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Polytope of Type {6,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,4}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 4
Schlafli Type : {6,6,4}
Number of vertices, edges, etc : 18, 108, 72, 8
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {6,3,4}*864, {6,6,4}*864e, {6,6,4}*864f
   3-fold quotients : {6,6,4}*576b
   4-fold quotients : {6,3,4}*432, {6,6,2}*432a
   6-fold quotients : {6,3,4}*288, {6,6,4}*288e, {6,6,4}*288f
   8-fold quotients : {6,3,2}*216
   9-fold quotients : {2,6,4}*192
   12-fold quotients : {6,3,4}*144, {6,6,2}*144b
   18-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   24-fold quotients : {6,3,2}*72
   36-fold quotients : {2,3,4}*48, {2,6,2}*48
   72-fold quotients : {2,3,2}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  5,  9)(  6, 10)(  7, 11)(  8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)
( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)
( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)
( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)
(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)
(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)
(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)
(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)
(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)
(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212)
(221,225)(222,226)(223,227)(224,228)(229,241)(230,242)(231,243)(232,244)
(233,249)(234,250)(235,251)(236,252)(237,245)(238,246)(239,247)(240,248)
(257,261)(258,262)(259,263)(260,264)(265,277)(266,278)(267,279)(268,280)
(269,285)(270,286)(271,287)(272,288)(273,281)(274,282)(275,283)(276,284)
(293,297)(294,298)(295,299)(296,300)(301,313)(302,314)(303,315)(304,316)
(305,321)(306,322)(307,323)(308,324)(309,317)(310,318)(311,319)(312,320)
(329,333)(330,334)(331,335)(332,336)(337,349)(338,350)(339,351)(340,352)
(341,357)(342,358)(343,359)(344,360)(345,353)(346,354)(347,355)(348,356)
(365,369)(366,370)(367,371)(368,372)(373,385)(374,386)(375,387)(376,388)
(377,393)(378,394)(379,395)(380,396)(381,389)(382,390)(383,391)(384,392)
(401,405)(402,406)(403,407)(404,408)(409,421)(410,422)(411,423)(412,424)
(413,429)(414,430)(415,431)(416,432)(417,425)(418,426)(419,427)(420,428);;
s1 := (  1, 13)(  2, 14)(  3, 16)(  4, 15)(  5, 17)(  6, 18)(  7, 20)(  8, 19)
(  9, 21)( 10, 22)( 11, 24)( 12, 23)( 27, 28)( 31, 32)( 35, 36)( 37, 85)
( 38, 86)( 39, 88)( 40, 87)( 41, 89)( 42, 90)( 43, 92)( 44, 91)( 45, 93)
( 46, 94)( 47, 96)( 48, 95)( 49, 73)( 50, 74)( 51, 76)( 52, 75)( 53, 77)
( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 82)( 59, 84)( 60, 83)( 61, 97)
( 62, 98)( 63,100)( 64, 99)( 65,101)( 66,102)( 67,104)( 68,103)( 69,105)
( 70,106)( 71,108)( 72,107)(109,121)(110,122)(111,124)(112,123)(113,125)
(114,126)(115,128)(116,127)(117,129)(118,130)(119,132)(120,131)(135,136)
(139,140)(143,144)(145,193)(146,194)(147,196)(148,195)(149,197)(150,198)
(151,200)(152,199)(153,201)(154,202)(155,204)(156,203)(157,181)(158,182)
(159,184)(160,183)(161,185)(162,186)(163,188)(164,187)(165,189)(166,190)
(167,192)(168,191)(169,205)(170,206)(171,208)(172,207)(173,209)(174,210)
(175,212)(176,211)(177,213)(178,214)(179,216)(180,215)(217,229)(218,230)
(219,232)(220,231)(221,233)(222,234)(223,236)(224,235)(225,237)(226,238)
(227,240)(228,239)(243,244)(247,248)(251,252)(253,301)(254,302)(255,304)
(256,303)(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)
(264,311)(265,289)(266,290)(267,292)(268,291)(269,293)(270,294)(271,296)
(272,295)(273,297)(274,298)(275,300)(276,299)(277,313)(278,314)(279,316)
(280,315)(281,317)(282,318)(283,320)(284,319)(285,321)(286,322)(287,324)
(288,323)(325,337)(326,338)(327,340)(328,339)(329,341)(330,342)(331,344)
(332,343)(333,345)(334,346)(335,348)(336,347)(351,352)(355,356)(359,360)
(361,409)(362,410)(363,412)(364,411)(365,413)(366,414)(367,416)(368,415)
(369,417)(370,418)(371,420)(372,419)(373,397)(374,398)(375,400)(376,399)
(377,401)(378,402)(379,404)(380,403)(381,405)(382,406)(383,408)(384,407)
(385,421)(386,422)(387,424)(388,423)(389,425)(390,426)(391,428)(392,427)
(393,429)(394,430)(395,432)(396,431);;
s2 := (  1,253)(  2,256)(  3,255)(  4,254)(  5,257)(  6,260)(  7,259)(  8,258)
(  9,261)( 10,264)( 11,263)( 12,262)( 13,285)( 14,288)( 15,287)( 16,286)
( 17,277)( 18,280)( 19,279)( 20,278)( 21,281)( 22,284)( 23,283)( 24,282)
( 25,269)( 26,272)( 27,271)( 28,270)( 29,273)( 30,276)( 31,275)( 32,274)
( 33,265)( 34,268)( 35,267)( 36,266)( 37,217)( 38,220)( 39,219)( 40,218)
( 41,221)( 42,224)( 43,223)( 44,222)( 45,225)( 46,228)( 47,227)( 48,226)
( 49,249)( 50,252)( 51,251)( 52,250)( 53,241)( 54,244)( 55,243)( 56,242)
( 57,245)( 58,248)( 59,247)( 60,246)( 61,233)( 62,236)( 63,235)( 64,234)
( 65,237)( 66,240)( 67,239)( 68,238)( 69,229)( 70,232)( 71,231)( 72,230)
( 73,289)( 74,292)( 75,291)( 76,290)( 77,293)( 78,296)( 79,295)( 80,294)
( 81,297)( 82,300)( 83,299)( 84,298)( 85,321)( 86,324)( 87,323)( 88,322)
( 89,313)( 90,316)( 91,315)( 92,314)( 93,317)( 94,320)( 95,319)( 96,318)
( 97,305)( 98,308)( 99,307)(100,306)(101,309)(102,312)(103,311)(104,310)
(105,301)(106,304)(107,303)(108,302)(109,361)(110,364)(111,363)(112,362)
(113,365)(114,368)(115,367)(116,366)(117,369)(118,372)(119,371)(120,370)
(121,393)(122,396)(123,395)(124,394)(125,385)(126,388)(127,387)(128,386)
(129,389)(130,392)(131,391)(132,390)(133,377)(134,380)(135,379)(136,378)
(137,381)(138,384)(139,383)(140,382)(141,373)(142,376)(143,375)(144,374)
(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)(152,330)
(153,333)(154,336)(155,335)(156,334)(157,357)(158,360)(159,359)(160,358)
(161,349)(162,352)(163,351)(164,350)(165,353)(166,356)(167,355)(168,354)
(169,341)(170,344)(171,343)(172,342)(173,345)(174,348)(175,347)(176,346)
(177,337)(178,340)(179,339)(180,338)(181,397)(182,400)(183,399)(184,398)
(185,401)(186,404)(187,403)(188,402)(189,405)(190,408)(191,407)(192,406)
(193,429)(194,432)(195,431)(196,430)(197,421)(198,424)(199,423)(200,422)
(201,425)(202,428)(203,427)(204,426)(205,413)(206,416)(207,415)(208,414)
(209,417)(210,420)(211,419)(212,418)(213,409)(214,412)(215,411)(216,410);;
s3 := (  1,110)(  2,109)(  3,112)(  4,111)(  5,114)(  6,113)(  7,116)(  8,115)
(  9,118)( 10,117)( 11,120)( 12,119)( 13,122)( 14,121)( 15,124)( 16,123)
( 17,126)( 18,125)( 19,128)( 20,127)( 21,130)( 22,129)( 23,132)( 24,131)
( 25,134)( 26,133)( 27,136)( 28,135)( 29,138)( 30,137)( 31,140)( 32,139)
( 33,142)( 34,141)( 35,144)( 36,143)( 37,146)( 38,145)( 39,148)( 40,147)
( 41,150)( 42,149)( 43,152)( 44,151)( 45,154)( 46,153)( 47,156)( 48,155)
( 49,158)( 50,157)( 51,160)( 52,159)( 53,162)( 54,161)( 55,164)( 56,163)
( 57,166)( 58,165)( 59,168)( 60,167)( 61,170)( 62,169)( 63,172)( 64,171)
( 65,174)( 66,173)( 67,176)( 68,175)( 69,178)( 70,177)( 71,180)( 72,179)
( 73,182)( 74,181)( 75,184)( 76,183)( 77,186)( 78,185)( 79,188)( 80,187)
( 81,190)( 82,189)( 83,192)( 84,191)( 85,194)( 86,193)( 87,196)( 88,195)
( 89,198)( 90,197)( 91,200)( 92,199)( 93,202)( 94,201)( 95,204)( 96,203)
( 97,206)( 98,205)( 99,208)(100,207)(101,210)(102,209)(103,212)(104,211)
(105,214)(106,213)(107,216)(108,215)(217,326)(218,325)(219,328)(220,327)
(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)(228,335)
(229,338)(230,337)(231,340)(232,339)(233,342)(234,341)(235,344)(236,343)
(237,346)(238,345)(239,348)(240,347)(241,350)(242,349)(243,352)(244,351)
(245,354)(246,353)(247,356)(248,355)(249,358)(250,357)(251,360)(252,359)
(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)(260,367)
(261,370)(262,369)(263,372)(264,371)(265,374)(266,373)(267,376)(268,375)
(269,378)(270,377)(271,380)(272,379)(273,382)(274,381)(275,384)(276,383)
(277,386)(278,385)(279,388)(280,387)(281,390)(282,389)(283,392)(284,391)
(285,394)(286,393)(287,396)(288,395)(289,398)(290,397)(291,400)(292,399)
(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)(300,407)
(301,410)(302,409)(303,412)(304,411)(305,414)(306,413)(307,416)(308,415)
(309,418)(310,417)(311,420)(312,419)(313,422)(314,421)(315,424)(316,423)
(317,426)(318,425)(319,428)(320,427)(321,430)(322,429)(323,432)(324,431);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*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, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(432)!(  5,  9)(  6, 10)(  7, 11)(  8, 12)( 13, 25)( 14, 26)( 15, 27)
( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)
( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)
( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)
( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)
( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)
(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)
(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)
(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)
(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)
(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)
(204,212)(221,225)(222,226)(223,227)(224,228)(229,241)(230,242)(231,243)
(232,244)(233,249)(234,250)(235,251)(236,252)(237,245)(238,246)(239,247)
(240,248)(257,261)(258,262)(259,263)(260,264)(265,277)(266,278)(267,279)
(268,280)(269,285)(270,286)(271,287)(272,288)(273,281)(274,282)(275,283)
(276,284)(293,297)(294,298)(295,299)(296,300)(301,313)(302,314)(303,315)
(304,316)(305,321)(306,322)(307,323)(308,324)(309,317)(310,318)(311,319)
(312,320)(329,333)(330,334)(331,335)(332,336)(337,349)(338,350)(339,351)
(340,352)(341,357)(342,358)(343,359)(344,360)(345,353)(346,354)(347,355)
(348,356)(365,369)(366,370)(367,371)(368,372)(373,385)(374,386)(375,387)
(376,388)(377,393)(378,394)(379,395)(380,396)(381,389)(382,390)(383,391)
(384,392)(401,405)(402,406)(403,407)(404,408)(409,421)(410,422)(411,423)
(412,424)(413,429)(414,430)(415,431)(416,432)(417,425)(418,426)(419,427)
(420,428);
s1 := Sym(432)!(  1, 13)(  2, 14)(  3, 16)(  4, 15)(  5, 17)(  6, 18)(  7, 20)
(  8, 19)(  9, 21)( 10, 22)( 11, 24)( 12, 23)( 27, 28)( 31, 32)( 35, 36)
( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 89)( 42, 90)( 43, 92)( 44, 91)
( 45, 93)( 46, 94)( 47, 96)( 48, 95)( 49, 73)( 50, 74)( 51, 76)( 52, 75)
( 53, 77)( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 82)( 59, 84)( 60, 83)
( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,101)( 66,102)( 67,104)( 68,103)
( 69,105)( 70,106)( 71,108)( 72,107)(109,121)(110,122)(111,124)(112,123)
(113,125)(114,126)(115,128)(116,127)(117,129)(118,130)(119,132)(120,131)
(135,136)(139,140)(143,144)(145,193)(146,194)(147,196)(148,195)(149,197)
(150,198)(151,200)(152,199)(153,201)(154,202)(155,204)(156,203)(157,181)
(158,182)(159,184)(160,183)(161,185)(162,186)(163,188)(164,187)(165,189)
(166,190)(167,192)(168,191)(169,205)(170,206)(171,208)(172,207)(173,209)
(174,210)(175,212)(176,211)(177,213)(178,214)(179,216)(180,215)(217,229)
(218,230)(219,232)(220,231)(221,233)(222,234)(223,236)(224,235)(225,237)
(226,238)(227,240)(228,239)(243,244)(247,248)(251,252)(253,301)(254,302)
(255,304)(256,303)(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)
(263,312)(264,311)(265,289)(266,290)(267,292)(268,291)(269,293)(270,294)
(271,296)(272,295)(273,297)(274,298)(275,300)(276,299)(277,313)(278,314)
(279,316)(280,315)(281,317)(282,318)(283,320)(284,319)(285,321)(286,322)
(287,324)(288,323)(325,337)(326,338)(327,340)(328,339)(329,341)(330,342)
(331,344)(332,343)(333,345)(334,346)(335,348)(336,347)(351,352)(355,356)
(359,360)(361,409)(362,410)(363,412)(364,411)(365,413)(366,414)(367,416)
(368,415)(369,417)(370,418)(371,420)(372,419)(373,397)(374,398)(375,400)
(376,399)(377,401)(378,402)(379,404)(380,403)(381,405)(382,406)(383,408)
(384,407)(385,421)(386,422)(387,424)(388,423)(389,425)(390,426)(391,428)
(392,427)(393,429)(394,430)(395,432)(396,431);
s2 := Sym(432)!(  1,253)(  2,256)(  3,255)(  4,254)(  5,257)(  6,260)(  7,259)
(  8,258)(  9,261)( 10,264)( 11,263)( 12,262)( 13,285)( 14,288)( 15,287)
( 16,286)( 17,277)( 18,280)( 19,279)( 20,278)( 21,281)( 22,284)( 23,283)
( 24,282)( 25,269)( 26,272)( 27,271)( 28,270)( 29,273)( 30,276)( 31,275)
( 32,274)( 33,265)( 34,268)( 35,267)( 36,266)( 37,217)( 38,220)( 39,219)
( 40,218)( 41,221)( 42,224)( 43,223)( 44,222)( 45,225)( 46,228)( 47,227)
( 48,226)( 49,249)( 50,252)( 51,251)( 52,250)( 53,241)( 54,244)( 55,243)
( 56,242)( 57,245)( 58,248)( 59,247)( 60,246)( 61,233)( 62,236)( 63,235)
( 64,234)( 65,237)( 66,240)( 67,239)( 68,238)( 69,229)( 70,232)( 71,231)
( 72,230)( 73,289)( 74,292)( 75,291)( 76,290)( 77,293)( 78,296)( 79,295)
( 80,294)( 81,297)( 82,300)( 83,299)( 84,298)( 85,321)( 86,324)( 87,323)
( 88,322)( 89,313)( 90,316)( 91,315)( 92,314)( 93,317)( 94,320)( 95,319)
( 96,318)( 97,305)( 98,308)( 99,307)(100,306)(101,309)(102,312)(103,311)
(104,310)(105,301)(106,304)(107,303)(108,302)(109,361)(110,364)(111,363)
(112,362)(113,365)(114,368)(115,367)(116,366)(117,369)(118,372)(119,371)
(120,370)(121,393)(122,396)(123,395)(124,394)(125,385)(126,388)(127,387)
(128,386)(129,389)(130,392)(131,391)(132,390)(133,377)(134,380)(135,379)
(136,378)(137,381)(138,384)(139,383)(140,382)(141,373)(142,376)(143,375)
(144,374)(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)
(152,330)(153,333)(154,336)(155,335)(156,334)(157,357)(158,360)(159,359)
(160,358)(161,349)(162,352)(163,351)(164,350)(165,353)(166,356)(167,355)
(168,354)(169,341)(170,344)(171,343)(172,342)(173,345)(174,348)(175,347)
(176,346)(177,337)(178,340)(179,339)(180,338)(181,397)(182,400)(183,399)
(184,398)(185,401)(186,404)(187,403)(188,402)(189,405)(190,408)(191,407)
(192,406)(193,429)(194,432)(195,431)(196,430)(197,421)(198,424)(199,423)
(200,422)(201,425)(202,428)(203,427)(204,426)(205,413)(206,416)(207,415)
(208,414)(209,417)(210,420)(211,419)(212,418)(213,409)(214,412)(215,411)
(216,410);
s3 := Sym(432)!(  1,110)(  2,109)(  3,112)(  4,111)(  5,114)(  6,113)(  7,116)
(  8,115)(  9,118)( 10,117)( 11,120)( 12,119)( 13,122)( 14,121)( 15,124)
( 16,123)( 17,126)( 18,125)( 19,128)( 20,127)( 21,130)( 22,129)( 23,132)
( 24,131)( 25,134)( 26,133)( 27,136)( 28,135)( 29,138)( 30,137)( 31,140)
( 32,139)( 33,142)( 34,141)( 35,144)( 36,143)( 37,146)( 38,145)( 39,148)
( 40,147)( 41,150)( 42,149)( 43,152)( 44,151)( 45,154)( 46,153)( 47,156)
( 48,155)( 49,158)( 50,157)( 51,160)( 52,159)( 53,162)( 54,161)( 55,164)
( 56,163)( 57,166)( 58,165)( 59,168)( 60,167)( 61,170)( 62,169)( 63,172)
( 64,171)( 65,174)( 66,173)( 67,176)( 68,175)( 69,178)( 70,177)( 71,180)
( 72,179)( 73,182)( 74,181)( 75,184)( 76,183)( 77,186)( 78,185)( 79,188)
( 80,187)( 81,190)( 82,189)( 83,192)( 84,191)( 85,194)( 86,193)( 87,196)
( 88,195)( 89,198)( 90,197)( 91,200)( 92,199)( 93,202)( 94,201)( 95,204)
( 96,203)( 97,206)( 98,205)( 99,208)(100,207)(101,210)(102,209)(103,212)
(104,211)(105,214)(106,213)(107,216)(108,215)(217,326)(218,325)(219,328)
(220,327)(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)
(228,335)(229,338)(230,337)(231,340)(232,339)(233,342)(234,341)(235,344)
(236,343)(237,346)(238,345)(239,348)(240,347)(241,350)(242,349)(243,352)
(244,351)(245,354)(246,353)(247,356)(248,355)(249,358)(250,357)(251,360)
(252,359)(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)
(260,367)(261,370)(262,369)(263,372)(264,371)(265,374)(266,373)(267,376)
(268,375)(269,378)(270,377)(271,380)(272,379)(273,382)(274,381)(275,384)
(276,383)(277,386)(278,385)(279,388)(280,387)(281,390)(282,389)(283,392)
(284,391)(285,394)(286,393)(287,396)(288,395)(289,398)(290,397)(291,400)
(292,399)(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)
(300,407)(301,410)(302,409)(303,412)(304,411)(305,414)(306,413)(307,416)
(308,415)(309,418)(310,417)(311,420)(312,419)(313,422)(314,421)(315,424)
(316,423)(317,426)(318,425)(319,428)(320,427)(321,430)(322,429)(323,432)
(324,431);
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*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, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1 >; 
 
References : None.
to this polytope