Polytope of Type {18,6,6}

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