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

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

to this polytope