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Polytope of Type {36,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,6,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,16621)
Rank : 4
Schlafli Type : {36,6,4}
Number of vertices, edges, etc : 36, 108, 12, 4
Order of s0s1s2s3 : 36
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 : {36,6,2}*864b, {18,6,4}*864b
   3-fold quotients : {36,2,4}*576, {12,6,4}*576b
   4-fold quotients : {9,6,4}*432, {18,6,2}*432b
   6-fold quotients : {36,2,2}*288, {18,2,4}*288, {12,6,2}*288b, {6,6,4}*288c
   8-fold quotients : {9,6,2}*216
   9-fold quotients : {12,2,4}*192
   12-fold quotients : {9,2,4}*144, {18,2,2}*144, {3,6,4}*144, {6,6,2}*144c
   18-fold quotients : {12,2,2}*96, {6,2,4}*96
   24-fold quotients : {9,2,2}*72, {3,6,2}*72
   27-fold quotients : {4,2,4}*64
   36-fold quotients : {3,2,4}*48, {6,2,2}*48
   54-fold quotients : {2,2,4}*32, {4,2,2}*32
   72-fold quotients : {3,2,2}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  3)(  4,  9)(  5,  8)(  6,  7)( 10, 19)( 11, 21)( 12, 20)( 13, 27)
( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 36)( 32, 35)
( 33, 34)( 37, 46)( 38, 48)( 39, 47)( 40, 54)( 41, 53)( 42, 52)( 43, 51)
( 44, 50)( 45, 49)( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 64, 73)( 65, 75)
( 66, 74)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 83, 84)
( 85, 90)( 86, 89)( 87, 88)( 91,100)( 92,102)( 93,101)( 94,108)( 95,107)
( 96,106)( 97,105)( 98,104)( 99,103)(109,163)(110,165)(111,164)(112,171)
(113,170)(114,169)(115,168)(116,167)(117,166)(118,181)(119,183)(120,182)
(121,189)(122,188)(123,187)(124,186)(125,185)(126,184)(127,172)(128,174)
(129,173)(130,180)(131,179)(132,178)(133,177)(134,176)(135,175)(136,190)
(137,192)(138,191)(139,198)(140,197)(141,196)(142,195)(143,194)(144,193)
(145,208)(146,210)(147,209)(148,216)(149,215)(150,214)(151,213)(152,212)
(153,211)(154,199)(155,201)(156,200)(157,207)(158,206)(159,205)(160,204)
(161,203)(162,202)(218,219)(220,225)(221,224)(222,223)(226,235)(227,237)
(228,236)(229,243)(230,242)(231,241)(232,240)(233,239)(234,238)(245,246)
(247,252)(248,251)(249,250)(253,262)(254,264)(255,263)(256,270)(257,269)
(258,268)(259,267)(260,266)(261,265)(272,273)(274,279)(275,278)(276,277)
(280,289)(281,291)(282,290)(283,297)(284,296)(285,295)(286,294)(287,293)
(288,292)(299,300)(301,306)(302,305)(303,304)(307,316)(308,318)(309,317)
(310,324)(311,323)(312,322)(313,321)(314,320)(315,319)(325,379)(326,381)
(327,380)(328,387)(329,386)(330,385)(331,384)(332,383)(333,382)(334,397)
(335,399)(336,398)(337,405)(338,404)(339,403)(340,402)(341,401)(342,400)
(343,388)(344,390)(345,389)(346,396)(347,395)(348,394)(349,393)(350,392)
(351,391)(352,406)(353,408)(354,407)(355,414)(356,413)(357,412)(358,411)
(359,410)(360,409)(361,424)(362,426)(363,425)(364,432)(365,431)(366,430)
(367,429)(368,428)(369,427)(370,415)(371,417)(372,416)(373,423)(374,422)
(375,421)(376,420)(377,419)(378,418);;
s1 := (  1,121)(  2,123)(  3,122)(  4,118)(  5,120)(  6,119)(  7,126)(  8,125)
(  9,124)( 10,112)( 11,114)( 12,113)( 13,109)( 14,111)( 15,110)( 16,117)
( 17,116)( 18,115)( 19,130)( 20,132)( 21,131)( 22,127)( 23,129)( 24,128)
( 25,135)( 26,134)( 27,133)( 28,148)( 29,150)( 30,149)( 31,145)( 32,147)
( 33,146)( 34,153)( 35,152)( 36,151)( 37,139)( 38,141)( 39,140)( 40,136)
( 41,138)( 42,137)( 43,144)( 44,143)( 45,142)( 46,157)( 47,159)( 48,158)
( 49,154)( 50,156)( 51,155)( 52,162)( 53,161)( 54,160)( 55,175)( 56,177)
( 57,176)( 58,172)( 59,174)( 60,173)( 61,180)( 62,179)( 63,178)( 64,166)
( 65,168)( 66,167)( 67,163)( 68,165)( 69,164)( 70,171)( 71,170)( 72,169)
( 73,184)( 74,186)( 75,185)( 76,181)( 77,183)( 78,182)( 79,189)( 80,188)
( 81,187)( 82,202)( 83,204)( 84,203)( 85,199)( 86,201)( 87,200)( 88,207)
( 89,206)( 90,205)( 91,193)( 92,195)( 93,194)( 94,190)( 95,192)( 96,191)
( 97,198)( 98,197)( 99,196)(100,211)(101,213)(102,212)(103,208)(104,210)
(105,209)(106,216)(107,215)(108,214)(217,337)(218,339)(219,338)(220,334)
(221,336)(222,335)(223,342)(224,341)(225,340)(226,328)(227,330)(228,329)
(229,325)(230,327)(231,326)(232,333)(233,332)(234,331)(235,346)(236,348)
(237,347)(238,343)(239,345)(240,344)(241,351)(242,350)(243,349)(244,364)
(245,366)(246,365)(247,361)(248,363)(249,362)(250,369)(251,368)(252,367)
(253,355)(254,357)(255,356)(256,352)(257,354)(258,353)(259,360)(260,359)
(261,358)(262,373)(263,375)(264,374)(265,370)(266,372)(267,371)(268,378)
(269,377)(270,376)(271,391)(272,393)(273,392)(274,388)(275,390)(276,389)
(277,396)(278,395)(279,394)(280,382)(281,384)(282,383)(283,379)(284,381)
(285,380)(286,387)(287,386)(288,385)(289,400)(290,402)(291,401)(292,397)
(293,399)(294,398)(295,405)(296,404)(297,403)(298,418)(299,420)(300,419)
(301,415)(302,417)(303,416)(304,423)(305,422)(306,421)(307,409)(308,411)
(309,410)(310,406)(311,408)(312,407)(313,414)(314,413)(315,412)(316,427)
(317,429)(318,428)(319,424)(320,426)(321,425)(322,432)(323,431)(324,430);;
s2 := ( 10, 19)( 11, 20)( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)( 17, 26)
( 18, 27)( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)
( 44, 53)( 45, 54)( 64, 73)( 65, 74)( 66, 75)( 67, 76)( 68, 77)( 69, 78)
( 70, 79)( 71, 80)( 72, 81)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)
( 96,105)( 97,106)( 98,107)( 99,108)(118,127)(119,128)(120,129)(121,130)
(122,131)(123,132)(124,133)(125,134)(126,135)(145,154)(146,155)(147,156)
(148,157)(149,158)(150,159)(151,160)(152,161)(153,162)(172,181)(173,182)
(174,183)(175,184)(176,185)(177,186)(178,187)(179,188)(180,189)(199,208)
(200,209)(201,210)(202,211)(203,212)(204,213)(205,214)(206,215)(207,216)
(217,244)(218,245)(219,246)(220,247)(221,248)(222,249)(223,250)(224,251)
(225,252)(226,262)(227,263)(228,264)(229,265)(230,266)(231,267)(232,268)
(233,269)(234,270)(235,253)(236,254)(237,255)(238,256)(239,257)(240,258)
(241,259)(242,260)(243,261)(271,298)(272,299)(273,300)(274,301)(275,302)
(276,303)(277,304)(278,305)(279,306)(280,316)(281,317)(282,318)(283,319)
(284,320)(285,321)(286,322)(287,323)(288,324)(289,307)(290,308)(291,309)
(292,310)(293,311)(294,312)(295,313)(296,314)(297,315)(325,352)(326,353)
(327,354)(328,355)(329,356)(330,357)(331,358)(332,359)(333,360)(334,370)
(335,371)(336,372)(337,373)(338,374)(339,375)(340,376)(341,377)(342,378)
(343,361)(344,362)(345,363)(346,364)(347,365)(348,366)(349,367)(350,368)
(351,369)(379,406)(380,407)(381,408)(382,409)(383,410)(384,411)(385,412)
(386,413)(387,414)(388,424)(389,425)(390,426)(391,427)(392,428)(393,429)
(394,430)(395,431)(396,432)(397,415)(398,416)(399,417)(400,418)(401,419)
(402,420)(403,421)(404,422)(405,423);;
s3 := (  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)(  8,224)
(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)( 16,232)
( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)( 40,256)
( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)( 56,272)
( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)( 96,312)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)
(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)(120,336)
(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)(128,344)
(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,352)
(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)
(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)(152,368)
(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)
(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)(168,384)
(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)(176,392)
(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)(184,400)
(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)(192,408)
(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)(200,416)
(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)(208,424)
(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)(216,432);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(432)!(  2,  3)(  4,  9)(  5,  8)(  6,  7)( 10, 19)( 11, 21)( 12, 20)
( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 36)
( 32, 35)( 33, 34)( 37, 46)( 38, 48)( 39, 47)( 40, 54)( 41, 53)( 42, 52)
( 43, 51)( 44, 50)( 45, 49)( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 64, 73)
( 65, 75)( 66, 74)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)
( 83, 84)( 85, 90)( 86, 89)( 87, 88)( 91,100)( 92,102)( 93,101)( 94,108)
( 95,107)( 96,106)( 97,105)( 98,104)( 99,103)(109,163)(110,165)(111,164)
(112,171)(113,170)(114,169)(115,168)(116,167)(117,166)(118,181)(119,183)
(120,182)(121,189)(122,188)(123,187)(124,186)(125,185)(126,184)(127,172)
(128,174)(129,173)(130,180)(131,179)(132,178)(133,177)(134,176)(135,175)
(136,190)(137,192)(138,191)(139,198)(140,197)(141,196)(142,195)(143,194)
(144,193)(145,208)(146,210)(147,209)(148,216)(149,215)(150,214)(151,213)
(152,212)(153,211)(154,199)(155,201)(156,200)(157,207)(158,206)(159,205)
(160,204)(161,203)(162,202)(218,219)(220,225)(221,224)(222,223)(226,235)
(227,237)(228,236)(229,243)(230,242)(231,241)(232,240)(233,239)(234,238)
(245,246)(247,252)(248,251)(249,250)(253,262)(254,264)(255,263)(256,270)
(257,269)(258,268)(259,267)(260,266)(261,265)(272,273)(274,279)(275,278)
(276,277)(280,289)(281,291)(282,290)(283,297)(284,296)(285,295)(286,294)
(287,293)(288,292)(299,300)(301,306)(302,305)(303,304)(307,316)(308,318)
(309,317)(310,324)(311,323)(312,322)(313,321)(314,320)(315,319)(325,379)
(326,381)(327,380)(328,387)(329,386)(330,385)(331,384)(332,383)(333,382)
(334,397)(335,399)(336,398)(337,405)(338,404)(339,403)(340,402)(341,401)
(342,400)(343,388)(344,390)(345,389)(346,396)(347,395)(348,394)(349,393)
(350,392)(351,391)(352,406)(353,408)(354,407)(355,414)(356,413)(357,412)
(358,411)(359,410)(360,409)(361,424)(362,426)(363,425)(364,432)(365,431)
(366,430)(367,429)(368,428)(369,427)(370,415)(371,417)(372,416)(373,423)
(374,422)(375,421)(376,420)(377,419)(378,418);
s1 := Sym(432)!(  1,121)(  2,123)(  3,122)(  4,118)(  5,120)(  6,119)(  7,126)
(  8,125)(  9,124)( 10,112)( 11,114)( 12,113)( 13,109)( 14,111)( 15,110)
( 16,117)( 17,116)( 18,115)( 19,130)( 20,132)( 21,131)( 22,127)( 23,129)
( 24,128)( 25,135)( 26,134)( 27,133)( 28,148)( 29,150)( 30,149)( 31,145)
( 32,147)( 33,146)( 34,153)( 35,152)( 36,151)( 37,139)( 38,141)( 39,140)
( 40,136)( 41,138)( 42,137)( 43,144)( 44,143)( 45,142)( 46,157)( 47,159)
( 48,158)( 49,154)( 50,156)( 51,155)( 52,162)( 53,161)( 54,160)( 55,175)
( 56,177)( 57,176)( 58,172)( 59,174)( 60,173)( 61,180)( 62,179)( 63,178)
( 64,166)( 65,168)( 66,167)( 67,163)( 68,165)( 69,164)( 70,171)( 71,170)
( 72,169)( 73,184)( 74,186)( 75,185)( 76,181)( 77,183)( 78,182)( 79,189)
( 80,188)( 81,187)( 82,202)( 83,204)( 84,203)( 85,199)( 86,201)( 87,200)
( 88,207)( 89,206)( 90,205)( 91,193)( 92,195)( 93,194)( 94,190)( 95,192)
( 96,191)( 97,198)( 98,197)( 99,196)(100,211)(101,213)(102,212)(103,208)
(104,210)(105,209)(106,216)(107,215)(108,214)(217,337)(218,339)(219,338)
(220,334)(221,336)(222,335)(223,342)(224,341)(225,340)(226,328)(227,330)
(228,329)(229,325)(230,327)(231,326)(232,333)(233,332)(234,331)(235,346)
(236,348)(237,347)(238,343)(239,345)(240,344)(241,351)(242,350)(243,349)
(244,364)(245,366)(246,365)(247,361)(248,363)(249,362)(250,369)(251,368)
(252,367)(253,355)(254,357)(255,356)(256,352)(257,354)(258,353)(259,360)
(260,359)(261,358)(262,373)(263,375)(264,374)(265,370)(266,372)(267,371)
(268,378)(269,377)(270,376)(271,391)(272,393)(273,392)(274,388)(275,390)
(276,389)(277,396)(278,395)(279,394)(280,382)(281,384)(282,383)(283,379)
(284,381)(285,380)(286,387)(287,386)(288,385)(289,400)(290,402)(291,401)
(292,397)(293,399)(294,398)(295,405)(296,404)(297,403)(298,418)(299,420)
(300,419)(301,415)(302,417)(303,416)(304,423)(305,422)(306,421)(307,409)
(308,411)(309,410)(310,406)(311,408)(312,407)(313,414)(314,413)(315,412)
(316,427)(317,429)(318,428)(319,424)(320,426)(321,425)(322,432)(323,431)
(324,430);
s2 := Sym(432)!( 10, 19)( 11, 20)( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)
( 17, 26)( 18, 27)( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)
( 43, 52)( 44, 53)( 45, 54)( 64, 73)( 65, 74)( 66, 75)( 67, 76)( 68, 77)
( 69, 78)( 70, 79)( 71, 80)( 72, 81)( 91,100)( 92,101)( 93,102)( 94,103)
( 95,104)( 96,105)( 97,106)( 98,107)( 99,108)(118,127)(119,128)(120,129)
(121,130)(122,131)(123,132)(124,133)(125,134)(126,135)(145,154)(146,155)
(147,156)(148,157)(149,158)(150,159)(151,160)(152,161)(153,162)(172,181)
(173,182)(174,183)(175,184)(176,185)(177,186)(178,187)(179,188)(180,189)
(199,208)(200,209)(201,210)(202,211)(203,212)(204,213)(205,214)(206,215)
(207,216)(217,244)(218,245)(219,246)(220,247)(221,248)(222,249)(223,250)
(224,251)(225,252)(226,262)(227,263)(228,264)(229,265)(230,266)(231,267)
(232,268)(233,269)(234,270)(235,253)(236,254)(237,255)(238,256)(239,257)
(240,258)(241,259)(242,260)(243,261)(271,298)(272,299)(273,300)(274,301)
(275,302)(276,303)(277,304)(278,305)(279,306)(280,316)(281,317)(282,318)
(283,319)(284,320)(285,321)(286,322)(287,323)(288,324)(289,307)(290,308)
(291,309)(292,310)(293,311)(294,312)(295,313)(296,314)(297,315)(325,352)
(326,353)(327,354)(328,355)(329,356)(330,357)(331,358)(332,359)(333,360)
(334,370)(335,371)(336,372)(337,373)(338,374)(339,375)(340,376)(341,377)
(342,378)(343,361)(344,362)(345,363)(346,364)(347,365)(348,366)(349,367)
(350,368)(351,369)(379,406)(380,407)(381,408)(382,409)(383,410)(384,411)
(385,412)(386,413)(387,414)(388,424)(389,425)(390,426)(391,427)(392,428)
(393,429)(394,430)(395,431)(396,432)(397,415)(398,416)(399,417)(400,418)
(401,419)(402,420)(403,421)(404,422)(405,423);
s3 := Sym(432)!(  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)
(  8,224)(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)
( 16,232)( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)
( 40,256)( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)
( 56,272)( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)
( 96,312)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)
(112,328)(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)
(120,336)(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)
(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)
(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)
(144,360)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)
(152,368)(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)
(160,376)(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)
(168,384)(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)
(176,392)(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)
(184,400)(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)
(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)
(200,416)(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)
(208,424)(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)
(216,432);
poly := sub<Sym(432)|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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope