Polytope of Type {2,12,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6,6}*1728e
if this polytope has a name.
Group : SmallGroup(1728,47394)
Rank : 5
Schlafli Type : {2,12,6,6}
Number of vertices, edges, etc : 2, 12, 36, 18, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   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 : {2,12,6,3}*864b, {2,6,6,6}*864c
   3-fold quotients : {2,12,2,6}*576, {2,4,6,6}*576c
   4-fold quotients : {2,6,6,3}*432b
   6-fold quotients : {2,12,2,3}*288, {2,4,6,3}*288, {2,2,6,6}*288b, {2,6,2,6}*288
   9-fold quotients : {2,12,2,2}*192, {2,4,2,6}*192
   12-fold quotients : {2,2,6,3}*144, {2,3,2,6}*144, {2,6,2,3}*144
   18-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96, {2,6,2,2}*96
   24-fold quotients : {2,3,2,3}*72
   27-fold quotients : {2,4,2,2}*64
   36-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (1,2);;
s1 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)( 49, 50)
( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)
( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)( 97, 98)
(100,101)(103,104)(106,107)(109,110)(111,138)(112,140)(113,139)(114,141)
(115,143)(116,142)(117,144)(118,146)(119,145)(120,147)(121,149)(122,148)
(123,150)(124,152)(125,151)(126,153)(127,155)(128,154)(129,156)(130,158)
(131,157)(132,159)(133,161)(134,160)(135,162)(136,164)(137,163)(165,192)
(166,194)(167,193)(168,195)(169,197)(170,196)(171,198)(172,200)(173,199)
(174,201)(175,203)(176,202)(177,204)(178,206)(179,205)(180,207)(181,209)
(182,208)(183,210)(184,212)(185,211)(186,213)(187,215)(188,214)(189,216)
(190,218)(191,217)(219,246)(220,248)(221,247)(222,249)(223,251)(224,250)
(225,252)(226,254)(227,253)(228,255)(229,257)(230,256)(231,258)(232,260)
(233,259)(234,261)(235,263)(236,262)(237,264)(238,266)(239,265)(240,267)
(241,269)(242,268)(243,270)(244,272)(245,271)(273,300)(274,302)(275,301)
(276,303)(277,305)(278,304)(279,306)(280,308)(281,307)(282,309)(283,311)
(284,310)(285,312)(286,314)(287,313)(288,315)(289,317)(290,316)(291,318)
(292,320)(293,319)(294,321)(295,323)(296,322)(297,324)(298,326)(299,325)
(328,329)(331,332)(334,335)(337,338)(340,341)(343,344)(346,347)(349,350)
(352,353)(355,356)(358,359)(361,362)(364,365)(367,368)(370,371)(373,374)
(376,377)(379,380)(382,383)(385,386)(388,389)(391,392)(394,395)(397,398)
(400,401)(403,404)(406,407)(409,410)(412,413)(415,416)(418,419)(421,422)
(424,425)(427,428)(430,431)(433,434);;
s2 := (  3,220)(  4,219)(  5,221)(  6,226)(  7,225)(  8,227)(  9,223)( 10,222)
( 11,224)( 12,229)( 13,228)( 14,230)( 15,235)( 16,234)( 17,236)( 18,232)
( 19,231)( 20,233)( 21,238)( 22,237)( 23,239)( 24,244)( 25,243)( 26,245)
( 27,241)( 28,240)( 29,242)( 30,247)( 31,246)( 32,248)( 33,253)( 34,252)
( 35,254)( 36,250)( 37,249)( 38,251)( 39,256)( 40,255)( 41,257)( 42,262)
( 43,261)( 44,263)( 45,259)( 46,258)( 47,260)( 48,265)( 49,264)( 50,266)
( 51,271)( 52,270)( 53,272)( 54,268)( 55,267)( 56,269)( 57,274)( 58,273)
( 59,275)( 60,280)( 61,279)( 62,281)( 63,277)( 64,276)( 65,278)( 66,283)
( 67,282)( 68,284)( 69,289)( 70,288)( 71,290)( 72,286)( 73,285)( 74,287)
( 75,292)( 76,291)( 77,293)( 78,298)( 79,297)( 80,299)( 81,295)( 82,294)
( 83,296)( 84,301)( 85,300)( 86,302)( 87,307)( 88,306)( 89,308)( 90,304)
( 91,303)( 92,305)( 93,310)( 94,309)( 95,311)( 96,316)( 97,315)( 98,317)
( 99,313)(100,312)(101,314)(102,319)(103,318)(104,320)(105,325)(106,324)
(107,326)(108,322)(109,321)(110,323)(111,355)(112,354)(113,356)(114,361)
(115,360)(116,362)(117,358)(118,357)(119,359)(120,364)(121,363)(122,365)
(123,370)(124,369)(125,371)(126,367)(127,366)(128,368)(129,373)(130,372)
(131,374)(132,379)(133,378)(134,380)(135,376)(136,375)(137,377)(138,328)
(139,327)(140,329)(141,334)(142,333)(143,335)(144,331)(145,330)(146,332)
(147,337)(148,336)(149,338)(150,343)(151,342)(152,344)(153,340)(154,339)
(155,341)(156,346)(157,345)(158,347)(159,352)(160,351)(161,353)(162,349)
(163,348)(164,350)(165,409)(166,408)(167,410)(168,415)(169,414)(170,416)
(171,412)(172,411)(173,413)(174,418)(175,417)(176,419)(177,424)(178,423)
(179,425)(180,421)(181,420)(182,422)(183,427)(184,426)(185,428)(186,433)
(187,432)(188,434)(189,430)(190,429)(191,431)(192,382)(193,381)(194,383)
(195,388)(196,387)(197,389)(198,385)(199,384)(200,386)(201,391)(202,390)
(203,392)(204,397)(205,396)(206,398)(207,394)(208,393)(209,395)(210,400)
(211,399)(212,401)(213,406)(214,405)(215,407)(216,403)(217,402)(218,404);;
s3 := (  3,330)(  4,331)(  5,332)(  6,327)(  7,328)(  8,329)(  9,333)( 10,334)
( 11,335)( 12,348)( 13,349)( 14,350)( 15,345)( 16,346)( 17,347)( 18,351)
( 19,352)( 20,353)( 21,339)( 22,340)( 23,341)( 24,336)( 25,337)( 26,338)
( 27,342)( 28,343)( 29,344)( 30,357)( 31,358)( 32,359)( 33,354)( 34,355)
( 35,356)( 36,360)( 37,361)( 38,362)( 39,375)( 40,376)( 41,377)( 42,372)
( 43,373)( 44,374)( 45,378)( 46,379)( 47,380)( 48,366)( 49,367)( 50,368)
( 51,363)( 52,364)( 53,365)( 54,369)( 55,370)( 56,371)( 57,384)( 58,385)
( 59,386)( 60,381)( 61,382)( 62,383)( 63,387)( 64,388)( 65,389)( 66,402)
( 67,403)( 68,404)( 69,399)( 70,400)( 71,401)( 72,405)( 73,406)( 74,407)
( 75,393)( 76,394)( 77,395)( 78,390)( 79,391)( 80,392)( 81,396)( 82,397)
( 83,398)( 84,411)( 85,412)( 86,413)( 87,408)( 88,409)( 89,410)( 90,414)
( 91,415)( 92,416)( 93,429)( 94,430)( 95,431)( 96,426)( 97,427)( 98,428)
( 99,432)(100,433)(101,434)(102,420)(103,421)(104,422)(105,417)(106,418)
(107,419)(108,423)(109,424)(110,425)(111,249)(112,250)(113,251)(114,246)
(115,247)(116,248)(117,252)(118,253)(119,254)(120,267)(121,268)(122,269)
(123,264)(124,265)(125,266)(126,270)(127,271)(128,272)(129,258)(130,259)
(131,260)(132,255)(133,256)(134,257)(135,261)(136,262)(137,263)(138,222)
(139,223)(140,224)(141,219)(142,220)(143,221)(144,225)(145,226)(146,227)
(147,240)(148,241)(149,242)(150,237)(151,238)(152,239)(153,243)(154,244)
(155,245)(156,231)(157,232)(158,233)(159,228)(160,229)(161,230)(162,234)
(163,235)(164,236)(165,303)(166,304)(167,305)(168,300)(169,301)(170,302)
(171,306)(172,307)(173,308)(174,321)(175,322)(176,323)(177,318)(178,319)
(179,320)(180,324)(181,325)(182,326)(183,312)(184,313)(185,314)(186,309)
(187,310)(188,311)(189,315)(190,316)(191,317)(192,276)(193,277)(194,278)
(195,273)(196,274)(197,275)(198,279)(199,280)(200,281)(201,294)(202,295)
(203,296)(204,291)(205,292)(206,293)(207,297)(208,298)(209,299)(210,285)
(211,286)(212,287)(213,282)(214,283)(215,284)(216,288)(217,289)(218,290);;
s4 := (  3,390)(  4,391)(  5,392)(  6,396)(  7,397)(  8,398)(  9,393)( 10,394)
( 11,395)( 12,381)( 13,382)( 14,383)( 15,387)( 16,388)( 17,389)( 18,384)
( 19,385)( 20,386)( 21,399)( 22,400)( 23,401)( 24,405)( 25,406)( 26,407)
( 27,402)( 28,403)( 29,404)( 30,417)( 31,418)( 32,419)( 33,423)( 34,424)
( 35,425)( 36,420)( 37,421)( 38,422)( 39,408)( 40,409)( 41,410)( 42,414)
( 43,415)( 44,416)( 45,411)( 46,412)( 47,413)( 48,426)( 49,427)( 50,428)
( 51,432)( 52,433)( 53,434)( 54,429)( 55,430)( 56,431)( 57,336)( 58,337)
( 59,338)( 60,342)( 61,343)( 62,344)( 63,339)( 64,340)( 65,341)( 66,327)
( 67,328)( 68,329)( 69,333)( 70,334)( 71,335)( 72,330)( 73,331)( 74,332)
( 75,345)( 76,346)( 77,347)( 78,351)( 79,352)( 80,353)( 81,348)( 82,349)
( 83,350)( 84,363)( 85,364)( 86,365)( 87,369)( 88,370)( 89,371)( 90,366)
( 91,367)( 92,368)( 93,354)( 94,355)( 95,356)( 96,360)( 97,361)( 98,362)
( 99,357)(100,358)(101,359)(102,372)(103,373)(104,374)(105,378)(106,379)
(107,380)(108,375)(109,376)(110,377)(111,309)(112,310)(113,311)(114,315)
(115,316)(116,317)(117,312)(118,313)(119,314)(120,300)(121,301)(122,302)
(123,306)(124,307)(125,308)(126,303)(127,304)(128,305)(129,318)(130,319)
(131,320)(132,324)(133,325)(134,326)(135,321)(136,322)(137,323)(138,282)
(139,283)(140,284)(141,288)(142,289)(143,290)(144,285)(145,286)(146,287)
(147,273)(148,274)(149,275)(150,279)(151,280)(152,281)(153,276)(154,277)
(155,278)(156,291)(157,292)(158,293)(159,297)(160,298)(161,299)(162,294)
(163,295)(164,296)(165,255)(166,256)(167,257)(168,261)(169,262)(170,263)
(171,258)(172,259)(173,260)(174,246)(175,247)(176,248)(177,252)(178,253)
(179,254)(180,249)(181,250)(182,251)(183,264)(184,265)(185,266)(186,270)
(187,271)(188,272)(189,267)(190,268)(191,269)(192,228)(193,229)(194,230)
(195,234)(196,235)(197,236)(198,231)(199,232)(200,233)(201,219)(202,220)
(203,221)(204,225)(205,226)(206,227)(207,222)(208,223)(209,224)(210,237)
(211,238)(212,239)(213,243)(214,244)(215,245)(216,240)(217,241)(218,242);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(434)!(1,2);
s1 := Sym(434)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)
( 73, 74)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)
( 97, 98)(100,101)(103,104)(106,107)(109,110)(111,138)(112,140)(113,139)
(114,141)(115,143)(116,142)(117,144)(118,146)(119,145)(120,147)(121,149)
(122,148)(123,150)(124,152)(125,151)(126,153)(127,155)(128,154)(129,156)
(130,158)(131,157)(132,159)(133,161)(134,160)(135,162)(136,164)(137,163)
(165,192)(166,194)(167,193)(168,195)(169,197)(170,196)(171,198)(172,200)
(173,199)(174,201)(175,203)(176,202)(177,204)(178,206)(179,205)(180,207)
(181,209)(182,208)(183,210)(184,212)(185,211)(186,213)(187,215)(188,214)
(189,216)(190,218)(191,217)(219,246)(220,248)(221,247)(222,249)(223,251)
(224,250)(225,252)(226,254)(227,253)(228,255)(229,257)(230,256)(231,258)
(232,260)(233,259)(234,261)(235,263)(236,262)(237,264)(238,266)(239,265)
(240,267)(241,269)(242,268)(243,270)(244,272)(245,271)(273,300)(274,302)
(275,301)(276,303)(277,305)(278,304)(279,306)(280,308)(281,307)(282,309)
(283,311)(284,310)(285,312)(286,314)(287,313)(288,315)(289,317)(290,316)
(291,318)(292,320)(293,319)(294,321)(295,323)(296,322)(297,324)(298,326)
(299,325)(328,329)(331,332)(334,335)(337,338)(340,341)(343,344)(346,347)
(349,350)(352,353)(355,356)(358,359)(361,362)(364,365)(367,368)(370,371)
(373,374)(376,377)(379,380)(382,383)(385,386)(388,389)(391,392)(394,395)
(397,398)(400,401)(403,404)(406,407)(409,410)(412,413)(415,416)(418,419)
(421,422)(424,425)(427,428)(430,431)(433,434);
s2 := Sym(434)!(  3,220)(  4,219)(  5,221)(  6,226)(  7,225)(  8,227)(  9,223)
( 10,222)( 11,224)( 12,229)( 13,228)( 14,230)( 15,235)( 16,234)( 17,236)
( 18,232)( 19,231)( 20,233)( 21,238)( 22,237)( 23,239)( 24,244)( 25,243)
( 26,245)( 27,241)( 28,240)( 29,242)( 30,247)( 31,246)( 32,248)( 33,253)
( 34,252)( 35,254)( 36,250)( 37,249)( 38,251)( 39,256)( 40,255)( 41,257)
( 42,262)( 43,261)( 44,263)( 45,259)( 46,258)( 47,260)( 48,265)( 49,264)
( 50,266)( 51,271)( 52,270)( 53,272)( 54,268)( 55,267)( 56,269)( 57,274)
( 58,273)( 59,275)( 60,280)( 61,279)( 62,281)( 63,277)( 64,276)( 65,278)
( 66,283)( 67,282)( 68,284)( 69,289)( 70,288)( 71,290)( 72,286)( 73,285)
( 74,287)( 75,292)( 76,291)( 77,293)( 78,298)( 79,297)( 80,299)( 81,295)
( 82,294)( 83,296)( 84,301)( 85,300)( 86,302)( 87,307)( 88,306)( 89,308)
( 90,304)( 91,303)( 92,305)( 93,310)( 94,309)( 95,311)( 96,316)( 97,315)
( 98,317)( 99,313)(100,312)(101,314)(102,319)(103,318)(104,320)(105,325)
(106,324)(107,326)(108,322)(109,321)(110,323)(111,355)(112,354)(113,356)
(114,361)(115,360)(116,362)(117,358)(118,357)(119,359)(120,364)(121,363)
(122,365)(123,370)(124,369)(125,371)(126,367)(127,366)(128,368)(129,373)
(130,372)(131,374)(132,379)(133,378)(134,380)(135,376)(136,375)(137,377)
(138,328)(139,327)(140,329)(141,334)(142,333)(143,335)(144,331)(145,330)
(146,332)(147,337)(148,336)(149,338)(150,343)(151,342)(152,344)(153,340)
(154,339)(155,341)(156,346)(157,345)(158,347)(159,352)(160,351)(161,353)
(162,349)(163,348)(164,350)(165,409)(166,408)(167,410)(168,415)(169,414)
(170,416)(171,412)(172,411)(173,413)(174,418)(175,417)(176,419)(177,424)
(178,423)(179,425)(180,421)(181,420)(182,422)(183,427)(184,426)(185,428)
(186,433)(187,432)(188,434)(189,430)(190,429)(191,431)(192,382)(193,381)
(194,383)(195,388)(196,387)(197,389)(198,385)(199,384)(200,386)(201,391)
(202,390)(203,392)(204,397)(205,396)(206,398)(207,394)(208,393)(209,395)
(210,400)(211,399)(212,401)(213,406)(214,405)(215,407)(216,403)(217,402)
(218,404);
s3 := Sym(434)!(  3,330)(  4,331)(  5,332)(  6,327)(  7,328)(  8,329)(  9,333)
( 10,334)( 11,335)( 12,348)( 13,349)( 14,350)( 15,345)( 16,346)( 17,347)
( 18,351)( 19,352)( 20,353)( 21,339)( 22,340)( 23,341)( 24,336)( 25,337)
( 26,338)( 27,342)( 28,343)( 29,344)( 30,357)( 31,358)( 32,359)( 33,354)
( 34,355)( 35,356)( 36,360)( 37,361)( 38,362)( 39,375)( 40,376)( 41,377)
( 42,372)( 43,373)( 44,374)( 45,378)( 46,379)( 47,380)( 48,366)( 49,367)
( 50,368)( 51,363)( 52,364)( 53,365)( 54,369)( 55,370)( 56,371)( 57,384)
( 58,385)( 59,386)( 60,381)( 61,382)( 62,383)( 63,387)( 64,388)( 65,389)
( 66,402)( 67,403)( 68,404)( 69,399)( 70,400)( 71,401)( 72,405)( 73,406)
( 74,407)( 75,393)( 76,394)( 77,395)( 78,390)( 79,391)( 80,392)( 81,396)
( 82,397)( 83,398)( 84,411)( 85,412)( 86,413)( 87,408)( 88,409)( 89,410)
( 90,414)( 91,415)( 92,416)( 93,429)( 94,430)( 95,431)( 96,426)( 97,427)
( 98,428)( 99,432)(100,433)(101,434)(102,420)(103,421)(104,422)(105,417)
(106,418)(107,419)(108,423)(109,424)(110,425)(111,249)(112,250)(113,251)
(114,246)(115,247)(116,248)(117,252)(118,253)(119,254)(120,267)(121,268)
(122,269)(123,264)(124,265)(125,266)(126,270)(127,271)(128,272)(129,258)
(130,259)(131,260)(132,255)(133,256)(134,257)(135,261)(136,262)(137,263)
(138,222)(139,223)(140,224)(141,219)(142,220)(143,221)(144,225)(145,226)
(146,227)(147,240)(148,241)(149,242)(150,237)(151,238)(152,239)(153,243)
(154,244)(155,245)(156,231)(157,232)(158,233)(159,228)(160,229)(161,230)
(162,234)(163,235)(164,236)(165,303)(166,304)(167,305)(168,300)(169,301)
(170,302)(171,306)(172,307)(173,308)(174,321)(175,322)(176,323)(177,318)
(178,319)(179,320)(180,324)(181,325)(182,326)(183,312)(184,313)(185,314)
(186,309)(187,310)(188,311)(189,315)(190,316)(191,317)(192,276)(193,277)
(194,278)(195,273)(196,274)(197,275)(198,279)(199,280)(200,281)(201,294)
(202,295)(203,296)(204,291)(205,292)(206,293)(207,297)(208,298)(209,299)
(210,285)(211,286)(212,287)(213,282)(214,283)(215,284)(216,288)(217,289)
(218,290);
s4 := Sym(434)!(  3,390)(  4,391)(  5,392)(  6,396)(  7,397)(  8,398)(  9,393)
( 10,394)( 11,395)( 12,381)( 13,382)( 14,383)( 15,387)( 16,388)( 17,389)
( 18,384)( 19,385)( 20,386)( 21,399)( 22,400)( 23,401)( 24,405)( 25,406)
( 26,407)( 27,402)( 28,403)( 29,404)( 30,417)( 31,418)( 32,419)( 33,423)
( 34,424)( 35,425)( 36,420)( 37,421)( 38,422)( 39,408)( 40,409)( 41,410)
( 42,414)( 43,415)( 44,416)( 45,411)( 46,412)( 47,413)( 48,426)( 49,427)
( 50,428)( 51,432)( 52,433)( 53,434)( 54,429)( 55,430)( 56,431)( 57,336)
( 58,337)( 59,338)( 60,342)( 61,343)( 62,344)( 63,339)( 64,340)( 65,341)
( 66,327)( 67,328)( 68,329)( 69,333)( 70,334)( 71,335)( 72,330)( 73,331)
( 74,332)( 75,345)( 76,346)( 77,347)( 78,351)( 79,352)( 80,353)( 81,348)
( 82,349)( 83,350)( 84,363)( 85,364)( 86,365)( 87,369)( 88,370)( 89,371)
( 90,366)( 91,367)( 92,368)( 93,354)( 94,355)( 95,356)( 96,360)( 97,361)
( 98,362)( 99,357)(100,358)(101,359)(102,372)(103,373)(104,374)(105,378)
(106,379)(107,380)(108,375)(109,376)(110,377)(111,309)(112,310)(113,311)
(114,315)(115,316)(116,317)(117,312)(118,313)(119,314)(120,300)(121,301)
(122,302)(123,306)(124,307)(125,308)(126,303)(127,304)(128,305)(129,318)
(130,319)(131,320)(132,324)(133,325)(134,326)(135,321)(136,322)(137,323)
(138,282)(139,283)(140,284)(141,288)(142,289)(143,290)(144,285)(145,286)
(146,287)(147,273)(148,274)(149,275)(150,279)(151,280)(152,281)(153,276)
(154,277)(155,278)(156,291)(157,292)(158,293)(159,297)(160,298)(161,299)
(162,294)(163,295)(164,296)(165,255)(166,256)(167,257)(168,261)(169,262)
(170,263)(171,258)(172,259)(173,260)(174,246)(175,247)(176,248)(177,252)
(178,253)(179,254)(180,249)(181,250)(182,251)(183,264)(184,265)(185,266)
(186,270)(187,271)(188,272)(189,267)(190,268)(191,269)(192,228)(193,229)
(194,230)(195,234)(196,235)(197,236)(198,231)(199,232)(200,233)(201,219)
(202,220)(203,221)(204,225)(205,226)(206,227)(207,222)(208,223)(209,224)
(210,237)(211,238)(212,239)(213,243)(214,244)(215,245)(216,240)(217,241)
(218,242);
poly := sub<Sym(434)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope