Polytope of Type {12,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,12}*1728a
if this polytope has a name.
Group : SmallGroup(1728,13967)
Rank : 4
Schlafli Type : {12,6,12}
Number of vertices, edges, etc : 12, 36, 36, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 6
Special Properties :
   Universal
   Orientable
   Flat
   Self-Dual
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 : {6,6,12}*864a, {12,6,6}*864a
   3-fold quotients : {12,2,12}*576
   4-fold quotients : {3,6,12}*432a, {12,6,3}*432a, {6,6,6}*432a
   6-fold quotients : {6,2,12}*288, {12,2,6}*288
   8-fold quotients : {3,6,6}*216a, {6,6,3}*216a
   9-fold quotients : {4,2,12}*192, {12,2,4}*192
   12-fold quotients : {3,2,12}*144, {12,2,3}*144, {6,2,6}*144
   16-fold quotients : {3,6,3}*108
   18-fold quotients : {2,2,12}*96, {12,2,2}*96, {4,2,6}*96, {6,2,4}*96
   24-fold quotients : {3,2,6}*72, {6,2,3}*72
   27-fold quotients : {4,2,4}*64
   36-fold quotients : {3,2,4}*48, {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
   48-fold quotients : {3,2,3}*36
   54-fold quotients : {2,2,4}*32, {4,2,2}*32
   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 := (  2,  3)(  5,  6)(  8,  9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)
( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)( 37, 46)
( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)( 45, 53)
( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)( 68, 78)
( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)( 91,100)
( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)( 99,107)
(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)(122,132)
(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)(145,154)
(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)(153,161)
(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)(176,186)
(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)(199,208)
(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)(207,215)
(217,244)(218,246)(219,245)(220,247)(221,249)(222,248)(223,250)(224,252)
(225,251)(226,262)(227,264)(228,263)(229,265)(230,267)(231,266)(232,268)
(233,270)(234,269)(235,253)(236,255)(237,254)(238,256)(239,258)(240,257)
(241,259)(242,261)(243,260)(271,298)(272,300)(273,299)(274,301)(275,303)
(276,302)(277,304)(278,306)(279,305)(280,316)(281,318)(282,317)(283,319)
(284,321)(285,320)(286,322)(287,324)(288,323)(289,307)(290,309)(291,308)
(292,310)(293,312)(294,311)(295,313)(296,315)(297,314)(325,352)(326,354)
(327,353)(328,355)(329,357)(330,356)(331,358)(332,360)(333,359)(334,370)
(335,372)(336,371)(337,373)(338,375)(339,374)(340,376)(341,378)(342,377)
(343,361)(344,363)(345,362)(346,364)(347,366)(348,365)(349,367)(350,369)
(351,368)(379,406)(380,408)(381,407)(382,409)(383,411)(384,410)(385,412)
(386,414)(387,413)(388,424)(389,426)(390,425)(391,427)(392,429)(393,428)
(394,430)(395,432)(396,431)(397,415)(398,417)(399,416)(400,418)(401,420)
(402,419)(403,421)(404,423)(405,422);;
s1 := (  1,226)(  2,228)(  3,227)(  4,230)(  5,229)(  6,231)(  7,234)(  8,233)
(  9,232)( 10,217)( 11,219)( 12,218)( 13,221)( 14,220)( 15,222)( 16,225)
( 17,224)( 18,223)( 19,235)( 20,237)( 21,236)( 22,239)( 23,238)( 24,240)
( 25,243)( 26,242)( 27,241)( 28,253)( 29,255)( 30,254)( 31,257)( 32,256)
( 33,258)( 34,261)( 35,260)( 36,259)( 37,244)( 38,246)( 39,245)( 40,248)
( 41,247)( 42,249)( 43,252)( 44,251)( 45,250)( 46,262)( 47,264)( 48,263)
( 49,266)( 50,265)( 51,267)( 52,270)( 53,269)( 54,268)( 55,280)( 56,282)
( 57,281)( 58,284)( 59,283)( 60,285)( 61,288)( 62,287)( 63,286)( 64,271)
( 65,273)( 66,272)( 67,275)( 68,274)( 69,276)( 70,279)( 71,278)( 72,277)
( 73,289)( 74,291)( 75,290)( 76,293)( 77,292)( 78,294)( 79,297)( 80,296)
( 81,295)( 82,307)( 83,309)( 84,308)( 85,311)( 86,310)( 87,312)( 88,315)
( 89,314)( 90,313)( 91,298)( 92,300)( 93,299)( 94,302)( 95,301)( 96,303)
( 97,306)( 98,305)( 99,304)(100,316)(101,318)(102,317)(103,320)(104,319)
(105,321)(106,324)(107,323)(108,322)(109,334)(110,336)(111,335)(112,338)
(113,337)(114,339)(115,342)(116,341)(117,340)(118,325)(119,327)(120,326)
(121,329)(122,328)(123,330)(124,333)(125,332)(126,331)(127,343)(128,345)
(129,344)(130,347)(131,346)(132,348)(133,351)(134,350)(135,349)(136,361)
(137,363)(138,362)(139,365)(140,364)(141,366)(142,369)(143,368)(144,367)
(145,352)(146,354)(147,353)(148,356)(149,355)(150,357)(151,360)(152,359)
(153,358)(154,370)(155,372)(156,371)(157,374)(158,373)(159,375)(160,378)
(161,377)(162,376)(163,388)(164,390)(165,389)(166,392)(167,391)(168,393)
(169,396)(170,395)(171,394)(172,379)(173,381)(174,380)(175,383)(176,382)
(177,384)(178,387)(179,386)(180,385)(181,397)(182,399)(183,398)(184,401)
(185,400)(186,402)(187,405)(188,404)(189,403)(190,415)(191,417)(192,416)
(193,419)(194,418)(195,420)(196,423)(197,422)(198,421)(199,406)(200,408)
(201,407)(202,410)(203,409)(204,411)(205,414)(206,413)(207,412)(208,424)
(209,426)(210,425)(211,428)(212,427)(213,429)(214,432)(215,431)(216,430);;
s2 := (  1,  4)(  2,  6)(  3,  5)(  8,  9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)
( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)( 35, 36)
( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)( 53, 54)
( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)( 65, 69)( 66, 68)( 71, 72)
( 73, 76)( 74, 78)( 75, 77)( 80, 81)( 82, 85)( 83, 87)( 84, 86)( 89, 90)
( 91, 94)( 92, 96)( 93, 95)( 98, 99)(100,103)(101,105)(102,104)(107,108)
(109,166)(110,168)(111,167)(112,163)(113,165)(114,164)(115,169)(116,171)
(117,170)(118,175)(119,177)(120,176)(121,172)(122,174)(123,173)(124,178)
(125,180)(126,179)(127,184)(128,186)(129,185)(130,181)(131,183)(132,182)
(133,187)(134,189)(135,188)(136,193)(137,195)(138,194)(139,190)(140,192)
(141,191)(142,196)(143,198)(144,197)(145,202)(146,204)(147,203)(148,199)
(149,201)(150,200)(151,205)(152,207)(153,206)(154,211)(155,213)(156,212)
(157,208)(158,210)(159,209)(160,214)(161,216)(162,215)(217,220)(218,222)
(219,221)(224,225)(226,229)(227,231)(228,230)(233,234)(235,238)(236,240)
(237,239)(242,243)(244,247)(245,249)(246,248)(251,252)(253,256)(254,258)
(255,257)(260,261)(262,265)(263,267)(264,266)(269,270)(271,274)(272,276)
(273,275)(278,279)(280,283)(281,285)(282,284)(287,288)(289,292)(290,294)
(291,293)(296,297)(298,301)(299,303)(300,302)(305,306)(307,310)(308,312)
(309,311)(314,315)(316,319)(317,321)(318,320)(323,324)(325,382)(326,384)
(327,383)(328,379)(329,381)(330,380)(331,385)(332,387)(333,386)(334,391)
(335,393)(336,392)(337,388)(338,390)(339,389)(340,394)(341,396)(342,395)
(343,400)(344,402)(345,401)(346,397)(347,399)(348,398)(349,403)(350,405)
(351,404)(352,409)(353,411)(354,410)(355,406)(356,408)(357,407)(358,412)
(359,414)(360,413)(361,418)(362,420)(363,419)(364,415)(365,417)(366,416)
(367,421)(368,423)(369,422)(370,427)(371,429)(372,428)(373,424)(374,426)
(375,425)(376,430)(377,432)(378,431);;
s3 := (  1,109)(  2,111)(  3,110)(  4,115)(  5,117)(  6,116)(  7,112)(  8,114)
(  9,113)( 10,118)( 11,120)( 12,119)( 13,124)( 14,126)( 15,125)( 16,121)
( 17,123)( 18,122)( 19,127)( 20,129)( 21,128)( 22,133)( 23,135)( 24,134)
( 25,130)( 26,132)( 27,131)( 28,136)( 29,138)( 30,137)( 31,142)( 32,144)
( 33,143)( 34,139)( 35,141)( 36,140)( 37,145)( 38,147)( 39,146)( 40,151)
( 41,153)( 42,152)( 43,148)( 44,150)( 45,149)( 46,154)( 47,156)( 48,155)
( 49,160)( 50,162)( 51,161)( 52,157)( 53,159)( 54,158)( 55,163)( 56,165)
( 57,164)( 58,169)( 59,171)( 60,170)( 61,166)( 62,168)( 63,167)( 64,172)
( 65,174)( 66,173)( 67,178)( 68,180)( 69,179)( 70,175)( 71,177)( 72,176)
( 73,181)( 74,183)( 75,182)( 76,187)( 77,189)( 78,188)( 79,184)( 80,186)
( 81,185)( 82,190)( 83,192)( 84,191)( 85,196)( 86,198)( 87,197)( 88,193)
( 89,195)( 90,194)( 91,199)( 92,201)( 93,200)( 94,205)( 95,207)( 96,206)
( 97,202)( 98,204)( 99,203)(100,208)(101,210)(102,209)(103,214)(104,216)
(105,215)(106,211)(107,213)(108,212)(217,325)(218,327)(219,326)(220,331)
(221,333)(222,332)(223,328)(224,330)(225,329)(226,334)(227,336)(228,335)
(229,340)(230,342)(231,341)(232,337)(233,339)(234,338)(235,343)(236,345)
(237,344)(238,349)(239,351)(240,350)(241,346)(242,348)(243,347)(244,352)
(245,354)(246,353)(247,358)(248,360)(249,359)(250,355)(251,357)(252,356)
(253,361)(254,363)(255,362)(256,367)(257,369)(258,368)(259,364)(260,366)
(261,365)(262,370)(263,372)(264,371)(265,376)(266,378)(267,377)(268,373)
(269,375)(270,374)(271,379)(272,381)(273,380)(274,385)(275,387)(276,386)
(277,382)(278,384)(279,383)(280,388)(281,390)(282,389)(283,394)(284,396)
(285,395)(286,391)(287,393)(288,392)(289,397)(290,399)(291,398)(292,403)
(293,405)(294,404)(295,400)(296,402)(297,401)(298,406)(299,408)(300,407)
(301,412)(302,414)(303,413)(304,409)(305,411)(306,410)(307,415)(308,417)
(309,416)(310,421)(311,423)(312,422)(313,418)(314,420)(315,419)(316,424)
(317,426)(318,425)(319,430)(320,432)(321,431)(322,427)(323,429)(324,428);;
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*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 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, 
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)!(  2,  3)(  5,  6)(  8,  9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)
( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)
( 37, 46)( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)
( 45, 53)( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)
( 68, 78)( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)
( 91,100)( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)
( 99,107)(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)
(122,132)(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)
(145,154)(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)
(153,161)(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)
(176,186)(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)
(199,208)(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)
(207,215)(217,244)(218,246)(219,245)(220,247)(221,249)(222,248)(223,250)
(224,252)(225,251)(226,262)(227,264)(228,263)(229,265)(230,267)(231,266)
(232,268)(233,270)(234,269)(235,253)(236,255)(237,254)(238,256)(239,258)
(240,257)(241,259)(242,261)(243,260)(271,298)(272,300)(273,299)(274,301)
(275,303)(276,302)(277,304)(278,306)(279,305)(280,316)(281,318)(282,317)
(283,319)(284,321)(285,320)(286,322)(287,324)(288,323)(289,307)(290,309)
(291,308)(292,310)(293,312)(294,311)(295,313)(296,315)(297,314)(325,352)
(326,354)(327,353)(328,355)(329,357)(330,356)(331,358)(332,360)(333,359)
(334,370)(335,372)(336,371)(337,373)(338,375)(339,374)(340,376)(341,378)
(342,377)(343,361)(344,363)(345,362)(346,364)(347,366)(348,365)(349,367)
(350,369)(351,368)(379,406)(380,408)(381,407)(382,409)(383,411)(384,410)
(385,412)(386,414)(387,413)(388,424)(389,426)(390,425)(391,427)(392,429)
(393,428)(394,430)(395,432)(396,431)(397,415)(398,417)(399,416)(400,418)
(401,420)(402,419)(403,421)(404,423)(405,422);
s1 := Sym(432)!(  1,226)(  2,228)(  3,227)(  4,230)(  5,229)(  6,231)(  7,234)
(  8,233)(  9,232)( 10,217)( 11,219)( 12,218)( 13,221)( 14,220)( 15,222)
( 16,225)( 17,224)( 18,223)( 19,235)( 20,237)( 21,236)( 22,239)( 23,238)
( 24,240)( 25,243)( 26,242)( 27,241)( 28,253)( 29,255)( 30,254)( 31,257)
( 32,256)( 33,258)( 34,261)( 35,260)( 36,259)( 37,244)( 38,246)( 39,245)
( 40,248)( 41,247)( 42,249)( 43,252)( 44,251)( 45,250)( 46,262)( 47,264)
( 48,263)( 49,266)( 50,265)( 51,267)( 52,270)( 53,269)( 54,268)( 55,280)
( 56,282)( 57,281)( 58,284)( 59,283)( 60,285)( 61,288)( 62,287)( 63,286)
( 64,271)( 65,273)( 66,272)( 67,275)( 68,274)( 69,276)( 70,279)( 71,278)
( 72,277)( 73,289)( 74,291)( 75,290)( 76,293)( 77,292)( 78,294)( 79,297)
( 80,296)( 81,295)( 82,307)( 83,309)( 84,308)( 85,311)( 86,310)( 87,312)
( 88,315)( 89,314)( 90,313)( 91,298)( 92,300)( 93,299)( 94,302)( 95,301)
( 96,303)( 97,306)( 98,305)( 99,304)(100,316)(101,318)(102,317)(103,320)
(104,319)(105,321)(106,324)(107,323)(108,322)(109,334)(110,336)(111,335)
(112,338)(113,337)(114,339)(115,342)(116,341)(117,340)(118,325)(119,327)
(120,326)(121,329)(122,328)(123,330)(124,333)(125,332)(126,331)(127,343)
(128,345)(129,344)(130,347)(131,346)(132,348)(133,351)(134,350)(135,349)
(136,361)(137,363)(138,362)(139,365)(140,364)(141,366)(142,369)(143,368)
(144,367)(145,352)(146,354)(147,353)(148,356)(149,355)(150,357)(151,360)
(152,359)(153,358)(154,370)(155,372)(156,371)(157,374)(158,373)(159,375)
(160,378)(161,377)(162,376)(163,388)(164,390)(165,389)(166,392)(167,391)
(168,393)(169,396)(170,395)(171,394)(172,379)(173,381)(174,380)(175,383)
(176,382)(177,384)(178,387)(179,386)(180,385)(181,397)(182,399)(183,398)
(184,401)(185,400)(186,402)(187,405)(188,404)(189,403)(190,415)(191,417)
(192,416)(193,419)(194,418)(195,420)(196,423)(197,422)(198,421)(199,406)
(200,408)(201,407)(202,410)(203,409)(204,411)(205,414)(206,413)(207,412)
(208,424)(209,426)(210,425)(211,428)(212,427)(213,429)(214,432)(215,431)
(216,430);
s2 := Sym(432)!(  1,  4)(  2,  6)(  3,  5)(  8,  9)( 10, 13)( 11, 15)( 12, 14)
( 17, 18)( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)
( 35, 36)( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)
( 53, 54)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)( 65, 69)( 66, 68)
( 71, 72)( 73, 76)( 74, 78)( 75, 77)( 80, 81)( 82, 85)( 83, 87)( 84, 86)
( 89, 90)( 91, 94)( 92, 96)( 93, 95)( 98, 99)(100,103)(101,105)(102,104)
(107,108)(109,166)(110,168)(111,167)(112,163)(113,165)(114,164)(115,169)
(116,171)(117,170)(118,175)(119,177)(120,176)(121,172)(122,174)(123,173)
(124,178)(125,180)(126,179)(127,184)(128,186)(129,185)(130,181)(131,183)
(132,182)(133,187)(134,189)(135,188)(136,193)(137,195)(138,194)(139,190)
(140,192)(141,191)(142,196)(143,198)(144,197)(145,202)(146,204)(147,203)
(148,199)(149,201)(150,200)(151,205)(152,207)(153,206)(154,211)(155,213)
(156,212)(157,208)(158,210)(159,209)(160,214)(161,216)(162,215)(217,220)
(218,222)(219,221)(224,225)(226,229)(227,231)(228,230)(233,234)(235,238)
(236,240)(237,239)(242,243)(244,247)(245,249)(246,248)(251,252)(253,256)
(254,258)(255,257)(260,261)(262,265)(263,267)(264,266)(269,270)(271,274)
(272,276)(273,275)(278,279)(280,283)(281,285)(282,284)(287,288)(289,292)
(290,294)(291,293)(296,297)(298,301)(299,303)(300,302)(305,306)(307,310)
(308,312)(309,311)(314,315)(316,319)(317,321)(318,320)(323,324)(325,382)
(326,384)(327,383)(328,379)(329,381)(330,380)(331,385)(332,387)(333,386)
(334,391)(335,393)(336,392)(337,388)(338,390)(339,389)(340,394)(341,396)
(342,395)(343,400)(344,402)(345,401)(346,397)(347,399)(348,398)(349,403)
(350,405)(351,404)(352,409)(353,411)(354,410)(355,406)(356,408)(357,407)
(358,412)(359,414)(360,413)(361,418)(362,420)(363,419)(364,415)(365,417)
(366,416)(367,421)(368,423)(369,422)(370,427)(371,429)(372,428)(373,424)
(374,426)(375,425)(376,430)(377,432)(378,431);
s3 := Sym(432)!(  1,109)(  2,111)(  3,110)(  4,115)(  5,117)(  6,116)(  7,112)
(  8,114)(  9,113)( 10,118)( 11,120)( 12,119)( 13,124)( 14,126)( 15,125)
( 16,121)( 17,123)( 18,122)( 19,127)( 20,129)( 21,128)( 22,133)( 23,135)
( 24,134)( 25,130)( 26,132)( 27,131)( 28,136)( 29,138)( 30,137)( 31,142)
( 32,144)( 33,143)( 34,139)( 35,141)( 36,140)( 37,145)( 38,147)( 39,146)
( 40,151)( 41,153)( 42,152)( 43,148)( 44,150)( 45,149)( 46,154)( 47,156)
( 48,155)( 49,160)( 50,162)( 51,161)( 52,157)( 53,159)( 54,158)( 55,163)
( 56,165)( 57,164)( 58,169)( 59,171)( 60,170)( 61,166)( 62,168)( 63,167)
( 64,172)( 65,174)( 66,173)( 67,178)( 68,180)( 69,179)( 70,175)( 71,177)
( 72,176)( 73,181)( 74,183)( 75,182)( 76,187)( 77,189)( 78,188)( 79,184)
( 80,186)( 81,185)( 82,190)( 83,192)( 84,191)( 85,196)( 86,198)( 87,197)
( 88,193)( 89,195)( 90,194)( 91,199)( 92,201)( 93,200)( 94,205)( 95,207)
( 96,206)( 97,202)( 98,204)( 99,203)(100,208)(101,210)(102,209)(103,214)
(104,216)(105,215)(106,211)(107,213)(108,212)(217,325)(218,327)(219,326)
(220,331)(221,333)(222,332)(223,328)(224,330)(225,329)(226,334)(227,336)
(228,335)(229,340)(230,342)(231,341)(232,337)(233,339)(234,338)(235,343)
(236,345)(237,344)(238,349)(239,351)(240,350)(241,346)(242,348)(243,347)
(244,352)(245,354)(246,353)(247,358)(248,360)(249,359)(250,355)(251,357)
(252,356)(253,361)(254,363)(255,362)(256,367)(257,369)(258,368)(259,364)
(260,366)(261,365)(262,370)(263,372)(264,371)(265,376)(266,378)(267,377)
(268,373)(269,375)(270,374)(271,379)(272,381)(273,380)(274,385)(275,387)
(276,386)(277,382)(278,384)(279,383)(280,388)(281,390)(282,389)(283,394)
(284,396)(285,395)(286,391)(287,393)(288,392)(289,397)(290,399)(291,398)
(292,403)(293,405)(294,404)(295,400)(296,402)(297,401)(298,406)(299,408)
(300,407)(301,412)(302,414)(303,413)(304,409)(305,411)(306,410)(307,415)
(308,417)(309,416)(310,421)(311,423)(312,422)(313,418)(314,420)(315,419)
(316,424)(317,426)(318,425)(319,430)(320,432)(321,431)(322,427)(323,429)
(324,428);
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*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
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, 
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