Polytope of Type {24,6,3,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6,3,2}*1728b
if this polytope has a name.
Group : SmallGroup(1728,36607)
Rank : 5
Schlafli Type : {24,6,3,2}
Number of vertices, edges, etc : 24, 72, 9, 3, 2
Order of s0s1s2s3s4 : 24
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
3-fold quotients : {24,2,3,2}*576, {8,6,3,2}*576
4-fold quotients : {6,6,3,2}*432b
6-fold quotients : {12,2,3,2}*288, {4,6,3,2}*288
9-fold quotients : {8,2,3,2}*192
12-fold quotients : {2,6,3,2}*144, {6,2,3,2}*144
18-fold quotients : {4,2,3,2}*96
24-fold quotients : {3,2,3,2}*72
36-fold quotients : {2,2,3,2}*48
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)( 55, 82)( 56, 84)( 57, 83)( 58, 85)( 59, 87)( 60, 86)
( 61, 88)( 62, 90)( 63, 89)( 64, 91)( 65, 93)( 66, 92)( 67, 94)( 68, 96)
( 69, 95)( 70, 97)( 71, 99)( 72, 98)( 73,100)( 74,102)( 75,101)( 76,103)
( 77,105)( 78,104)( 79,106)( 80,108)( 81,107)(109,163)(110,165)(111,164)
(112,166)(113,168)(114,167)(115,169)(116,171)(117,170)(118,172)(119,174)
(120,173)(121,175)(122,177)(123,176)(124,178)(125,180)(126,179)(127,181)
(128,183)(129,182)(130,184)(131,186)(132,185)(133,187)(134,189)(135,188)
(136,190)(137,192)(138,191)(139,193)(140,195)(141,194)(142,196)(143,198)
(144,197)(145,199)(146,201)(147,200)(148,202)(149,204)(150,203)(151,205)
(152,207)(153,206)(154,208)(155,210)(156,209)(157,211)(158,213)(159,212)
(160,214)(161,216)(162,215)(217,271)(218,273)(219,272)(220,274)(221,276)
(222,275)(223,277)(224,279)(225,278)(226,280)(227,282)(228,281)(229,283)
(230,285)(231,284)(232,286)(233,288)(234,287)(235,289)(236,291)(237,290)
(238,292)(239,294)(240,293)(241,295)(242,297)(243,296)(244,298)(245,300)
(246,299)(247,301)(248,303)(249,302)(250,304)(251,306)(252,305)(253,307)
(254,309)(255,308)(256,310)(257,312)(258,311)(259,313)(260,315)(261,314)
(262,316)(263,318)(264,317)(265,319)(266,321)(267,320)(268,322)(269,324)
(270,323)(325,352)(326,354)(327,353)(328,355)(329,357)(330,356)(331,358)
(332,360)(333,359)(334,361)(335,363)(336,362)(337,364)(338,366)(339,365)
(340,367)(341,369)(342,368)(343,370)(344,372)(345,371)(346,373)(347,375)
(348,374)(349,376)(350,378)(351,377)(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)( 55,299)( 56,298)
( 57,300)( 58,305)( 59,304)( 60,306)( 61,302)( 62,301)( 63,303)( 64,308)
( 65,307)( 66,309)( 67,314)( 68,313)( 69,315)( 70,311)( 71,310)( 72,312)
( 73,317)( 74,316)( 75,318)( 76,323)( 77,322)( 78,324)( 79,320)( 80,319)
( 81,321)( 82,272)( 83,271)( 84,273)( 85,278)( 86,277)( 87,279)( 88,275)
( 89,274)( 90,276)( 91,281)( 92,280)( 93,282)( 94,287)( 95,286)( 96,288)
( 97,284)( 98,283)( 99,285)(100,290)(101,289)(102,291)(103,296)(104,295)
(105,297)(106,293)(107,292)(108,294)(109,380)(110,379)(111,381)(112,386)
(113,385)(114,387)(115,383)(116,382)(117,384)(118,389)(119,388)(120,390)
(121,395)(122,394)(123,396)(124,392)(125,391)(126,393)(127,398)(128,397)
(129,399)(130,404)(131,403)(132,405)(133,401)(134,400)(135,402)(136,407)
(137,406)(138,408)(139,413)(140,412)(141,414)(142,410)(143,409)(144,411)
(145,416)(146,415)(147,417)(148,422)(149,421)(150,423)(151,419)(152,418)
(153,420)(154,425)(155,424)(156,426)(157,431)(158,430)(159,432)(160,428)
(161,427)(162,429)(163,326)(164,325)(165,327)(166,332)(167,331)(168,333)
(169,329)(170,328)(171,330)(172,335)(173,334)(174,336)(175,341)(176,340)
(177,342)(178,338)(179,337)(180,339)(181,344)(182,343)(183,345)(184,350)
(185,349)(186,351)(187,347)(188,346)(189,348)(190,353)(191,352)(192,354)
(193,359)(194,358)(195,360)(196,356)(197,355)(198,357)(199,362)(200,361)
(201,363)(202,368)(203,367)(204,369)(205,365)(206,364)(207,366)(208,371)
(209,370)(210,372)(211,377)(212,376)(213,378)(214,374)(215,373)(216,375);;
s2 := ( 1,382)( 2,383)( 3,384)( 4,379)( 5,380)( 6,381)( 7,385)( 8,386)
( 9,387)( 10,400)( 11,401)( 12,402)( 13,397)( 14,398)( 15,399)( 16,403)
( 17,404)( 18,405)( 19,391)( 20,392)( 21,393)( 22,388)( 23,389)( 24,390)
( 25,394)( 26,395)( 27,396)( 28,409)( 29,410)( 30,411)( 31,406)( 32,407)
( 33,408)( 34,412)( 35,413)( 36,414)( 37,427)( 38,428)( 39,429)( 40,424)
( 41,425)( 42,426)( 43,430)( 44,431)( 45,432)( 46,418)( 47,419)( 48,420)
( 49,415)( 50,416)( 51,417)( 52,421)( 53,422)( 54,423)( 55,355)( 56,356)
( 57,357)( 58,352)( 59,353)( 60,354)( 61,358)( 62,359)( 63,360)( 64,373)
( 65,374)( 66,375)( 67,370)( 68,371)( 69,372)( 70,376)( 71,377)( 72,378)
( 73,364)( 74,365)( 75,366)( 76,361)( 77,362)( 78,363)( 79,367)( 80,368)
( 81,369)( 82,328)( 83,329)( 84,330)( 85,325)( 86,326)( 87,327)( 88,331)
( 89,332)( 90,333)( 91,346)( 92,347)( 93,348)( 94,343)( 95,344)( 96,345)
( 97,349)( 98,350)( 99,351)(100,337)(101,338)(102,339)(103,334)(104,335)
(105,336)(106,340)(107,341)(108,342)(109,220)(110,221)(111,222)(112,217)
(113,218)(114,219)(115,223)(116,224)(117,225)(118,238)(119,239)(120,240)
(121,235)(122,236)(123,237)(124,241)(125,242)(126,243)(127,229)(128,230)
(129,231)(130,226)(131,227)(132,228)(133,232)(134,233)(135,234)(136,247)
(137,248)(138,249)(139,244)(140,245)(141,246)(142,250)(143,251)(144,252)
(145,265)(146,266)(147,267)(148,262)(149,263)(150,264)(151,268)(152,269)
(153,270)(154,256)(155,257)(156,258)(157,253)(158,254)(159,255)(160,259)
(161,260)(162,261)(163,274)(164,275)(165,276)(166,271)(167,272)(168,273)
(169,277)(170,278)(171,279)(172,292)(173,293)(174,294)(175,289)(176,290)
(177,291)(178,295)(179,296)(180,297)(181,283)(182,284)(183,285)(184,280)
(185,281)(186,282)(187,286)(188,287)(189,288)(190,301)(191,302)(192,303)
(193,298)(194,299)(195,300)(196,304)(197,305)(198,306)(199,319)(200,320)
(201,321)(202,316)(203,317)(204,318)(205,322)(206,323)(207,324)(208,310)
(209,311)(210,312)(211,307)(212,308)(213,309)(214,313)(215,314)(216,315);;
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)( 55,361)( 56,362)
( 57,363)( 58,367)( 59,368)( 60,369)( 61,364)( 62,365)( 63,366)( 64,352)
( 65,353)( 66,354)( 67,358)( 68,359)( 69,360)( 70,355)( 71,356)( 72,357)
( 73,370)( 74,371)( 75,372)( 76,376)( 77,377)( 78,378)( 79,373)( 80,374)
( 81,375)( 82,334)( 83,335)( 84,336)( 85,340)( 86,341)( 87,342)( 88,337)
( 89,338)( 90,339)( 91,325)( 92,326)( 93,327)( 94,331)( 95,332)( 96,333)
( 97,328)( 98,329)( 99,330)(100,343)(101,344)(102,345)(103,349)(104,350)
(105,351)(106,346)(107,347)(108,348)(109,226)(110,227)(111,228)(112,232)
(113,233)(114,234)(115,229)(116,230)(117,231)(118,217)(119,218)(120,219)
(121,223)(122,224)(123,225)(124,220)(125,221)(126,222)(127,235)(128,236)
(129,237)(130,241)(131,242)(132,243)(133,238)(134,239)(135,240)(136,253)
(137,254)(138,255)(139,259)(140,260)(141,261)(142,256)(143,257)(144,258)
(145,244)(146,245)(147,246)(148,250)(149,251)(150,252)(151,247)(152,248)
(153,249)(154,262)(155,263)(156,264)(157,268)(158,269)(159,270)(160,265)
(161,266)(162,267)(163,280)(164,281)(165,282)(166,286)(167,287)(168,288)
(169,283)(170,284)(171,285)(172,271)(173,272)(174,273)(175,277)(176,278)
(177,279)(178,274)(179,275)(180,276)(181,289)(182,290)(183,291)(184,295)
(185,296)(186,297)(187,292)(188,293)(189,294)(190,307)(191,308)(192,309)
(193,313)(194,314)(195,315)(196,310)(197,311)(198,312)(199,298)(200,299)
(201,300)(202,304)(203,305)(204,306)(205,301)(206,302)(207,303)(208,316)
(209,317)(210,318)(211,322)(212,323)(213,324)(214,319)(215,320)(216,321);;
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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 55, 82)( 56, 84)( 57, 83)( 58, 85)( 59, 87)
( 60, 86)( 61, 88)( 62, 90)( 63, 89)( 64, 91)( 65, 93)( 66, 92)( 67, 94)
( 68, 96)( 69, 95)( 70, 97)( 71, 99)( 72, 98)( 73,100)( 74,102)( 75,101)
( 76,103)( 77,105)( 78,104)( 79,106)( 80,108)( 81,107)(109,163)(110,165)
(111,164)(112,166)(113,168)(114,167)(115,169)(116,171)(117,170)(118,172)
(119,174)(120,173)(121,175)(122,177)(123,176)(124,178)(125,180)(126,179)
(127,181)(128,183)(129,182)(130,184)(131,186)(132,185)(133,187)(134,189)
(135,188)(136,190)(137,192)(138,191)(139,193)(140,195)(141,194)(142,196)
(143,198)(144,197)(145,199)(146,201)(147,200)(148,202)(149,204)(150,203)
(151,205)(152,207)(153,206)(154,208)(155,210)(156,209)(157,211)(158,213)
(159,212)(160,214)(161,216)(162,215)(217,271)(218,273)(219,272)(220,274)
(221,276)(222,275)(223,277)(224,279)(225,278)(226,280)(227,282)(228,281)
(229,283)(230,285)(231,284)(232,286)(233,288)(234,287)(235,289)(236,291)
(237,290)(238,292)(239,294)(240,293)(241,295)(242,297)(243,296)(244,298)
(245,300)(246,299)(247,301)(248,303)(249,302)(250,304)(251,306)(252,305)
(253,307)(254,309)(255,308)(256,310)(257,312)(258,311)(259,313)(260,315)
(261,314)(262,316)(263,318)(264,317)(265,319)(266,321)(267,320)(268,322)
(269,324)(270,323)(325,352)(326,354)(327,353)(328,355)(329,357)(330,356)
(331,358)(332,360)(333,359)(334,361)(335,363)(336,362)(337,364)(338,366)
(339,365)(340,367)(341,369)(342,368)(343,370)(344,372)(345,371)(346,373)
(347,375)(348,374)(349,376)(350,378)(351,377)(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)( 55,299)
( 56,298)( 57,300)( 58,305)( 59,304)( 60,306)( 61,302)( 62,301)( 63,303)
( 64,308)( 65,307)( 66,309)( 67,314)( 68,313)( 69,315)( 70,311)( 71,310)
( 72,312)( 73,317)( 74,316)( 75,318)( 76,323)( 77,322)( 78,324)( 79,320)
( 80,319)( 81,321)( 82,272)( 83,271)( 84,273)( 85,278)( 86,277)( 87,279)
( 88,275)( 89,274)( 90,276)( 91,281)( 92,280)( 93,282)( 94,287)( 95,286)
( 96,288)( 97,284)( 98,283)( 99,285)(100,290)(101,289)(102,291)(103,296)
(104,295)(105,297)(106,293)(107,292)(108,294)(109,380)(110,379)(111,381)
(112,386)(113,385)(114,387)(115,383)(116,382)(117,384)(118,389)(119,388)
(120,390)(121,395)(122,394)(123,396)(124,392)(125,391)(126,393)(127,398)
(128,397)(129,399)(130,404)(131,403)(132,405)(133,401)(134,400)(135,402)
(136,407)(137,406)(138,408)(139,413)(140,412)(141,414)(142,410)(143,409)
(144,411)(145,416)(146,415)(147,417)(148,422)(149,421)(150,423)(151,419)
(152,418)(153,420)(154,425)(155,424)(156,426)(157,431)(158,430)(159,432)
(160,428)(161,427)(162,429)(163,326)(164,325)(165,327)(166,332)(167,331)
(168,333)(169,329)(170,328)(171,330)(172,335)(173,334)(174,336)(175,341)
(176,340)(177,342)(178,338)(179,337)(180,339)(181,344)(182,343)(183,345)
(184,350)(185,349)(186,351)(187,347)(188,346)(189,348)(190,353)(191,352)
(192,354)(193,359)(194,358)(195,360)(196,356)(197,355)(198,357)(199,362)
(200,361)(201,363)(202,368)(203,367)(204,369)(205,365)(206,364)(207,366)
(208,371)(209,370)(210,372)(211,377)(212,376)(213,378)(214,374)(215,373)
(216,375);
s2 := Sym(434)!( 1,382)( 2,383)( 3,384)( 4,379)( 5,380)( 6,381)( 7,385)
( 8,386)( 9,387)( 10,400)( 11,401)( 12,402)( 13,397)( 14,398)( 15,399)
( 16,403)( 17,404)( 18,405)( 19,391)( 20,392)( 21,393)( 22,388)( 23,389)
( 24,390)( 25,394)( 26,395)( 27,396)( 28,409)( 29,410)( 30,411)( 31,406)
( 32,407)( 33,408)( 34,412)( 35,413)( 36,414)( 37,427)( 38,428)( 39,429)
( 40,424)( 41,425)( 42,426)( 43,430)( 44,431)( 45,432)( 46,418)( 47,419)
( 48,420)( 49,415)( 50,416)( 51,417)( 52,421)( 53,422)( 54,423)( 55,355)
( 56,356)( 57,357)( 58,352)( 59,353)( 60,354)( 61,358)( 62,359)( 63,360)
( 64,373)( 65,374)( 66,375)( 67,370)( 68,371)( 69,372)( 70,376)( 71,377)
( 72,378)( 73,364)( 74,365)( 75,366)( 76,361)( 77,362)( 78,363)( 79,367)
( 80,368)( 81,369)( 82,328)( 83,329)( 84,330)( 85,325)( 86,326)( 87,327)
( 88,331)( 89,332)( 90,333)( 91,346)( 92,347)( 93,348)( 94,343)( 95,344)
( 96,345)( 97,349)( 98,350)( 99,351)(100,337)(101,338)(102,339)(103,334)
(104,335)(105,336)(106,340)(107,341)(108,342)(109,220)(110,221)(111,222)
(112,217)(113,218)(114,219)(115,223)(116,224)(117,225)(118,238)(119,239)
(120,240)(121,235)(122,236)(123,237)(124,241)(125,242)(126,243)(127,229)
(128,230)(129,231)(130,226)(131,227)(132,228)(133,232)(134,233)(135,234)
(136,247)(137,248)(138,249)(139,244)(140,245)(141,246)(142,250)(143,251)
(144,252)(145,265)(146,266)(147,267)(148,262)(149,263)(150,264)(151,268)
(152,269)(153,270)(154,256)(155,257)(156,258)(157,253)(158,254)(159,255)
(160,259)(161,260)(162,261)(163,274)(164,275)(165,276)(166,271)(167,272)
(168,273)(169,277)(170,278)(171,279)(172,292)(173,293)(174,294)(175,289)
(176,290)(177,291)(178,295)(179,296)(180,297)(181,283)(182,284)(183,285)
(184,280)(185,281)(186,282)(187,286)(188,287)(189,288)(190,301)(191,302)
(192,303)(193,298)(194,299)(195,300)(196,304)(197,305)(198,306)(199,319)
(200,320)(201,321)(202,316)(203,317)(204,318)(205,322)(206,323)(207,324)
(208,310)(209,311)(210,312)(211,307)(212,308)(213,309)(214,313)(215,314)
(216,315);
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)( 55,361)
( 56,362)( 57,363)( 58,367)( 59,368)( 60,369)( 61,364)( 62,365)( 63,366)
( 64,352)( 65,353)( 66,354)( 67,358)( 68,359)( 69,360)( 70,355)( 71,356)
( 72,357)( 73,370)( 74,371)( 75,372)( 76,376)( 77,377)( 78,378)( 79,373)
( 80,374)( 81,375)( 82,334)( 83,335)( 84,336)( 85,340)( 86,341)( 87,342)
( 88,337)( 89,338)( 90,339)( 91,325)( 92,326)( 93,327)( 94,331)( 95,332)
( 96,333)( 97,328)( 98,329)( 99,330)(100,343)(101,344)(102,345)(103,349)
(104,350)(105,351)(106,346)(107,347)(108,348)(109,226)(110,227)(111,228)
(112,232)(113,233)(114,234)(115,229)(116,230)(117,231)(118,217)(119,218)
(120,219)(121,223)(122,224)(123,225)(124,220)(125,221)(126,222)(127,235)
(128,236)(129,237)(130,241)(131,242)(132,243)(133,238)(134,239)(135,240)
(136,253)(137,254)(138,255)(139,259)(140,260)(141,261)(142,256)(143,257)
(144,258)(145,244)(146,245)(147,246)(148,250)(149,251)(150,252)(151,247)
(152,248)(153,249)(154,262)(155,263)(156,264)(157,268)(158,269)(159,270)
(160,265)(161,266)(162,267)(163,280)(164,281)(165,282)(166,286)(167,287)
(168,288)(169,283)(170,284)(171,285)(172,271)(173,272)(174,273)(175,277)
(176,278)(177,279)(178,274)(179,275)(180,276)(181,289)(182,290)(183,291)
(184,295)(185,296)(186,297)(187,292)(188,293)(189,294)(190,307)(191,308)
(192,309)(193,313)(194,314)(195,315)(196,310)(197,311)(198,312)(199,298)
(200,299)(201,300)(202,304)(203,305)(204,306)(205,301)(206,302)(207,303)
(208,316)(209,317)(210,318)(211,322)(212,323)(213,324)(214,319)(215,320)
(216,321);
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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