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