(137,154)(138,153)(139,155)(140,156)(141,160)
(142,159)(143,158)(144,157)(145,146)(149,152)(150,151)(161,210)(162,209)
(163,211)(164,212)(165,216)(166,215)(167,214)(168,213)(169,202)(170,201)
(171,203)(172,204)(173,208)(174,207)(175,206)(176,205)(177,234)(178,233)
(179,235)(180,236)(181,240)(182,239)(183,238)(184,237)(185,226)(186,225)
(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,218)(194,217)
(195,219)(196,220)(197,224)(198,223)(199,222)(200,221)(241,249)(242,250)
(243,252)(244,251)(245,255)(246,256)(247,253)(248,254)(257,273)(258,274)
(259,276)(260,275)(261,279)(262,280)(263,277)(264,278)(267,268)(269,271)
(270,272)(281,329)(282,330)(283,332)(284,331)(285,335)(286,336)(287,333)
(288,334)(289,321)(290,322)(291,324)(292,323)(293,327)(294,328)(295,325)
(296,326)(297,353)(298,354)(299,356)(300,355)(301,359)(302,360)(303,357)
(304,358)(305,345)(306,346)(307,348)(308,347)(309,351)(310,352)(311,349)
(312,350)(313,337)(314,338)(315,340)(316,339)(317,343)(318,344)(319,341)
(320,342)(361,370)(362,369)(363,371)(364,372)(365,376)(366,375)(367,374)
(368,373)(377,394)(378,393)(379,395)(380,396)(381,400)(382,399)(383,398)
(384,397)(385,386)(389,392)(390,391)(401,450)(402,449)(403,451)(404,452)
(405,456)(406,455)(407,454)(408,453)(409,442)(410,441)(411,443)(412,444)
(413,448)(414,447)(415,446)(416,445)(417,474)(418,473)(419,475)(420,476)
(421,480)(422,479)(423,478)(424,477)(425,466)(426,465)(427,467)(428,468)
(429,472)(430,471)(431,470)(432,469)(433,458)(434,457)(435,459)(436,460)
(437,464)(438,463)(439,462)(440,461);;
s2 := ( 1,161)( 2,162)( 3,167)( 4,168)( 5,166)( 6,165)( 7,163)( 8,164)
( 9,169)( 10,170)( 11,175)( 12,176)( 13,174)( 14,173)( 15,171)( 16,172)
( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)( 24,180)
( 25,185)( 26,186)( 27,191)( 28,192)( 29,190)( 30,189)( 31,187)( 32,188)
( 33,193)( 34,194)( 35,199)( 36,200)( 37,198)( 38,197)( 39,195)( 40,196)
( 41,121)( 42,122)( 43,127)( 44,128)( 45,126)( 46,125)( 47,123)( 48,124)
( 49,129)( 50,130)( 51,135)( 52,136)( 53,134)( 54,133)( 55,131)( 56,132)
( 57,137)( 58,138)( 59,143)( 60,144)( 61,142)( 62,141)( 63,139)( 64,140)
( 65,145)( 66,146)( 67,151)( 68,152)( 69,150)( 70,149)( 71,147)( 72,148)
( 73,153)( 74,154)( 75,159)( 76,160)( 77,158)( 78,157)( 79,155)( 80,156)
( 81,201)( 82,202)( 83,207)( 84,208)( 85,206)( 86,205)( 87,203)( 88,204)
( 89,209)( 90,210)( 91,215)( 92,216)( 93,214)( 94,213)( 95,211)( 96,212)
( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)(104,220)
(105,225)(106,226)(107,231)(108,232)(109,230)(110,229)(111,227)(112,228)
(113,233)(114,234)(115,239)(116,240)(117,238)(118,237)(119,235)(120,236)
(241,401)(242,402)(243,407)(244,408)(245,406)(246,405)(247,403)(248,404)
(249,409)(250,410)(251,415)(252,416)(253,414)(254,413)(255,411)(256,412)
(257,417)(258,418)(259,423)(260,424)(261,422)(262,421)(263,419)(264,420)
(265,425)(266,426)(267,431)(268,432)(269,430)(270,429)(271,427)(272,428)
(273,433)(274,434)(275,439)(276,440)(277,438)(278,437)(279,435)(280,436)
(281,361)(282,362)(283,367)(284,368)(285,366)(286,365)(287,363)(288,364)
(289,369)(290,370)(291,375)(292,376)(293,374)(294,373)(295,371)(296,372)
(297,377)(298,378)(299,383)(300,384)(301,382)(302,381)(303,379)(304,380)
(305,385)(306,386)(307,391)(308,392)(309,390)(310,389)(311,387)(312,388)
(313,393)(314,394)(315,399)(316,400)(317,398)(318,397)(319,395)(320,396)
(321,441)(322,442)(323,447)(324,448)(325,446)(326,445)(327,443)(328,444)
(329,449)(330,450)(331,455)(332,456)(333,454)(334,453)(335,451)(336,452)
(337,457)(338,458)(339,463)(340,464)(341,462)(342,461)(343,459)(344,460)
(345,465)(346,466)(347,471)(348,472)(349,470)(350,469)(351,467)(352,468)
(353,473)(354,474)(355,479)(356,480)(357,478)(358,477)(359,475)(360,476);;
s3 := ( 1,363)( 2,364)( 3,361)( 4,362)( 5,366)( 6,365)( 7,367)( 8,368)
( 9,371)( 10,372)( 11,369)( 12,370)( 13,374)( 14,373)( 15,375)( 16,376)
( 17,379)( 18,380)( 19,377)( 20,378)( 21,382)( 22,381)( 23,383)( 24,384)
( 25,387)( 26,388)( 27,385)( 28,386)( 29,390)( 30,389)( 31,391)( 32,392)
( 33,395)( 34,396)( 35,393)( 36,394)( 37,398)( 38,397)( 39,399)( 40,400)
( 41,443)( 42,444)( 43,441)( 44,442)( 45,446)( 46,445)( 47,447)( 48,448)
( 49,451)( 50,452)( 51,449)( 52,450)( 53,454)( 54,453)( 55,455)( 56,456)
( 57,459)( 58,460)( 59,457)( 60,458)( 61,462)( 62,461)( 63,463)( 64,464)
( 65,467)( 66,468)( 67,465)( 68,466)( 69,470)( 70,469)( 71,471)( 72,472)
( 73,475)( 74,476)( 75,473)( 76,474)( 77,478)( 78,477)( 79,479)( 80,480)
( 81,403)( 82,404)( 83,401)( 84,402)( 85,406)( 86,405)( 87,407)( 88,408)
( 89,411)( 90,412)( 91,409)( 92,410)( 93,414)( 94,413)( 95,415)( 96,416)
( 97,419)( 98,420)( 99,417)(100,418)(101,422)(102,421)(103,423)(104,424)
(105,427)(106,428)(107,425)(108,426)(109,430)(110,429)(111,431)(112,432)
(113,435)(114,436)(115,433)(116,434)(117,438)(118,437)(119,439)(120,440)
(121,243)(122,244)(123,241)(124,242)(125,246)(126,245)(127,247)(128,248)
(129,251)(130,252)(131,249)(132,250)(133,254)(134,253)(135,255)(136,256)
(137,259)(138,260)(139,257)(140,258)(141,262)(142,261)(143,263)(144,264)
(145,267)(146,268)(147,265)(148,266)(149,270)(150,269)(151,271)(152,272)
(153,275)(154,276)(155,273)(156,274)(157,278)(158,277)(159,279)(160,280)
(161,323)(162,324)(163,321)(164,322)(165,326)(166,325)(167,327)(168,328)
(169,331)(170,332)(171,329)(172,330)(173,334)(174,333)(175,335)(176,336)
(177,339)(178,340)(179,337)(180,338)(181,342)(182,341)(183,343)(184,344)
(185,347)(186,348)(187,345)(188,346)(189,350)(190,349)(191,351)(192,352)
(193,355)(194,356)(195,353)(196,354)(197,358)(198,357)(199,359)(200,360)
(201,283)(202,284)(203,281)(204,282)(205,286)(206,285)(207,287)(208,288)
(209,291)(210,292)(211,289)(212,290)(213,294)(214,293)(215,295)(216,296)
(217,299)(218,300)(219,297)(220,298)(221,302)(222,301)(223,303)(224,304)
(225,307)(226,308)(227,305)(228,306)(229,310)(230,309)(231,311)(232,312)
(233,315)(234,316)(235,313)(236,314)(237,318)(238,317)(239,319)(240,320);;
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 9, 33)( 10, 34)( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)
( 16, 40)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 49, 73)( 50, 74)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)
( 56, 80)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 89,113)( 90,114)( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)
( 96,120)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)
(136,160)(137,145)(138,146)(139,147)(140,148)(141,149)(142,150)(143,151)
(144,152)(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)
(176,200)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(209,233)(210,234)(211,235)(212,236)(213,237)(214,238)(215,239)
(216,240)(217,225)(218,226)(219,227)(220,228)(221,229)(222,230)(223,231)
(224,232)(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)
(256,280)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(289,313)(290,314)(291,315)(292,316)(293,317)(294,318)(295,319)
(296,320)(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)
(304,312)(329,353)(330,354)(331,355)(332,356)(333,357)(334,358)(335,359)
(336,360)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)
(344,352)(369,393)(370,394)(371,395)(372,396)(373,397)(374,398)(375,399)
(376,400)(377,385)(378,386)(379,387)(380,388)(381,389)(382,390)(383,391)
(384,392)(409,433)(410,434)(411,435)(412,436)(413,437)(414,438)(415,439)
(416,440)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)
(424,432)(449,473)(450,474)(451,475)(452,476)(453,477)(454,478)(455,479)
(456,480)(457,465)(458,466)(459,467)(460,468)(461,469)(462,470)(463,471)
(464,472);
s1 := Sym(480)!( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)
( 8, 14)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)
( 24, 38)( 27, 28)( 29, 31)( 30, 32)( 41, 89)( 42, 90)( 43, 92)( 44, 91)
( 45, 95)( 46, 96)( 47, 93)( 48, 94)( 49, 81)( 50, 82)( 51, 84)( 52, 83)
( 53, 87)( 54, 88)( 55, 85)( 56, 86)( 57,113)( 58,114)( 59,116)( 60,115)
( 61,119)( 62,120)( 63,117)( 64,118)( 65,105)( 66,106)( 67,108)( 68,107)
( 69,111)( 70,112)( 71,109)( 72,110)( 73, 97)( 74, 98)( 75,100)( 76, 99)
( 77,103)( 78,104)( 79,101)( 80,102)(121,130)(122,129)(123,131)(124,132)
(125,136)(126,135)(127,134)(128,133)(137,154)(138,153)(139,155)(140,156)
(141,160)(142,159)(143,158)(144,157)(145,146)(149,152)(150,151)(161,210)
(162,209)(163,211)(164,212)(165,216)(166,215)(167,214)(168,213)(169,202)
(170,201)(171,203)(172,204)(173,208)(174,207)(175,206)(176,205)(177,234)
(178,233)(179,235)(180,236)(181,240)(182,239)(183,238)(184,237)(185,226)
(186,225)(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,218)
(194,217)(195,219)(196,220)(197,224)(198,223)(199,222)(200,221)(241,249)
(242,250)(243,252)(244,251)(245,255)(246,256)(247,253)(248,254)(257,273)
(258,274)(259,276)(260,275)(261,279)(262,280)(263,277)(264,278)(267,268)
(269,271)(270,272)(281,329)(282,330)(283,332)(284,331)(285,335)(286,336)
(287,333)(288,334)(289,321)(290,322)(291,324)(292,323)(293,327)(294,328)
(295,325)(296,326)(297,353)(298,354)(299,356)(300,355)(301,359)(302,360)
(303,357)(304,358)(305,345)(306,346)(307,348)(308,347)(309,351)(310,352)
(311,349)(312,350)(313,337)(314,338)(315,340)(316,339)(317,343)(318,344)
(319,341)(320,342)(361,370)(362,369)(363,371)(364,372)(365,376)(366,375)
(367,374)(368,373)(377,394)(378,393)(379,395)(380,396)(381,400)(382,399)
(383,398)(384,397)(385,386)(389,392)(390,391)(401,450)(402,449)(403,451)
(404,452)(405,456)(406,455)(407,454)(408,453)(409,442)(410,441)(411,443)
(412,444)(413,448)(414,447)(415,446)(416,445)(417,474)(418,473)(419,475)
(420,476)(421,480)(422,479)(423,478)(424,477)(425,466)(426,465)(427,467)
(428,468)(429,472)(430,471)(431,470)(432,469)(433,458)(434,457)(435,459)
(436,460)(437,464)(438,463)(439,462)(440,461);
s2 := Sym(480)!( 1,161)( 2,162)( 3,167)( 4,168)( 5,166)( 6,165)( 7,163)
( 8,164)( 9,169)( 10,170)( 11,175)( 12,176)( 13,174)( 14,173)( 15,171)
( 16,172)( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)
( 24,180)( 25,185)( 26,186)( 27,191)( 28,192)( 29,190)( 30,189)( 31,187)
( 32,188)( 33,193)( 34,194)( 35,199)( 36,200)( 37,198)( 38,197)( 39,195)
( 40,196)( 41,121)( 42,122)( 43,127)( 44,128)( 45,126)( 46,125)( 47,123)
( 48,124)( 49,129)( 50,130)( 51,135)( 52,136)( 53,134)( 54,133)( 55,131)
( 56,132)( 57,137)( 58,138)( 59,143)( 60,144)( 61,142)( 62,141)( 63,139)
( 64,140)( 65,145)( 66,146)( 67,151)( 68,152)( 69,150)( 70,149)( 71,147)
( 72,148)( 73,153)( 74,154)( 75,159)( 76,160)( 77,158)( 78,157)( 79,155)
( 80,156)( 81,201)( 82,202)( 83,207)( 84,208)( 85,206)( 86,205)( 87,203)
( 88,204)( 89,209)( 90,210)( 91,215)( 92,216)( 93,214)( 94,213)( 95,211)
( 96,212)( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)
(104,220)(105,225)(106,226)(107,231)(108,232)(109,230)(110,229)(111,227)
(112,228)(113,233)(114,234)(115,239)(116,240)(117,238)(118,237)(119,235)
(120,236)(241,401)(242,402)(243,407)(244,408)(245,406)(246,405)(247,403)
(248,404)(249,409)(250,410)(251,415)(252,416)(253,414)(254,413)(255,411)
(256,412)(257,417)(258,418)(259,423)(260,424)(261,422)(262,421)(263,419)
(264,420)(265,425)(266,426)(267,431)(268,432)(269,430)(270,429)(271,427)
(272,428)(273,433)(274,434)(275,439)(276,440)(277,438)(278,437)(279,435)
(280,436)(281,361)(282,362)(283,367)(284,368)(285,366)(286,365)(287,363)
(288,364)(289,369)(290,370)(291,375)(292,376)(293,374)(294,373)(295,371)
(296,372)(297,377)(298,378)(299,383)(300,384)(301,382)(302,381)(303,379)
(304,380)(305,385)(306,386)(307,391)(308,392)(309,390)(310,389)(311,387)
(312,388)(313,393)(314,394)(315,399)(316,400)(317,398)(318,397)(319,395)
(320,396)(321,441)(322,442)(323,447)(324,448)(325,446)(326,445)(327,443)
(328,444)(329,449)(330,450)(331,455)(332,456)(333,454)(334,453)(335,451)
(336,452)(337,457)(338,458)(339,463)(340,464)(341,462)(342,461)(343,459)
(344,460)(345,465)(346,466)(347,471)(348,472)(349,470)(350,469)(351,467)
(352,468)(353,473)(354,474)(355,479)(356,480)(357,478)(358,477)(359,475)
(360,476);
s3 := Sym(480)!( 1,363)( 2,364)( 3,361)( 4,362)( 5,366)( 6,365)( 7,367)
( 8,368)( 9,371)( 10,372)( 11,369)( 12,370)( 13,374)( 14,373)( 15,375)
( 16,376)( 17,379)( 18,380)( 19,377)( 20,378)( 21,382)( 22,381)( 23,383)
( 24,384)( 25,387)( 26,388)( 27,385)( 28,386)( 29,390)( 30,389)( 31,391)
( 32,392)( 33,395)( 34,396)( 35,393)( 36,394)( 37,398)( 38,397)( 39,399)
( 40,400)( 41,443)( 42,444)( 43,441)( 44,442)( 45,446)( 46,445)( 47,447)
( 48,448)( 49,451)( 50,452)( 51,449)( 52,450)( 53,454)( 54,453)( 55,455)
( 56,456)( 57,459)( 58,460)( 59,457)( 60,458)( 61,462)( 62,461)( 63,463)
( 64,464)( 65,467)( 66,468)( 67,465)( 68,466)( 69,470)( 70,469)( 71,471)
( 72,472)( 73,475)( 74,476)( 75,473)( 76,474)( 77,478)( 78,477)( 79,479)
( 80,480)( 81,403)( 82,404)( 83,401)( 84,402)( 85,406)( 86,405)( 87,407)
( 88,408)( 89,411)( 90,412)( 91,409)( 92,410)( 93,414)( 94,413)( 95,415)
( 96,416)( 97,419)( 98,420)( 99,417)(100,418)(101,422)(102,421)(103,423)
(104,424)(105,427)(106,428)(107,425)(108,426)(109,430)(110,429)(111,431)
(112,432)(113,435)(114,436)(115,433)(116,434)(117,438)(118,437)(119,439)
(120,440)(121,243)(122,244)(123,241)(124,242)(125,246)(126,245)(127,247)
(128,248)(129,251)(130,252)(131,249)(132,250)(133,254)(134,253)(135,255)
(136,256)(137,259)(138,260)(139,257)(140,258)(141,262)(142,261)(143,263)
(144,264)(145,267)(146,268)(147,265)(148,266)(149,270)(150,269)(151,271)
(152,272)(153,275)(154,276)(155,273)(156,274)(157,278)(158,277)(159,279)
(160,280)(161,323)(162,324)(163,321)(164,322)(165,326)(166,325)(167,327)
(168,328)(169,331)(170,332)(171,329)(172,330)(173,334)(174,333)(175,335)
(176,336)(177,339)(178,340)(179,337)(180,338)(181,342)(182,341)(183,343)
(184,344)(185,347)(186,348)(187,345)(188,346)(189,350)(190,349)(191,351)
(192,352)(193,355)(194,356)(195,353)(196,354)(197,358)(198,357)(199,359)
(200,360)(201,283)(202,284)(203,281)(204,282)(205,286)(206,285)(207,287)
(208,288)(209,291)(210,292)(211,289)(212,290)(213,294)(214,293)(215,295)
(216,296)(217,299)(218,300)(219,297)(220,298)(221,302)(222,301)(223,303)
(224,304)(225,307)(226,308)(227,305)(228,306)(229,310)(230,309)(231,311)
(232,312)(233,315)(234,316)(235,313)(236,314)(237,318)(238,317)(239,319)
(240,320);
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope