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

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

to this polytope