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Polytope of Type {15,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,8,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,239485)
Rank : 4
Schlafli Type : {15,8,4}
Number of vertices, edges, etc : 30, 120, 32, 4
Order of s0s1s2s3 : 60
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 : {15,4,4}*960b, {15,8,2}*960
   4-fold quotients : {15,4,2}*480
   5-fold quotients : {3,8,4}*384
   8-fold quotients : {15,2,4}*240, {15,4,2}*240
   10-fold quotients : {3,4,4}*192b, {3,8,2}*192
   16-fold quotients : {15,2,2}*120
   20-fold quotients : {3,4,2}*96
   24-fold quotients : {5,2,4}*80
   40-fold quotients : {3,2,4}*48, {3,4,2}*48
   48-fold quotients : {5,2,2}*40
   80-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  3,  4)(  5,  7)(  6,  8)(  9, 33)( 10, 34)( 11, 36)( 12, 35)( 13, 39)
( 14, 40)( 15, 37)( 16, 38)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 31)
( 22, 32)( 23, 29)( 24, 30)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 87)
( 46, 88)( 47, 85)( 48, 86)( 49,113)( 50,114)( 51,116)( 52,115)( 53,119)
( 54,120)( 55,117)( 56,118)( 57,105)( 58,106)( 59,108)( 60,107)( 61,111)
( 62,112)( 63,109)( 64,110)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,103)
( 70,104)( 71,101)( 72,102)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 95)
( 78, 96)( 79, 93)( 80, 94)(123,124)(125,127)(126,128)(129,153)(130,154)
(131,156)(132,155)(133,159)(134,160)(135,157)(136,158)(137,145)(138,146)
(139,148)(140,147)(141,151)(142,152)(143,149)(144,150)(161,201)(162,202)
(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,233)(170,234)
(171,236)(172,235)(173,239)(174,240)(175,237)(176,238)(177,225)(178,226)
(179,228)(180,227)(181,231)(182,232)(183,229)(184,230)(185,217)(186,218)
(187,220)(188,219)(189,223)(190,224)(191,221)(192,222)(193,209)(194,210)
(195,212)(196,211)(197,215)(198,216)(199,213)(200,214)(241,242)(245,248)
(246,247)(249,274)(250,273)(251,275)(252,276)(253,280)(254,279)(255,278)
(256,277)(257,266)(258,265)(259,267)(260,268)(261,272)(262,271)(263,270)
(264,269)(281,322)(282,321)(283,323)(284,324)(285,328)(286,327)(287,326)
(288,325)(289,354)(290,353)(291,355)(292,356)(293,360)(294,359)(295,358)
(296,357)(297,346)(298,345)(299,347)(300,348)(301,352)(302,351)(303,350)
(304,349)(305,338)(306,337)(307,339)(308,340)(309,344)(310,343)(311,342)
(312,341)(313,330)(314,329)(315,331)(316,332)(317,336)(318,335)(319,334)
(320,333)(361,362)(365,368)(366,367)(369,394)(370,393)(371,395)(372,396)
(373,400)(374,399)(375,398)(376,397)(377,386)(378,385)(379,387)(380,388)
(381,392)(382,391)(383,390)(384,389)(401,442)(402,441)(403,443)(404,444)
(405,448)(406,447)(407,446)(408,445)(409,474)(410,473)(411,475)(412,476)
(413,480)(414,479)(415,478)(416,477)(417,466)(418,465)(419,467)(420,468)
(421,472)(422,471)(423,470)(424,469)(425,458)(426,457)(427,459)(428,460)
(429,464)(430,463)(431,462)(432,461)(433,450)(434,449)(435,451)(436,452)
(437,456)(438,455)(439,454)(440,453);;
s1 := (  1, 49)(  2, 50)(  3, 55)(  4, 56)(  5, 54)(  6, 53)(  7, 51)(  8, 52)
(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)( 16, 44)
( 17, 73)( 18, 74)( 19, 79)( 20, 80)( 21, 78)( 22, 77)( 23, 75)( 24, 76)
( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)( 32, 68)
( 33, 57)( 34, 58)( 35, 63)( 36, 64)( 37, 62)( 38, 61)( 39, 59)( 40, 60)
( 81, 89)( 82, 90)( 83, 95)( 84, 96)( 85, 94)( 86, 93)( 87, 91)( 88, 92)
( 97,113)( 98,114)( 99,119)(100,120)(101,118)(102,117)(103,115)(104,116)
(107,111)(108,112)(109,110)(121,169)(122,170)(123,175)(124,176)(125,174)
(126,173)(127,171)(128,172)(129,161)(130,162)(131,167)(132,168)(133,166)
(134,165)(135,163)(136,164)(137,193)(138,194)(139,199)(140,200)(141,198)
(142,197)(143,195)(144,196)(145,185)(146,186)(147,191)(148,192)(149,190)
(150,189)(151,187)(152,188)(153,177)(154,178)(155,183)(156,184)(157,182)
(158,181)(159,179)(160,180)(201,209)(202,210)(203,215)(204,216)(205,214)
(206,213)(207,211)(208,212)(217,233)(218,234)(219,239)(220,240)(221,238)
(222,237)(223,235)(224,236)(227,231)(228,232)(229,230)(241,290)(242,289)
(243,296)(244,295)(245,293)(246,294)(247,292)(248,291)(249,282)(250,281)
(251,288)(252,287)(253,285)(254,286)(255,284)(256,283)(257,314)(258,313)
(259,320)(260,319)(261,317)(262,318)(263,316)(264,315)(265,306)(266,305)
(267,312)(268,311)(269,309)(270,310)(271,308)(272,307)(273,298)(274,297)
(275,304)(276,303)(277,301)(278,302)(279,300)(280,299)(321,330)(322,329)
(323,336)(324,335)(325,333)(326,334)(327,332)(328,331)(337,354)(338,353)
(339,360)(340,359)(341,357)(342,358)(343,356)(344,355)(345,346)(347,352)
(348,351)(361,410)(362,409)(363,416)(364,415)(365,413)(366,414)(367,412)
(368,411)(369,402)(370,401)(371,408)(372,407)(373,405)(374,406)(375,404)
(376,403)(377,434)(378,433)(379,440)(380,439)(381,437)(382,438)(383,436)
(384,435)(385,426)(386,425)(387,432)(388,431)(389,429)(390,430)(391,428)
(392,427)(393,418)(394,417)(395,424)(396,423)(397,421)(398,422)(399,420)
(400,419)(441,450)(442,449)(443,456)(444,455)(445,453)(446,454)(447,452)
(448,451)(457,474)(458,473)(459,480)(460,479)(461,477)(462,478)(463,476)
(464,475)(465,466)(467,472)(468,471);;
s2 := (  1,243)(  2,244)(  3,242)(  4,241)(  5,247)(  6,248)(  7,246)(  8,245)
(  9,251)( 10,252)( 11,250)( 12,249)( 13,255)( 14,256)( 15,254)( 16,253)
( 17,259)( 18,260)( 19,258)( 20,257)( 21,263)( 22,264)( 23,262)( 24,261)
( 25,267)( 26,268)( 27,266)( 28,265)( 29,271)( 30,272)( 31,270)( 32,269)
( 33,275)( 34,276)( 35,274)( 36,273)( 37,279)( 38,280)( 39,278)( 40,277)
( 41,283)( 42,284)( 43,282)( 44,281)( 45,287)( 46,288)( 47,286)( 48,285)
( 49,291)( 50,292)( 51,290)( 52,289)( 53,295)( 54,296)( 55,294)( 56,293)
( 57,299)( 58,300)( 59,298)( 60,297)( 61,303)( 62,304)( 63,302)( 64,301)
( 65,307)( 66,308)( 67,306)( 68,305)( 69,311)( 70,312)( 71,310)( 72,309)
( 73,315)( 74,316)( 75,314)( 76,313)( 77,319)( 78,320)( 79,318)( 80,317)
( 81,323)( 82,324)( 83,322)( 84,321)( 85,327)( 86,328)( 87,326)( 88,325)
( 89,331)( 90,332)( 91,330)( 92,329)( 93,335)( 94,336)( 95,334)( 96,333)
( 97,339)( 98,340)( 99,338)(100,337)(101,343)(102,344)(103,342)(104,341)
(105,347)(106,348)(107,346)(108,345)(109,351)(110,352)(111,350)(112,349)
(113,355)(114,356)(115,354)(116,353)(117,359)(118,360)(119,358)(120,357)
(121,363)(122,364)(123,362)(124,361)(125,367)(126,368)(127,366)(128,365)
(129,371)(130,372)(131,370)(132,369)(133,375)(134,376)(135,374)(136,373)
(137,379)(138,380)(139,378)(140,377)(141,383)(142,384)(143,382)(144,381)
(145,387)(146,388)(147,386)(148,385)(149,391)(150,392)(151,390)(152,389)
(153,395)(154,396)(155,394)(156,393)(157,399)(158,400)(159,398)(160,397)
(161,403)(162,404)(163,402)(164,401)(165,407)(166,408)(167,406)(168,405)
(169,411)(170,412)(171,410)(172,409)(173,415)(174,416)(175,414)(176,413)
(177,419)(178,420)(179,418)(180,417)(181,423)(182,424)(183,422)(184,421)
(185,427)(186,428)(187,426)(188,425)(189,431)(190,432)(191,430)(192,429)
(193,435)(194,436)(195,434)(196,433)(197,439)(198,440)(199,438)(200,437)
(201,443)(202,444)(203,442)(204,441)(205,447)(206,448)(207,446)(208,445)
(209,451)(210,452)(211,450)(212,449)(213,455)(214,456)(215,454)(216,453)
(217,459)(218,460)(219,458)(220,457)(221,463)(222,464)(223,462)(224,461)
(225,467)(226,468)(227,466)(228,465)(229,471)(230,472)(231,470)(232,469)
(233,475)(234,476)(235,474)(236,473)(237,479)(238,480)(239,478)(240,477);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!(  3,  4)(  5,  7)(  6,  8)(  9, 33)( 10, 34)( 11, 36)( 12, 35)
( 13, 39)( 14, 40)( 15, 37)( 16, 38)( 17, 25)( 18, 26)( 19, 28)( 20, 27)
( 21, 31)( 22, 32)( 23, 29)( 24, 30)( 41, 81)( 42, 82)( 43, 84)( 44, 83)
( 45, 87)( 46, 88)( 47, 85)( 48, 86)( 49,113)( 50,114)( 51,116)( 52,115)
( 53,119)( 54,120)( 55,117)( 56,118)( 57,105)( 58,106)( 59,108)( 60,107)
( 61,111)( 62,112)( 63,109)( 64,110)( 65, 97)( 66, 98)( 67,100)( 68, 99)
( 69,103)( 70,104)( 71,101)( 72,102)( 73, 89)( 74, 90)( 75, 92)( 76, 91)
( 77, 95)( 78, 96)( 79, 93)( 80, 94)(123,124)(125,127)(126,128)(129,153)
(130,154)(131,156)(132,155)(133,159)(134,160)(135,157)(136,158)(137,145)
(138,146)(139,148)(140,147)(141,151)(142,152)(143,149)(144,150)(161,201)
(162,202)(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,233)
(170,234)(171,236)(172,235)(173,239)(174,240)(175,237)(176,238)(177,225)
(178,226)(179,228)(180,227)(181,231)(182,232)(183,229)(184,230)(185,217)
(186,218)(187,220)(188,219)(189,223)(190,224)(191,221)(192,222)(193,209)
(194,210)(195,212)(196,211)(197,215)(198,216)(199,213)(200,214)(241,242)
(245,248)(246,247)(249,274)(250,273)(251,275)(252,276)(253,280)(254,279)
(255,278)(256,277)(257,266)(258,265)(259,267)(260,268)(261,272)(262,271)
(263,270)(264,269)(281,322)(282,321)(283,323)(284,324)(285,328)(286,327)
(287,326)(288,325)(289,354)(290,353)(291,355)(292,356)(293,360)(294,359)
(295,358)(296,357)(297,346)(298,345)(299,347)(300,348)(301,352)(302,351)
(303,350)(304,349)(305,338)(306,337)(307,339)(308,340)(309,344)(310,343)
(311,342)(312,341)(313,330)(314,329)(315,331)(316,332)(317,336)(318,335)
(319,334)(320,333)(361,362)(365,368)(366,367)(369,394)(370,393)(371,395)
(372,396)(373,400)(374,399)(375,398)(376,397)(377,386)(378,385)(379,387)
(380,388)(381,392)(382,391)(383,390)(384,389)(401,442)(402,441)(403,443)
(404,444)(405,448)(406,447)(407,446)(408,445)(409,474)(410,473)(411,475)
(412,476)(413,480)(414,479)(415,478)(416,477)(417,466)(418,465)(419,467)
(420,468)(421,472)(422,471)(423,470)(424,469)(425,458)(426,457)(427,459)
(428,460)(429,464)(430,463)(431,462)(432,461)(433,450)(434,449)(435,451)
(436,452)(437,456)(438,455)(439,454)(440,453);
s1 := Sym(480)!(  1, 49)(  2, 50)(  3, 55)(  4, 56)(  5, 54)(  6, 53)(  7, 51)
(  8, 52)(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)
( 16, 44)( 17, 73)( 18, 74)( 19, 79)( 20, 80)( 21, 78)( 22, 77)( 23, 75)
( 24, 76)( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)
( 32, 68)( 33, 57)( 34, 58)( 35, 63)( 36, 64)( 37, 62)( 38, 61)( 39, 59)
( 40, 60)( 81, 89)( 82, 90)( 83, 95)( 84, 96)( 85, 94)( 86, 93)( 87, 91)
( 88, 92)( 97,113)( 98,114)( 99,119)(100,120)(101,118)(102,117)(103,115)
(104,116)(107,111)(108,112)(109,110)(121,169)(122,170)(123,175)(124,176)
(125,174)(126,173)(127,171)(128,172)(129,161)(130,162)(131,167)(132,168)
(133,166)(134,165)(135,163)(136,164)(137,193)(138,194)(139,199)(140,200)
(141,198)(142,197)(143,195)(144,196)(145,185)(146,186)(147,191)(148,192)
(149,190)(150,189)(151,187)(152,188)(153,177)(154,178)(155,183)(156,184)
(157,182)(158,181)(159,179)(160,180)(201,209)(202,210)(203,215)(204,216)
(205,214)(206,213)(207,211)(208,212)(217,233)(218,234)(219,239)(220,240)
(221,238)(222,237)(223,235)(224,236)(227,231)(228,232)(229,230)(241,290)
(242,289)(243,296)(244,295)(245,293)(246,294)(247,292)(248,291)(249,282)
(250,281)(251,288)(252,287)(253,285)(254,286)(255,284)(256,283)(257,314)
(258,313)(259,320)(260,319)(261,317)(262,318)(263,316)(264,315)(265,306)
(266,305)(267,312)(268,311)(269,309)(270,310)(271,308)(272,307)(273,298)
(274,297)(275,304)(276,303)(277,301)(278,302)(279,300)(280,299)(321,330)
(322,329)(323,336)(324,335)(325,333)(326,334)(327,332)(328,331)(337,354)
(338,353)(339,360)(340,359)(341,357)(342,358)(343,356)(344,355)(345,346)
(347,352)(348,351)(361,410)(362,409)(363,416)(364,415)(365,413)(366,414)
(367,412)(368,411)(369,402)(370,401)(371,408)(372,407)(373,405)(374,406)
(375,404)(376,403)(377,434)(378,433)(379,440)(380,439)(381,437)(382,438)
(383,436)(384,435)(385,426)(386,425)(387,432)(388,431)(389,429)(390,430)
(391,428)(392,427)(393,418)(394,417)(395,424)(396,423)(397,421)(398,422)
(399,420)(400,419)(441,450)(442,449)(443,456)(444,455)(445,453)(446,454)
(447,452)(448,451)(457,474)(458,473)(459,480)(460,479)(461,477)(462,478)
(463,476)(464,475)(465,466)(467,472)(468,471);
s2 := Sym(480)!(  1,243)(  2,244)(  3,242)(  4,241)(  5,247)(  6,248)(  7,246)
(  8,245)(  9,251)( 10,252)( 11,250)( 12,249)( 13,255)( 14,256)( 15,254)
( 16,253)( 17,259)( 18,260)( 19,258)( 20,257)( 21,263)( 22,264)( 23,262)
( 24,261)( 25,267)( 26,268)( 27,266)( 28,265)( 29,271)( 30,272)( 31,270)
( 32,269)( 33,275)( 34,276)( 35,274)( 36,273)( 37,279)( 38,280)( 39,278)
( 40,277)( 41,283)( 42,284)( 43,282)( 44,281)( 45,287)( 46,288)( 47,286)
( 48,285)( 49,291)( 50,292)( 51,290)( 52,289)( 53,295)( 54,296)( 55,294)
( 56,293)( 57,299)( 58,300)( 59,298)( 60,297)( 61,303)( 62,304)( 63,302)
( 64,301)( 65,307)( 66,308)( 67,306)( 68,305)( 69,311)( 70,312)( 71,310)
( 72,309)( 73,315)( 74,316)( 75,314)( 76,313)( 77,319)( 78,320)( 79,318)
( 80,317)( 81,323)( 82,324)( 83,322)( 84,321)( 85,327)( 86,328)( 87,326)
( 88,325)( 89,331)( 90,332)( 91,330)( 92,329)( 93,335)( 94,336)( 95,334)
( 96,333)( 97,339)( 98,340)( 99,338)(100,337)(101,343)(102,344)(103,342)
(104,341)(105,347)(106,348)(107,346)(108,345)(109,351)(110,352)(111,350)
(112,349)(113,355)(114,356)(115,354)(116,353)(117,359)(118,360)(119,358)
(120,357)(121,363)(122,364)(123,362)(124,361)(125,367)(126,368)(127,366)
(128,365)(129,371)(130,372)(131,370)(132,369)(133,375)(134,376)(135,374)
(136,373)(137,379)(138,380)(139,378)(140,377)(141,383)(142,384)(143,382)
(144,381)(145,387)(146,388)(147,386)(148,385)(149,391)(150,392)(151,390)
(152,389)(153,395)(154,396)(155,394)(156,393)(157,399)(158,400)(159,398)
(160,397)(161,403)(162,404)(163,402)(164,401)(165,407)(166,408)(167,406)
(168,405)(169,411)(170,412)(171,410)(172,409)(173,415)(174,416)(175,414)
(176,413)(177,419)(178,420)(179,418)(180,417)(181,423)(182,424)(183,422)
(184,421)(185,427)(186,428)(187,426)(188,425)(189,431)(190,432)(191,430)
(192,429)(193,435)(194,436)(195,434)(196,433)(197,439)(198,440)(199,438)
(200,437)(201,443)(202,444)(203,442)(204,441)(205,447)(206,448)(207,446)
(208,445)(209,451)(210,452)(211,450)(212,449)(213,455)(214,456)(215,454)
(216,453)(217,459)(218,460)(219,458)(220,457)(221,463)(222,464)(223,462)
(224,461)(225,467)(226,468)(227,466)(228,465)(229,471)(230,472)(231,470)
(232,469)(233,475)(234,476)(235,474)(236,473)(237,479)(238,480)(239,478)
(240,477);
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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