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