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Polytope of Type {4,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,6}*1728c
if this polytope has a name.
Group : SmallGroup(1728,18160)
Rank : 4
Schlafli Type : {4,12,6}
Number of vertices, edges, etc : 4, 72, 108, 18
Order of s0s1s2s3 : 12
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 : {4,6,6}*864c, {2,12,6}*864c
   3-fold quotients : {4,12,6}*576c
   4-fold quotients : {4,6,3}*432a, {2,6,6}*432a
   6-fold quotients : {4,6,6}*288c, {2,12,6}*288c
   8-fold quotients : {2,6,3}*216
   9-fold quotients : {4,4,6}*192
   12-fold quotients : {4,6,3}*144, {2,6,6}*144b
   18-fold quotients : {2,4,6}*96a, {4,2,6}*96
   24-fold quotients : {2,6,3}*72
   27-fold quotients : {4,4,2}*64
   36-fold quotients : {4,2,3}*48, {2,2,6}*48
   54-fold quotients : {2,4,2}*32, {4,2,2}*32
   72-fold quotients : {2,2,3}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)(  8,224)
(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)( 16,232)
( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)( 40,256)
( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)( 56,272)
( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)( 96,312)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)
(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)(120,336)
(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)(128,344)
(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,352)
(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)
(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)(152,368)
(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)
(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)(168,384)
(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)(176,392)
(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)(184,400)
(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)(192,408)
(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)(200,416)
(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)(208,424)
(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)(216,432);;
s1 := (  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)
(109,163)(110,165)(111,164)(112,166)(113,168)(114,167)(115,169)(116,171)
(117,170)(118,181)(119,183)(120,182)(121,184)(122,186)(123,185)(124,187)
(125,189)(126,188)(127,172)(128,174)(129,173)(130,175)(131,177)(132,176)
(133,178)(134,180)(135,179)(136,190)(137,192)(138,191)(139,193)(140,195)
(141,194)(142,196)(143,198)(144,197)(145,208)(146,210)(147,209)(148,211)
(149,213)(150,212)(151,214)(152,216)(153,215)(154,199)(155,201)(156,200)
(157,202)(158,204)(159,203)(160,205)(161,207)(162,206)(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)(325,406)(326,408)(327,407)(328,409)
(329,411)(330,410)(331,412)(332,414)(333,413)(334,424)(335,426)(336,425)
(337,427)(338,429)(339,428)(340,430)(341,432)(342,431)(343,415)(344,417)
(345,416)(346,418)(347,420)(348,419)(349,421)(350,423)(351,422)(352,379)
(353,381)(354,380)(355,382)(356,384)(357,383)(358,385)(359,387)(360,386)
(361,397)(362,399)(363,398)(364,400)(365,402)(366,401)(367,403)(368,405)
(369,404)(370,388)(371,390)(372,389)(373,391)(374,393)(375,392)(376,394)
(377,396)(378,395);;
s2 := (  1,118)(  2,119)(  3,120)(  4,126)(  5,124)(  6,125)(  7,122)(  8,123)
(  9,121)( 10,109)( 11,110)( 12,111)( 13,117)( 14,115)( 15,116)( 16,113)
( 17,114)( 18,112)( 19,127)( 20,128)( 21,129)( 22,135)( 23,133)( 24,134)
( 25,131)( 26,132)( 27,130)( 28,145)( 29,146)( 30,147)( 31,153)( 32,151)
( 33,152)( 34,149)( 35,150)( 36,148)( 37,136)( 38,137)( 39,138)( 40,144)
( 41,142)( 42,143)( 43,140)( 44,141)( 45,139)( 46,154)( 47,155)( 48,156)
( 49,162)( 50,160)( 51,161)( 52,158)( 53,159)( 54,157)( 55,172)( 56,173)
( 57,174)( 58,180)( 59,178)( 60,179)( 61,176)( 62,177)( 63,175)( 64,163)
( 65,164)( 66,165)( 67,171)( 68,169)( 69,170)( 70,167)( 71,168)( 72,166)
( 73,181)( 74,182)( 75,183)( 76,189)( 77,187)( 78,188)( 79,185)( 80,186)
( 81,184)( 82,199)( 83,200)( 84,201)( 85,207)( 86,205)( 87,206)( 88,203)
( 89,204)( 90,202)( 91,190)( 92,191)( 93,192)( 94,198)( 95,196)( 96,197)
( 97,194)( 98,195)( 99,193)(100,208)(101,209)(102,210)(103,216)(104,214)
(105,215)(106,212)(107,213)(108,211)(217,334)(218,335)(219,336)(220,342)
(221,340)(222,341)(223,338)(224,339)(225,337)(226,325)(227,326)(228,327)
(229,333)(230,331)(231,332)(232,329)(233,330)(234,328)(235,343)(236,344)
(237,345)(238,351)(239,349)(240,350)(241,347)(242,348)(243,346)(244,361)
(245,362)(246,363)(247,369)(248,367)(249,368)(250,365)(251,366)(252,364)
(253,352)(254,353)(255,354)(256,360)(257,358)(258,359)(259,356)(260,357)
(261,355)(262,370)(263,371)(264,372)(265,378)(266,376)(267,377)(268,374)
(269,375)(270,373)(271,388)(272,389)(273,390)(274,396)(275,394)(276,395)
(277,392)(278,393)(279,391)(280,379)(281,380)(282,381)(283,387)(284,385)
(285,386)(286,383)(287,384)(288,382)(289,397)(290,398)(291,399)(292,405)
(293,403)(294,404)(295,401)(296,402)(297,400)(298,415)(299,416)(300,417)
(301,423)(302,421)(303,422)(304,419)(305,420)(306,418)(307,406)(308,407)
(309,408)(310,414)(311,412)(312,413)(313,410)(314,411)(315,409)(316,424)
(317,425)(318,426)(319,432)(320,430)(321,431)(322,428)(323,429)(324,427);;
s3 := (  1,  4)(  2,  5)(  3,  6)( 10, 22)( 11, 23)( 12, 24)( 13, 19)( 14, 20)
( 15, 21)( 16, 25)( 17, 26)( 18, 27)( 28, 31)( 29, 32)( 30, 33)( 37, 49)
( 38, 50)( 39, 51)( 40, 46)( 41, 47)( 42, 48)( 43, 52)( 44, 53)( 45, 54)
( 55, 58)( 56, 59)( 57, 60)( 64, 76)( 65, 77)( 66, 78)( 67, 73)( 68, 74)
( 69, 75)( 70, 79)( 71, 80)( 72, 81)( 82, 85)( 83, 86)( 84, 87)( 91,103)
( 92,104)( 93,105)( 94,100)( 95,101)( 96,102)( 97,106)( 98,107)( 99,108)
(109,112)(110,113)(111,114)(118,130)(119,131)(120,132)(121,127)(122,128)
(123,129)(124,133)(125,134)(126,135)(136,139)(137,140)(138,141)(145,157)
(146,158)(147,159)(148,154)(149,155)(150,156)(151,160)(152,161)(153,162)
(163,166)(164,167)(165,168)(172,184)(173,185)(174,186)(175,181)(176,182)
(177,183)(178,187)(179,188)(180,189)(190,193)(191,194)(192,195)(199,211)
(200,212)(201,213)(202,208)(203,209)(204,210)(205,214)(206,215)(207,216)
(217,220)(218,221)(219,222)(226,238)(227,239)(228,240)(229,235)(230,236)
(231,237)(232,241)(233,242)(234,243)(244,247)(245,248)(246,249)(253,265)
(254,266)(255,267)(256,262)(257,263)(258,264)(259,268)(260,269)(261,270)
(271,274)(272,275)(273,276)(280,292)(281,293)(282,294)(283,289)(284,290)
(285,291)(286,295)(287,296)(288,297)(298,301)(299,302)(300,303)(307,319)
(308,320)(309,321)(310,316)(311,317)(312,318)(313,322)(314,323)(315,324)
(325,328)(326,329)(327,330)(334,346)(335,347)(336,348)(337,343)(338,344)
(339,345)(340,349)(341,350)(342,351)(352,355)(353,356)(354,357)(361,373)
(362,374)(363,375)(364,370)(365,371)(366,372)(367,376)(368,377)(369,378)
(379,382)(380,383)(381,384)(388,400)(389,401)(390,402)(391,397)(392,398)
(393,399)(394,403)(395,404)(396,405)(406,409)(407,410)(408,411)(415,427)
(416,428)(417,429)(418,424)(419,425)(420,426)(421,430)(422,431)(423,432);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(432)!(  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)
(  8,224)(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)
( 16,232)( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)
( 40,256)( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)
( 56,272)( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)
( 96,312)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)
(112,328)(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)
(120,336)(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)
(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)
(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)
(144,360)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)
(152,368)(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)
(160,376)(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)
(168,384)(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)
(176,392)(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)
(184,400)(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)
(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)
(200,416)(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)
(208,424)(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)
(216,432);
s1 := 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)(109,163)(110,165)(111,164)(112,166)(113,168)(114,167)(115,169)
(116,171)(117,170)(118,181)(119,183)(120,182)(121,184)(122,186)(123,185)
(124,187)(125,189)(126,188)(127,172)(128,174)(129,173)(130,175)(131,177)
(132,176)(133,178)(134,180)(135,179)(136,190)(137,192)(138,191)(139,193)
(140,195)(141,194)(142,196)(143,198)(144,197)(145,208)(146,210)(147,209)
(148,211)(149,213)(150,212)(151,214)(152,216)(153,215)(154,199)(155,201)
(156,200)(157,202)(158,204)(159,203)(160,205)(161,207)(162,206)(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)(325,406)(326,408)(327,407)
(328,409)(329,411)(330,410)(331,412)(332,414)(333,413)(334,424)(335,426)
(336,425)(337,427)(338,429)(339,428)(340,430)(341,432)(342,431)(343,415)
(344,417)(345,416)(346,418)(347,420)(348,419)(349,421)(350,423)(351,422)
(352,379)(353,381)(354,380)(355,382)(356,384)(357,383)(358,385)(359,387)
(360,386)(361,397)(362,399)(363,398)(364,400)(365,402)(366,401)(367,403)
(368,405)(369,404)(370,388)(371,390)(372,389)(373,391)(374,393)(375,392)
(376,394)(377,396)(378,395);
s2 := Sym(432)!(  1,118)(  2,119)(  3,120)(  4,126)(  5,124)(  6,125)(  7,122)
(  8,123)(  9,121)( 10,109)( 11,110)( 12,111)( 13,117)( 14,115)( 15,116)
( 16,113)( 17,114)( 18,112)( 19,127)( 20,128)( 21,129)( 22,135)( 23,133)
( 24,134)( 25,131)( 26,132)( 27,130)( 28,145)( 29,146)( 30,147)( 31,153)
( 32,151)( 33,152)( 34,149)( 35,150)( 36,148)( 37,136)( 38,137)( 39,138)
( 40,144)( 41,142)( 42,143)( 43,140)( 44,141)( 45,139)( 46,154)( 47,155)
( 48,156)( 49,162)( 50,160)( 51,161)( 52,158)( 53,159)( 54,157)( 55,172)
( 56,173)( 57,174)( 58,180)( 59,178)( 60,179)( 61,176)( 62,177)( 63,175)
( 64,163)( 65,164)( 66,165)( 67,171)( 68,169)( 69,170)( 70,167)( 71,168)
( 72,166)( 73,181)( 74,182)( 75,183)( 76,189)( 77,187)( 78,188)( 79,185)
( 80,186)( 81,184)( 82,199)( 83,200)( 84,201)( 85,207)( 86,205)( 87,206)
( 88,203)( 89,204)( 90,202)( 91,190)( 92,191)( 93,192)( 94,198)( 95,196)
( 96,197)( 97,194)( 98,195)( 99,193)(100,208)(101,209)(102,210)(103,216)
(104,214)(105,215)(106,212)(107,213)(108,211)(217,334)(218,335)(219,336)
(220,342)(221,340)(222,341)(223,338)(224,339)(225,337)(226,325)(227,326)
(228,327)(229,333)(230,331)(231,332)(232,329)(233,330)(234,328)(235,343)
(236,344)(237,345)(238,351)(239,349)(240,350)(241,347)(242,348)(243,346)
(244,361)(245,362)(246,363)(247,369)(248,367)(249,368)(250,365)(251,366)
(252,364)(253,352)(254,353)(255,354)(256,360)(257,358)(258,359)(259,356)
(260,357)(261,355)(262,370)(263,371)(264,372)(265,378)(266,376)(267,377)
(268,374)(269,375)(270,373)(271,388)(272,389)(273,390)(274,396)(275,394)
(276,395)(277,392)(278,393)(279,391)(280,379)(281,380)(282,381)(283,387)
(284,385)(285,386)(286,383)(287,384)(288,382)(289,397)(290,398)(291,399)
(292,405)(293,403)(294,404)(295,401)(296,402)(297,400)(298,415)(299,416)
(300,417)(301,423)(302,421)(303,422)(304,419)(305,420)(306,418)(307,406)
(308,407)(309,408)(310,414)(311,412)(312,413)(313,410)(314,411)(315,409)
(316,424)(317,425)(318,426)(319,432)(320,430)(321,431)(322,428)(323,429)
(324,427);
s3 := Sym(432)!(  1,  4)(  2,  5)(  3,  6)( 10, 22)( 11, 23)( 12, 24)( 13, 19)
( 14, 20)( 15, 21)( 16, 25)( 17, 26)( 18, 27)( 28, 31)( 29, 32)( 30, 33)
( 37, 49)( 38, 50)( 39, 51)( 40, 46)( 41, 47)( 42, 48)( 43, 52)( 44, 53)
( 45, 54)( 55, 58)( 56, 59)( 57, 60)( 64, 76)( 65, 77)( 66, 78)( 67, 73)
( 68, 74)( 69, 75)( 70, 79)( 71, 80)( 72, 81)( 82, 85)( 83, 86)( 84, 87)
( 91,103)( 92,104)( 93,105)( 94,100)( 95,101)( 96,102)( 97,106)( 98,107)
( 99,108)(109,112)(110,113)(111,114)(118,130)(119,131)(120,132)(121,127)
(122,128)(123,129)(124,133)(125,134)(126,135)(136,139)(137,140)(138,141)
(145,157)(146,158)(147,159)(148,154)(149,155)(150,156)(151,160)(152,161)
(153,162)(163,166)(164,167)(165,168)(172,184)(173,185)(174,186)(175,181)
(176,182)(177,183)(178,187)(179,188)(180,189)(190,193)(191,194)(192,195)
(199,211)(200,212)(201,213)(202,208)(203,209)(204,210)(205,214)(206,215)
(207,216)(217,220)(218,221)(219,222)(226,238)(227,239)(228,240)(229,235)
(230,236)(231,237)(232,241)(233,242)(234,243)(244,247)(245,248)(246,249)
(253,265)(254,266)(255,267)(256,262)(257,263)(258,264)(259,268)(260,269)
(261,270)(271,274)(272,275)(273,276)(280,292)(281,293)(282,294)(283,289)
(284,290)(285,291)(286,295)(287,296)(288,297)(298,301)(299,302)(300,303)
(307,319)(308,320)(309,321)(310,316)(311,317)(312,318)(313,322)(314,323)
(315,324)(325,328)(326,329)(327,330)(334,346)(335,347)(336,348)(337,343)
(338,344)(339,345)(340,349)(341,350)(342,351)(352,355)(353,356)(354,357)
(361,373)(362,374)(363,375)(364,370)(365,371)(366,372)(367,376)(368,377)
(369,378)(379,382)(380,383)(381,384)(388,400)(389,401)(390,402)(391,397)
(392,398)(393,399)(394,403)(395,404)(396,405)(406,409)(407,410)(408,411)
(415,427)(416,428)(417,429)(418,424)(419,425)(420,426)(421,430)(422,431)
(423,432);
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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2 >; 
 
References : None.
to this polytope