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

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

to this polytope