Polytope of Type {4,60,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,60,4}*1920e
if this polytope has a name.
Group : SmallGroup(1920,239398)
Rank : 4
Schlafli Type : {4,60,4}
Number of vertices, edges, etc : 4, 120, 120, 4
Order of s0s1s2s3 : 60
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 : {4,60,2}*960c, {4,30,4}*960c
4-fold quotients : {4,30,2}*480b
5-fold quotients : {4,12,4}*384e
8-fold quotients : {4,15,2}*240
10-fold quotients : {4,12,2}*192c, {4,6,4}*192c
20-fold quotients : {4,6,2}*96c
40-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 63)( 2, 64)( 3, 61)( 4, 62)( 5, 67)( 6, 68)( 7, 65)( 8, 66)
( 9, 71)( 10, 72)( 11, 69)( 12, 70)( 13, 75)( 14, 76)( 15, 73)( 16, 74)
( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)( 24, 82)
( 25, 87)( 26, 88)( 27, 85)( 28, 86)( 29, 91)( 30, 92)( 31, 89)( 32, 90)
( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 99)( 38,100)( 39, 97)( 40, 98)
( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)( 46,108)( 47,105)( 48,106)
( 49,111)( 50,112)( 51,109)( 52,110)( 53,115)( 54,116)( 55,113)( 56,114)
( 57,119)( 58,120)( 59,117)( 60,118)(121,183)(122,184)(123,181)(124,182)
(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)(132,190)
(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)(140,198)
(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)(148,206)
(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)(156,214)
(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)(164,222)
(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)(172,230)
(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)(180,238)
(241,303)(242,304)(243,301)(244,302)(245,307)(246,308)(247,305)(248,306)
(249,311)(250,312)(251,309)(252,310)(253,315)(254,316)(255,313)(256,314)
(257,319)(258,320)(259,317)(260,318)(261,323)(262,324)(263,321)(264,322)
(265,327)(266,328)(267,325)(268,326)(269,331)(270,332)(271,329)(272,330)
(273,335)(274,336)(275,333)(276,334)(277,339)(278,340)(279,337)(280,338)
(281,343)(282,344)(283,341)(284,342)(285,347)(286,348)(287,345)(288,346)
(289,351)(290,352)(291,349)(292,350)(293,355)(294,356)(295,353)(296,354)
(297,359)(298,360)(299,357)(300,358)(361,423)(362,424)(363,421)(364,422)
(365,427)(366,428)(367,425)(368,426)(369,431)(370,432)(371,429)(372,430)
(373,435)(374,436)(375,433)(376,434)(377,439)(378,440)(379,437)(380,438)
(381,443)(382,444)(383,441)(384,442)(385,447)(386,448)(387,445)(388,446)
(389,451)(390,452)(391,449)(392,450)(393,455)(394,456)(395,453)(396,454)
(397,459)(398,460)(399,457)(400,458)(401,463)(402,464)(403,461)(404,462)
(405,467)(406,468)(407,465)(408,466)(409,471)(410,472)(411,469)(412,470)
(413,475)(414,476)(415,473)(416,474)(417,479)(418,480)(419,477)(420,478);;
s1 := ( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 16)
( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)
( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)
( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)
( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)
( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)
(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)
(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)
(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)
(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)
(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)
(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)
(217,225)(218,226)(219,228)(220,227)(241,301)(242,302)(243,304)(244,303)
(245,317)(246,318)(247,320)(248,319)(249,313)(250,314)(251,316)(252,315)
(253,309)(254,310)(255,312)(256,311)(257,305)(258,306)(259,308)(260,307)
(261,341)(262,342)(263,344)(264,343)(265,357)(266,358)(267,360)(268,359)
(269,353)(270,354)(271,356)(272,355)(273,349)(274,350)(275,352)(276,351)
(277,345)(278,346)(279,348)(280,347)(281,321)(282,322)(283,324)(284,323)
(285,337)(286,338)(287,340)(288,339)(289,333)(290,334)(291,336)(292,335)
(293,329)(294,330)(295,332)(296,331)(297,325)(298,326)(299,328)(300,327)
(361,421)(362,422)(363,424)(364,423)(365,437)(366,438)(367,440)(368,439)
(369,433)(370,434)(371,436)(372,435)(373,429)(374,430)(375,432)(376,431)
(377,425)(378,426)(379,428)(380,427)(381,461)(382,462)(383,464)(384,463)
(385,477)(386,478)(387,480)(388,479)(389,473)(390,474)(391,476)(392,475)
(393,469)(394,470)(395,472)(396,471)(397,465)(398,466)(399,468)(400,467)
(401,441)(402,442)(403,444)(404,443)(405,457)(406,458)(407,460)(408,459)
(409,453)(410,454)(411,456)(412,455)(413,449)(414,450)(415,452)(416,451)
(417,445)(418,446)(419,448)(420,447);;
s2 := ( 1,265)( 2,268)( 3,267)( 4,266)( 5,261)( 6,264)( 7,263)( 8,262)
( 9,277)( 10,280)( 11,279)( 12,278)( 13,273)( 14,276)( 15,275)( 16,274)
( 17,269)( 18,272)( 19,271)( 20,270)( 21,245)( 22,248)( 23,247)( 24,246)
( 25,241)( 26,244)( 27,243)( 28,242)( 29,257)( 30,260)( 31,259)( 32,258)
( 33,253)( 34,256)( 35,255)( 36,254)( 37,249)( 38,252)( 39,251)( 40,250)
( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)( 48,282)
( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)( 56,294)
( 57,289)( 58,292)( 59,291)( 60,290)( 61,325)( 62,328)( 63,327)( 64,326)
( 65,321)( 66,324)( 67,323)( 68,322)( 69,337)( 70,340)( 71,339)( 72,338)
( 73,333)( 74,336)( 75,335)( 76,334)( 77,329)( 78,332)( 79,331)( 80,330)
( 81,305)( 82,308)( 83,307)( 84,306)( 85,301)( 86,304)( 87,303)( 88,302)
( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)( 96,314)
( 97,309)( 98,312)( 99,311)(100,310)(101,345)(102,348)(103,347)(104,346)
(105,341)(106,344)(107,343)(108,342)(109,357)(110,360)(111,359)(112,358)
(113,353)(114,356)(115,355)(116,354)(117,349)(118,352)(119,351)(120,350)
(121,385)(122,388)(123,387)(124,386)(125,381)(126,384)(127,383)(128,382)
(129,397)(130,400)(131,399)(132,398)(133,393)(134,396)(135,395)(136,394)
(137,389)(138,392)(139,391)(140,390)(141,365)(142,368)(143,367)(144,366)
(145,361)(146,364)(147,363)(148,362)(149,377)(150,380)(151,379)(152,378)
(153,373)(154,376)(155,375)(156,374)(157,369)(158,372)(159,371)(160,370)
(161,405)(162,408)(163,407)(164,406)(165,401)(166,404)(167,403)(168,402)
(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)(176,414)
(177,409)(178,412)(179,411)(180,410)(181,445)(182,448)(183,447)(184,446)
(185,441)(186,444)(187,443)(188,442)(189,457)(190,460)(191,459)(192,458)
(193,453)(194,456)(195,455)(196,454)(197,449)(198,452)(199,451)(200,450)
(201,425)(202,428)(203,427)(204,426)(205,421)(206,424)(207,423)(208,422)
(209,437)(210,440)(211,439)(212,438)(213,433)(214,436)(215,435)(216,434)
(217,429)(218,432)(219,431)(220,430)(221,465)(222,468)(223,467)(224,466)
(225,461)(226,464)(227,463)(228,462)(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 := (241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)
(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)
(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)
(273,393)(274,394)(275,395)(276,396)(277,397)(278,398)(279,399)(280,400)
(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)(288,408)
(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)(296,416)
(297,417)(298,418)(299,419)(300,420)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)
(313,433)(314,434)(315,435)(316,436)(317,437)(318,438)(319,439)(320,440)
(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)(328,448)
(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)(336,456)
(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)(344,464)
(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)(352,472)
(353,473)(354,474)(355,475)(356,476)(357,477)(358,478)(359,479)(360,480);;
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*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 1, 63)( 2, 64)( 3, 61)( 4, 62)( 5, 67)( 6, 68)( 7, 65)
( 8, 66)( 9, 71)( 10, 72)( 11, 69)( 12, 70)( 13, 75)( 14, 76)( 15, 73)
( 16, 74)( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)
( 24, 82)( 25, 87)( 26, 88)( 27, 85)( 28, 86)( 29, 91)( 30, 92)( 31, 89)
( 32, 90)( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 99)( 38,100)( 39, 97)
( 40, 98)( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)( 46,108)( 47,105)
( 48,106)( 49,111)( 50,112)( 51,109)( 52,110)( 53,115)( 54,116)( 55,113)
( 56,114)( 57,119)( 58,120)( 59,117)( 60,118)(121,183)(122,184)(123,181)
(124,182)(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)
(132,190)(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)
(140,198)(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)
(148,206)(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)
(156,214)(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)
(164,222)(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)
(172,230)(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)
(180,238)(241,303)(242,304)(243,301)(244,302)(245,307)(246,308)(247,305)
(248,306)(249,311)(250,312)(251,309)(252,310)(253,315)(254,316)(255,313)
(256,314)(257,319)(258,320)(259,317)(260,318)(261,323)(262,324)(263,321)
(264,322)(265,327)(266,328)(267,325)(268,326)(269,331)(270,332)(271,329)
(272,330)(273,335)(274,336)(275,333)(276,334)(277,339)(278,340)(279,337)
(280,338)(281,343)(282,344)(283,341)(284,342)(285,347)(286,348)(287,345)
(288,346)(289,351)(290,352)(291,349)(292,350)(293,355)(294,356)(295,353)
(296,354)(297,359)(298,360)(299,357)(300,358)(361,423)(362,424)(363,421)
(364,422)(365,427)(366,428)(367,425)(368,426)(369,431)(370,432)(371,429)
(372,430)(373,435)(374,436)(375,433)(376,434)(377,439)(378,440)(379,437)
(380,438)(381,443)(382,444)(383,441)(384,442)(385,447)(386,448)(387,445)
(388,446)(389,451)(390,452)(391,449)(392,450)(393,455)(394,456)(395,453)
(396,454)(397,459)(398,460)(399,457)(400,458)(401,463)(402,464)(403,461)
(404,462)(405,467)(406,468)(407,465)(408,466)(409,471)(410,472)(411,469)
(412,470)(413,475)(414,476)(415,473)(416,474)(417,479)(418,480)(419,477)
(420,478);
s1 := Sym(480)!( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)
( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)
( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)
( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)
( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)
( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)
(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)
(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)
(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)
(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)
(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)
(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)
(216,231)(217,225)(218,226)(219,228)(220,227)(241,301)(242,302)(243,304)
(244,303)(245,317)(246,318)(247,320)(248,319)(249,313)(250,314)(251,316)
(252,315)(253,309)(254,310)(255,312)(256,311)(257,305)(258,306)(259,308)
(260,307)(261,341)(262,342)(263,344)(264,343)(265,357)(266,358)(267,360)
(268,359)(269,353)(270,354)(271,356)(272,355)(273,349)(274,350)(275,352)
(276,351)(277,345)(278,346)(279,348)(280,347)(281,321)(282,322)(283,324)
(284,323)(285,337)(286,338)(287,340)(288,339)(289,333)(290,334)(291,336)
(292,335)(293,329)(294,330)(295,332)(296,331)(297,325)(298,326)(299,328)
(300,327)(361,421)(362,422)(363,424)(364,423)(365,437)(366,438)(367,440)
(368,439)(369,433)(370,434)(371,436)(372,435)(373,429)(374,430)(375,432)
(376,431)(377,425)(378,426)(379,428)(380,427)(381,461)(382,462)(383,464)
(384,463)(385,477)(386,478)(387,480)(388,479)(389,473)(390,474)(391,476)
(392,475)(393,469)(394,470)(395,472)(396,471)(397,465)(398,466)(399,468)
(400,467)(401,441)(402,442)(403,444)(404,443)(405,457)(406,458)(407,460)
(408,459)(409,453)(410,454)(411,456)(412,455)(413,449)(414,450)(415,452)
(416,451)(417,445)(418,446)(419,448)(420,447);
s2 := Sym(480)!( 1,265)( 2,268)( 3,267)( 4,266)( 5,261)( 6,264)( 7,263)
( 8,262)( 9,277)( 10,280)( 11,279)( 12,278)( 13,273)( 14,276)( 15,275)
( 16,274)( 17,269)( 18,272)( 19,271)( 20,270)( 21,245)( 22,248)( 23,247)
( 24,246)( 25,241)( 26,244)( 27,243)( 28,242)( 29,257)( 30,260)( 31,259)
( 32,258)( 33,253)( 34,256)( 35,255)( 36,254)( 37,249)( 38,252)( 39,251)
( 40,250)( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)
( 48,282)( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)
( 56,294)( 57,289)( 58,292)( 59,291)( 60,290)( 61,325)( 62,328)( 63,327)
( 64,326)( 65,321)( 66,324)( 67,323)( 68,322)( 69,337)( 70,340)( 71,339)
( 72,338)( 73,333)( 74,336)( 75,335)( 76,334)( 77,329)( 78,332)( 79,331)
( 80,330)( 81,305)( 82,308)( 83,307)( 84,306)( 85,301)( 86,304)( 87,303)
( 88,302)( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)
( 96,314)( 97,309)( 98,312)( 99,311)(100,310)(101,345)(102,348)(103,347)
(104,346)(105,341)(106,344)(107,343)(108,342)(109,357)(110,360)(111,359)
(112,358)(113,353)(114,356)(115,355)(116,354)(117,349)(118,352)(119,351)
(120,350)(121,385)(122,388)(123,387)(124,386)(125,381)(126,384)(127,383)
(128,382)(129,397)(130,400)(131,399)(132,398)(133,393)(134,396)(135,395)
(136,394)(137,389)(138,392)(139,391)(140,390)(141,365)(142,368)(143,367)
(144,366)(145,361)(146,364)(147,363)(148,362)(149,377)(150,380)(151,379)
(152,378)(153,373)(154,376)(155,375)(156,374)(157,369)(158,372)(159,371)
(160,370)(161,405)(162,408)(163,407)(164,406)(165,401)(166,404)(167,403)
(168,402)(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)
(176,414)(177,409)(178,412)(179,411)(180,410)(181,445)(182,448)(183,447)
(184,446)(185,441)(186,444)(187,443)(188,442)(189,457)(190,460)(191,459)
(192,458)(193,453)(194,456)(195,455)(196,454)(197,449)(198,452)(199,451)
(200,450)(201,425)(202,428)(203,427)(204,426)(205,421)(206,424)(207,423)
(208,422)(209,437)(210,440)(211,439)(212,438)(213,433)(214,436)(215,435)
(216,434)(217,429)(218,432)(219,431)(220,430)(221,465)(222,468)(223,467)
(224,466)(225,461)(226,464)(227,463)(228,462)(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)!(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)
(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)
(264,384)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)
(272,392)(273,393)(274,394)(275,395)(276,396)(277,397)(278,398)(279,399)
(280,400)(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)
(288,408)(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)
(296,416)(297,417)(298,418)(299,419)(300,420)(301,421)(302,422)(303,423)
(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)
(312,432)(313,433)(314,434)(315,435)(316,436)(317,437)(318,438)(319,439)
(320,440)(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)
(328,448)(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)
(336,456)(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)
(344,464)(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)
(352,472)(353,473)(354,474)(355,475)(356,476)(357,477)(358,478)(359,479)
(360,480);
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*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope