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Polytope of Type {18,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6,4}*1728
if this polytope has a name.
Group : SmallGroup(1728,46114)
Rank : 4
Schlafli Type : {18,6,4}
Number of vertices, edges, etc : 18, 108, 24, 8
Order of s0s1s2s3 : 18
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 : {18,6,4}*864c
   3-fold quotients : {6,6,4}*576a
   4-fold quotients : {18,6,2}*432a
   6-fold quotients : {6,6,4}*288d
   9-fold quotients : {2,6,4}*192
   12-fold quotients : {18,2,2}*144, {6,6,2}*144a
   18-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   24-fold quotients : {9,2,2}*72
   36-fold quotients : {2,3,4}*48, {2,6,2}*48, {6,2,2}*48
   72-fold quotients : {2,3,2}*24, {3,2,2}*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, 33)( 14, 34)( 15, 35)( 16, 36)
( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)
( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 69)( 50, 70)( 51, 71)( 52, 72)
( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 61)( 58, 62)( 59, 63)( 60, 64)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85,105)( 86,106)( 87,107)( 88,108)
( 89,101)( 90,102)( 91,103)( 92,104)( 93, 97)( 94, 98)( 95, 99)( 96,100)
(113,117)(114,118)(115,119)(116,120)(121,141)(122,142)(123,143)(124,144)
(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)
(149,153)(150,154)(151,155)(152,156)(157,177)(158,178)(159,179)(160,180)
(161,173)(162,174)(163,175)(164,176)(165,169)(166,170)(167,171)(168,172)
(185,189)(186,190)(187,191)(188,192)(193,213)(194,214)(195,215)(196,216)
(197,209)(198,210)(199,211)(200,212)(201,205)(202,206)(203,207)(204,208)
(221,225)(222,226)(223,227)(224,228)(229,249)(230,250)(231,251)(232,252)
(233,245)(234,246)(235,247)(236,248)(237,241)(238,242)(239,243)(240,244)
(257,261)(258,262)(259,263)(260,264)(265,285)(266,286)(267,287)(268,288)
(269,281)(270,282)(271,283)(272,284)(273,277)(274,278)(275,279)(276,280)
(293,297)(294,298)(295,299)(296,300)(301,321)(302,322)(303,323)(304,324)
(305,317)(306,318)(307,319)(308,320)(309,313)(310,314)(311,315)(312,316)
(329,333)(330,334)(331,335)(332,336)(337,357)(338,358)(339,359)(340,360)
(341,353)(342,354)(343,355)(344,356)(345,349)(346,350)(347,351)(348,352)
(365,369)(366,370)(367,371)(368,372)(373,393)(374,394)(375,395)(376,396)
(377,389)(378,390)(379,391)(380,392)(381,385)(382,386)(383,387)(384,388)
(401,405)(402,406)(403,407)(404,408)(409,429)(410,430)(411,431)(412,432)
(413,425)(414,426)(415,427)(416,428)(417,421)(418,422)(419,423)(420,424);;
s1 := (  1, 13)(  2, 14)(  3, 16)(  4, 15)(  5, 21)(  6, 22)(  7, 24)(  8, 23)
(  9, 17)( 10, 18)( 11, 20)( 12, 19)( 25, 33)( 26, 34)( 27, 36)( 28, 35)
( 31, 32)( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 93)( 42, 94)( 43, 96)
( 44, 95)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49, 73)( 50, 74)( 51, 76)
( 52, 75)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 77)( 58, 78)( 59, 80)
( 60, 79)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)
( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)(109,121)(110,122)(111,124)
(112,123)(113,129)(114,130)(115,132)(116,131)(117,125)(118,126)(119,128)
(120,127)(133,141)(134,142)(135,144)(136,143)(139,140)(145,193)(146,194)
(147,196)(148,195)(149,201)(150,202)(151,204)(152,203)(153,197)(154,198)
(155,200)(156,199)(157,181)(158,182)(159,184)(160,183)(161,189)(162,190)
(163,192)(164,191)(165,185)(166,186)(167,188)(168,187)(169,213)(170,214)
(171,216)(172,215)(173,209)(174,210)(175,212)(176,211)(177,205)(178,206)
(179,208)(180,207)(217,229)(218,230)(219,232)(220,231)(221,237)(222,238)
(223,240)(224,239)(225,233)(226,234)(227,236)(228,235)(241,249)(242,250)
(243,252)(244,251)(247,248)(253,301)(254,302)(255,304)(256,303)(257,309)
(258,310)(259,312)(260,311)(261,305)(262,306)(263,308)(264,307)(265,289)
(266,290)(267,292)(268,291)(269,297)(270,298)(271,300)(272,299)(273,293)
(274,294)(275,296)(276,295)(277,321)(278,322)(279,324)(280,323)(281,317)
(282,318)(283,320)(284,319)(285,313)(286,314)(287,316)(288,315)(325,337)
(326,338)(327,340)(328,339)(329,345)(330,346)(331,348)(332,347)(333,341)
(334,342)(335,344)(336,343)(349,357)(350,358)(351,360)(352,359)(355,356)
(361,409)(362,410)(363,412)(364,411)(365,417)(366,418)(367,420)(368,419)
(369,413)(370,414)(371,416)(372,415)(373,397)(374,398)(375,400)(376,399)
(377,405)(378,406)(379,408)(380,407)(381,401)(382,402)(383,404)(384,403)
(385,429)(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)(392,427)
(393,421)(394,422)(395,424)(396,423);;
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)( 13,265)( 14,268)( 15,267)( 16,266)
( 17,269)( 18,272)( 19,271)( 20,270)( 21,273)( 22,276)( 23,275)( 24,274)
( 25,277)( 26,280)( 27,279)( 28,278)( 29,281)( 30,284)( 31,283)( 32,282)
( 33,285)( 34,288)( 35,287)( 36,286)( 37,217)( 38,220)( 39,219)( 40,218)
( 41,221)( 42,224)( 43,223)( 44,222)( 45,225)( 46,228)( 47,227)( 48,226)
( 49,229)( 50,232)( 51,231)( 52,230)( 53,233)( 54,236)( 55,235)( 56,234)
( 57,237)( 58,240)( 59,239)( 60,238)( 61,241)( 62,244)( 63,243)( 64,242)
( 65,245)( 66,248)( 67,247)( 68,246)( 69,249)( 70,252)( 71,251)( 72,250)
( 73,289)( 74,292)( 75,291)( 76,290)( 77,293)( 78,296)( 79,295)( 80,294)
( 81,297)( 82,300)( 83,299)( 84,298)( 85,301)( 86,304)( 87,303)( 88,302)
( 89,305)( 90,308)( 91,307)( 92,306)( 93,309)( 94,312)( 95,311)( 96,310)
( 97,313)( 98,316)( 99,315)(100,314)(101,317)(102,320)(103,319)(104,318)
(105,321)(106,324)(107,323)(108,322)(109,361)(110,364)(111,363)(112,362)
(113,365)(114,368)(115,367)(116,366)(117,369)(118,372)(119,371)(120,370)
(121,373)(122,376)(123,375)(124,374)(125,377)(126,380)(127,379)(128,378)
(129,381)(130,384)(131,383)(132,382)(133,385)(134,388)(135,387)(136,386)
(137,389)(138,392)(139,391)(140,390)(141,393)(142,396)(143,395)(144,394)
(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)(152,330)
(153,333)(154,336)(155,335)(156,334)(157,337)(158,340)(159,339)(160,338)
(161,341)(162,344)(163,343)(164,342)(165,345)(166,348)(167,347)(168,346)
(169,349)(170,352)(171,351)(172,350)(173,353)(174,356)(175,355)(176,354)
(177,357)(178,360)(179,359)(180,358)(181,397)(182,400)(183,399)(184,398)
(185,401)(186,404)(187,403)(188,402)(189,405)(190,408)(191,407)(192,406)
(193,409)(194,412)(195,411)(196,410)(197,413)(198,416)(199,415)(200,414)
(201,417)(202,420)(203,419)(204,418)(205,421)(206,424)(207,423)(208,422)
(209,425)(210,428)(211,427)(212,426)(213,429)(214,432)(215,431)(216,430);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, 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*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)!(  5,  9)(  6, 10)(  7, 11)(  8, 12)( 13, 33)( 14, 34)( 15, 35)
( 16, 36)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)
( 24, 28)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 69)( 50, 70)( 51, 71)
( 52, 72)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 61)( 58, 62)( 59, 63)
( 60, 64)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85,105)( 86,106)( 87,107)
( 88,108)( 89,101)( 90,102)( 91,103)( 92,104)( 93, 97)( 94, 98)( 95, 99)
( 96,100)(113,117)(114,118)(115,119)(116,120)(121,141)(122,142)(123,143)
(124,144)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)
(132,136)(149,153)(150,154)(151,155)(152,156)(157,177)(158,178)(159,179)
(160,180)(161,173)(162,174)(163,175)(164,176)(165,169)(166,170)(167,171)
(168,172)(185,189)(186,190)(187,191)(188,192)(193,213)(194,214)(195,215)
(196,216)(197,209)(198,210)(199,211)(200,212)(201,205)(202,206)(203,207)
(204,208)(221,225)(222,226)(223,227)(224,228)(229,249)(230,250)(231,251)
(232,252)(233,245)(234,246)(235,247)(236,248)(237,241)(238,242)(239,243)
(240,244)(257,261)(258,262)(259,263)(260,264)(265,285)(266,286)(267,287)
(268,288)(269,281)(270,282)(271,283)(272,284)(273,277)(274,278)(275,279)
(276,280)(293,297)(294,298)(295,299)(296,300)(301,321)(302,322)(303,323)
(304,324)(305,317)(306,318)(307,319)(308,320)(309,313)(310,314)(311,315)
(312,316)(329,333)(330,334)(331,335)(332,336)(337,357)(338,358)(339,359)
(340,360)(341,353)(342,354)(343,355)(344,356)(345,349)(346,350)(347,351)
(348,352)(365,369)(366,370)(367,371)(368,372)(373,393)(374,394)(375,395)
(376,396)(377,389)(378,390)(379,391)(380,392)(381,385)(382,386)(383,387)
(384,388)(401,405)(402,406)(403,407)(404,408)(409,429)(410,430)(411,431)
(412,432)(413,425)(414,426)(415,427)(416,428)(417,421)(418,422)(419,423)
(420,424);
s1 := Sym(432)!(  1, 13)(  2, 14)(  3, 16)(  4, 15)(  5, 21)(  6, 22)(  7, 24)
(  8, 23)(  9, 17)( 10, 18)( 11, 20)( 12, 19)( 25, 33)( 26, 34)( 27, 36)
( 28, 35)( 31, 32)( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 93)( 42, 94)
( 43, 96)( 44, 95)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49, 73)( 50, 74)
( 51, 76)( 52, 75)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 77)( 58, 78)
( 59, 80)( 60, 79)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)
( 67,104)( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)(109,121)(110,122)
(111,124)(112,123)(113,129)(114,130)(115,132)(116,131)(117,125)(118,126)
(119,128)(120,127)(133,141)(134,142)(135,144)(136,143)(139,140)(145,193)
(146,194)(147,196)(148,195)(149,201)(150,202)(151,204)(152,203)(153,197)
(154,198)(155,200)(156,199)(157,181)(158,182)(159,184)(160,183)(161,189)
(162,190)(163,192)(164,191)(165,185)(166,186)(167,188)(168,187)(169,213)
(170,214)(171,216)(172,215)(173,209)(174,210)(175,212)(176,211)(177,205)
(178,206)(179,208)(180,207)(217,229)(218,230)(219,232)(220,231)(221,237)
(222,238)(223,240)(224,239)(225,233)(226,234)(227,236)(228,235)(241,249)
(242,250)(243,252)(244,251)(247,248)(253,301)(254,302)(255,304)(256,303)
(257,309)(258,310)(259,312)(260,311)(261,305)(262,306)(263,308)(264,307)
(265,289)(266,290)(267,292)(268,291)(269,297)(270,298)(271,300)(272,299)
(273,293)(274,294)(275,296)(276,295)(277,321)(278,322)(279,324)(280,323)
(281,317)(282,318)(283,320)(284,319)(285,313)(286,314)(287,316)(288,315)
(325,337)(326,338)(327,340)(328,339)(329,345)(330,346)(331,348)(332,347)
(333,341)(334,342)(335,344)(336,343)(349,357)(350,358)(351,360)(352,359)
(355,356)(361,409)(362,410)(363,412)(364,411)(365,417)(366,418)(367,420)
(368,419)(369,413)(370,414)(371,416)(372,415)(373,397)(374,398)(375,400)
(376,399)(377,405)(378,406)(379,408)(380,407)(381,401)(382,402)(383,404)
(384,403)(385,429)(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)
(392,427)(393,421)(394,422)(395,424)(396,423);
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)( 13,265)( 14,268)( 15,267)
( 16,266)( 17,269)( 18,272)( 19,271)( 20,270)( 21,273)( 22,276)( 23,275)
( 24,274)( 25,277)( 26,280)( 27,279)( 28,278)( 29,281)( 30,284)( 31,283)
( 32,282)( 33,285)( 34,288)( 35,287)( 36,286)( 37,217)( 38,220)( 39,219)
( 40,218)( 41,221)( 42,224)( 43,223)( 44,222)( 45,225)( 46,228)( 47,227)
( 48,226)( 49,229)( 50,232)( 51,231)( 52,230)( 53,233)( 54,236)( 55,235)
( 56,234)( 57,237)( 58,240)( 59,239)( 60,238)( 61,241)( 62,244)( 63,243)
( 64,242)( 65,245)( 66,248)( 67,247)( 68,246)( 69,249)( 70,252)( 71,251)
( 72,250)( 73,289)( 74,292)( 75,291)( 76,290)( 77,293)( 78,296)( 79,295)
( 80,294)( 81,297)( 82,300)( 83,299)( 84,298)( 85,301)( 86,304)( 87,303)
( 88,302)( 89,305)( 90,308)( 91,307)( 92,306)( 93,309)( 94,312)( 95,311)
( 96,310)( 97,313)( 98,316)( 99,315)(100,314)(101,317)(102,320)(103,319)
(104,318)(105,321)(106,324)(107,323)(108,322)(109,361)(110,364)(111,363)
(112,362)(113,365)(114,368)(115,367)(116,366)(117,369)(118,372)(119,371)
(120,370)(121,373)(122,376)(123,375)(124,374)(125,377)(126,380)(127,379)
(128,378)(129,381)(130,384)(131,383)(132,382)(133,385)(134,388)(135,387)
(136,386)(137,389)(138,392)(139,391)(140,390)(141,393)(142,396)(143,395)
(144,394)(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)
(152,330)(153,333)(154,336)(155,335)(156,334)(157,337)(158,340)(159,339)
(160,338)(161,341)(162,344)(163,343)(164,342)(165,345)(166,348)(167,347)
(168,346)(169,349)(170,352)(171,351)(172,350)(173,353)(174,356)(175,355)
(176,354)(177,357)(178,360)(179,359)(180,358)(181,397)(182,400)(183,399)
(184,398)(185,401)(186,404)(187,403)(188,402)(189,405)(190,408)(191,407)
(192,406)(193,409)(194,412)(195,411)(196,410)(197,413)(198,416)(199,415)
(200,414)(201,417)(202,420)(203,419)(204,418)(205,421)(206,424)(207,423)
(208,422)(209,425)(210,428)(211,427)(212,426)(213,429)(214,432)(215,431)
(216,430);
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
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*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