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Polytope of Type {6,4,18}

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