Polytope of Type {2,3,6,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,24}*1728b
if this polytope has a name.
Group : SmallGroup(1728,36607)
Rank : 5
Schlafli Type : {2,3,6,24}
Number of vertices, edges, etc : 2, 3, 9, 72, 24
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 : {2,3,6,12}*864b
3-fold quotients : {2,3,2,24}*576, {2,3,6,8}*576
4-fold quotients : {2,3,6,6}*432b
6-fold quotients : {2,3,2,12}*288, {2,3,6,4}*288
9-fold quotients : {2,3,2,8}*192
12-fold quotients : {2,3,2,6}*144, {2,3,6,2}*144
18-fold quotients : {2,3,2,4}*96
24-fold quotients : {2,3,2,3}*72
36-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,381)( 4,382)( 5,383)( 6,387)( 7,388)( 8,389)( 9,384)( 10,385)
( 11,386)( 12,399)( 13,400)( 14,401)( 15,405)( 16,406)( 17,407)( 18,402)
( 19,403)( 20,404)( 21,390)( 22,391)( 23,392)( 24,396)( 25,397)( 26,398)
( 27,393)( 28,394)( 29,395)( 30,408)( 31,409)( 32,410)( 33,414)( 34,415)
( 35,416)( 36,411)( 37,412)( 38,413)( 39,426)( 40,427)( 41,428)( 42,432)
( 43,433)( 44,434)( 45,429)( 46,430)( 47,431)( 48,417)( 49,418)( 50,419)
( 51,423)( 52,424)( 53,425)( 54,420)( 55,421)( 56,422)( 57,354)( 58,355)
( 59,356)( 60,360)( 61,361)( 62,362)( 63,357)( 64,358)( 65,359)( 66,372)
( 67,373)( 68,374)( 69,378)( 70,379)( 71,380)( 72,375)( 73,376)( 74,377)
( 75,363)( 76,364)( 77,365)( 78,369)( 79,370)( 80,371)( 81,366)( 82,367)
( 83,368)( 84,327)( 85,328)( 86,329)( 87,333)( 88,334)( 89,335)( 90,330)
( 91,331)( 92,332)( 93,345)( 94,346)( 95,347)( 96,351)( 97,352)( 98,353)
( 99,348)(100,349)(101,350)(102,336)(103,337)(104,338)(105,342)(106,343)
(107,344)(108,339)(109,340)(110,341)(111,219)(112,220)(113,221)(114,225)
(115,226)(116,227)(117,222)(118,223)(119,224)(120,237)(121,238)(122,239)
(123,243)(124,244)(125,245)(126,240)(127,241)(128,242)(129,228)(130,229)
(131,230)(132,234)(133,235)(134,236)(135,231)(136,232)(137,233)(138,246)
(139,247)(140,248)(141,252)(142,253)(143,254)(144,249)(145,250)(146,251)
(147,264)(148,265)(149,266)(150,270)(151,271)(152,272)(153,267)(154,268)
(155,269)(156,255)(157,256)(158,257)(159,261)(160,262)(161,263)(162,258)
(163,259)(164,260)(165,273)(166,274)(167,275)(168,279)(169,280)(170,281)
(171,276)(172,277)(173,278)(174,291)(175,292)(176,293)(177,297)(178,298)
(179,299)(180,294)(181,295)(182,296)(183,282)(184,283)(185,284)(186,288)
(187,289)(188,290)(189,285)(190,286)(191,287)(192,300)(193,301)(194,302)
(195,306)(196,307)(197,308)(198,303)(199,304)(200,305)(201,318)(202,319)
(203,320)(204,324)(205,325)(206,326)(207,321)(208,322)(209,323)(210,309)
(211,310)(212,311)(213,315)(214,316)(215,317)(216,312)(217,313)(218,314);;
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)( 57,366)( 58,367)
( 59,368)( 60,363)( 61,364)( 62,365)( 63,369)( 64,370)( 65,371)( 66,357)
( 67,358)( 68,359)( 69,354)( 70,355)( 71,356)( 72,360)( 73,361)( 74,362)
( 75,375)( 76,376)( 77,377)( 78,372)( 79,373)( 80,374)( 81,378)( 82,379)
( 83,380)( 84,339)( 85,340)( 86,341)( 87,336)( 88,337)( 89,338)( 90,342)
( 91,343)( 92,344)( 93,330)( 94,331)( 95,332)( 96,327)( 97,328)( 98,329)
( 99,333)(100,334)(101,335)(102,348)(103,349)(104,350)(105,345)(106,346)
(107,347)(108,351)(109,352)(110,353)(111,231)(112,232)(113,233)(114,228)
(115,229)(116,230)(117,234)(118,235)(119,236)(120,222)(121,223)(122,224)
(123,219)(124,220)(125,221)(126,225)(127,226)(128,227)(129,240)(130,241)
(131,242)(132,237)(133,238)(134,239)(135,243)(136,244)(137,245)(138,258)
(139,259)(140,260)(141,255)(142,256)(143,257)(144,261)(145,262)(146,263)
(147,249)(148,250)(149,251)(150,246)(151,247)(152,248)(153,252)(154,253)
(155,254)(156,267)(157,268)(158,269)(159,264)(160,265)(161,266)(162,270)
(163,271)(164,272)(165,285)(166,286)(167,287)(168,282)(169,283)(170,284)
(171,288)(172,289)(173,290)(174,276)(175,277)(176,278)(177,273)(178,274)
(179,275)(180,279)(181,280)(182,281)(183,294)(184,295)(185,296)(186,291)
(187,292)(188,293)(189,297)(190,298)(191,299)(192,312)(193,313)(194,314)
(195,309)(196,310)(197,311)(198,315)(199,316)(200,317)(201,303)(202,304)
(203,305)(204,300)(205,301)(206,302)(207,306)(208,307)(209,308)(210,321)
(211,322)(212,323)(213,318)(214,319)(215,320)(216,324)(217,325)(218,326);;
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)( 57,300)( 58,302)
( 59,301)( 60,306)( 61,308)( 62,307)( 63,303)( 64,305)( 65,304)( 66,309)
( 67,311)( 68,310)( 69,315)( 70,317)( 71,316)( 72,312)( 73,314)( 74,313)
( 75,318)( 76,320)( 77,319)( 78,324)( 79,326)( 80,325)( 81,321)( 82,323)
( 83,322)( 84,273)( 85,275)( 86,274)( 87,279)( 88,281)( 89,280)( 90,276)
( 91,278)( 92,277)( 93,282)( 94,284)( 95,283)( 96,288)( 97,290)( 98,289)
( 99,285)(100,287)(101,286)(102,291)(103,293)(104,292)(105,297)(106,299)
(107,298)(108,294)(109,296)(110,295)(111,381)(112,383)(113,382)(114,387)
(115,389)(116,388)(117,384)(118,386)(119,385)(120,390)(121,392)(122,391)
(123,396)(124,398)(125,397)(126,393)(127,395)(128,394)(129,399)(130,401)
(131,400)(132,405)(133,407)(134,406)(135,402)(136,404)(137,403)(138,408)
(139,410)(140,409)(141,414)(142,416)(143,415)(144,411)(145,413)(146,412)
(147,417)(148,419)(149,418)(150,423)(151,425)(152,424)(153,420)(154,422)
(155,421)(156,426)(157,428)(158,427)(159,432)(160,434)(161,433)(162,429)
(163,431)(164,430)(165,327)(166,329)(167,328)(168,333)(169,335)(170,334)
(171,330)(172,332)(173,331)(174,336)(175,338)(176,337)(177,342)(178,344)
(179,343)(180,339)(181,341)(182,340)(183,345)(184,347)(185,346)(186,351)
(187,353)(188,352)(189,348)(190,350)(191,349)(192,354)(193,356)(194,355)
(195,360)(196,362)(197,361)(198,357)(199,359)(200,358)(201,363)(202,365)
(203,364)(204,369)(205,371)(206,370)(207,366)(208,368)(209,367)(210,372)
(211,374)(212,373)(213,378)(214,380)(215,379)(216,375)(217,377)(218,376);;
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, 85)( 58, 84)( 59, 86)( 60, 88)( 61, 87)( 62, 89)
( 63, 91)( 64, 90)( 65, 92)( 66, 94)( 67, 93)( 68, 95)( 69, 97)( 70, 96)
( 71, 98)( 72,100)( 73, 99)( 74,101)( 75,103)( 76,102)( 77,104)( 78,106)
( 79,105)( 80,107)( 81,109)( 82,108)( 83,110)(111,166)(112,165)(113,167)
(114,169)(115,168)(116,170)(117,172)(118,171)(119,173)(120,175)(121,174)
(122,176)(123,178)(124,177)(125,179)(126,181)(127,180)(128,182)(129,184)
(130,183)(131,185)(132,187)(133,186)(134,188)(135,190)(136,189)(137,191)
(138,193)(139,192)(140,194)(141,196)(142,195)(143,197)(144,199)(145,198)
(146,200)(147,202)(148,201)(149,203)(150,205)(151,204)(152,206)(153,208)
(154,207)(155,209)(156,211)(157,210)(158,212)(159,214)(160,213)(161,215)
(162,217)(163,216)(164,218)(219,274)(220,273)(221,275)(222,277)(223,276)
(224,278)(225,280)(226,279)(227,281)(228,283)(229,282)(230,284)(231,286)
(232,285)(233,287)(234,289)(235,288)(236,290)(237,292)(238,291)(239,293)
(240,295)(241,294)(242,296)(243,298)(244,297)(245,299)(246,301)(247,300)
(248,302)(249,304)(250,303)(251,305)(252,307)(253,306)(254,308)(255,310)
(256,309)(257,311)(258,313)(259,312)(260,314)(261,316)(262,315)(263,317)
(264,319)(265,318)(266,320)(267,322)(268,321)(269,323)(270,325)(271,324)
(272,326)(327,355)(328,354)(329,356)(330,358)(331,357)(332,359)(333,361)
(334,360)(335,362)(336,364)(337,363)(338,365)(339,367)(340,366)(341,368)
(342,370)(343,369)(344,371)(345,373)(346,372)(347,374)(348,376)(349,375)
(350,377)(351,379)(352,378)(353,380)(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,
s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*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*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)!( 3,381)( 4,382)( 5,383)( 6,387)( 7,388)( 8,389)( 9,384)
( 10,385)( 11,386)( 12,399)( 13,400)( 14,401)( 15,405)( 16,406)( 17,407)
( 18,402)( 19,403)( 20,404)( 21,390)( 22,391)( 23,392)( 24,396)( 25,397)
( 26,398)( 27,393)( 28,394)( 29,395)( 30,408)( 31,409)( 32,410)( 33,414)
( 34,415)( 35,416)( 36,411)( 37,412)( 38,413)( 39,426)( 40,427)( 41,428)
( 42,432)( 43,433)( 44,434)( 45,429)( 46,430)( 47,431)( 48,417)( 49,418)
( 50,419)( 51,423)( 52,424)( 53,425)( 54,420)( 55,421)( 56,422)( 57,354)
( 58,355)( 59,356)( 60,360)( 61,361)( 62,362)( 63,357)( 64,358)( 65,359)
( 66,372)( 67,373)( 68,374)( 69,378)( 70,379)( 71,380)( 72,375)( 73,376)
( 74,377)( 75,363)( 76,364)( 77,365)( 78,369)( 79,370)( 80,371)( 81,366)
( 82,367)( 83,368)( 84,327)( 85,328)( 86,329)( 87,333)( 88,334)( 89,335)
( 90,330)( 91,331)( 92,332)( 93,345)( 94,346)( 95,347)( 96,351)( 97,352)
( 98,353)( 99,348)(100,349)(101,350)(102,336)(103,337)(104,338)(105,342)
(106,343)(107,344)(108,339)(109,340)(110,341)(111,219)(112,220)(113,221)
(114,225)(115,226)(116,227)(117,222)(118,223)(119,224)(120,237)(121,238)
(122,239)(123,243)(124,244)(125,245)(126,240)(127,241)(128,242)(129,228)
(130,229)(131,230)(132,234)(133,235)(134,236)(135,231)(136,232)(137,233)
(138,246)(139,247)(140,248)(141,252)(142,253)(143,254)(144,249)(145,250)
(146,251)(147,264)(148,265)(149,266)(150,270)(151,271)(152,272)(153,267)
(154,268)(155,269)(156,255)(157,256)(158,257)(159,261)(160,262)(161,263)
(162,258)(163,259)(164,260)(165,273)(166,274)(167,275)(168,279)(169,280)
(170,281)(171,276)(172,277)(173,278)(174,291)(175,292)(176,293)(177,297)
(178,298)(179,299)(180,294)(181,295)(182,296)(183,282)(184,283)(185,284)
(186,288)(187,289)(188,290)(189,285)(190,286)(191,287)(192,300)(193,301)
(194,302)(195,306)(196,307)(197,308)(198,303)(199,304)(200,305)(201,318)
(202,319)(203,320)(204,324)(205,325)(206,326)(207,321)(208,322)(209,323)
(210,309)(211,310)(212,311)(213,315)(214,316)(215,317)(216,312)(217,313)
(218,314);
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)( 57,366)
( 58,367)( 59,368)( 60,363)( 61,364)( 62,365)( 63,369)( 64,370)( 65,371)
( 66,357)( 67,358)( 68,359)( 69,354)( 70,355)( 71,356)( 72,360)( 73,361)
( 74,362)( 75,375)( 76,376)( 77,377)( 78,372)( 79,373)( 80,374)( 81,378)
( 82,379)( 83,380)( 84,339)( 85,340)( 86,341)( 87,336)( 88,337)( 89,338)
( 90,342)( 91,343)( 92,344)( 93,330)( 94,331)( 95,332)( 96,327)( 97,328)
( 98,329)( 99,333)(100,334)(101,335)(102,348)(103,349)(104,350)(105,345)
(106,346)(107,347)(108,351)(109,352)(110,353)(111,231)(112,232)(113,233)
(114,228)(115,229)(116,230)(117,234)(118,235)(119,236)(120,222)(121,223)
(122,224)(123,219)(124,220)(125,221)(126,225)(127,226)(128,227)(129,240)
(130,241)(131,242)(132,237)(133,238)(134,239)(135,243)(136,244)(137,245)
(138,258)(139,259)(140,260)(141,255)(142,256)(143,257)(144,261)(145,262)
(146,263)(147,249)(148,250)(149,251)(150,246)(151,247)(152,248)(153,252)
(154,253)(155,254)(156,267)(157,268)(158,269)(159,264)(160,265)(161,266)
(162,270)(163,271)(164,272)(165,285)(166,286)(167,287)(168,282)(169,283)
(170,284)(171,288)(172,289)(173,290)(174,276)(175,277)(176,278)(177,273)
(178,274)(179,275)(180,279)(181,280)(182,281)(183,294)(184,295)(185,296)
(186,291)(187,292)(188,293)(189,297)(190,298)(191,299)(192,312)(193,313)
(194,314)(195,309)(196,310)(197,311)(198,315)(199,316)(200,317)(201,303)
(202,304)(203,305)(204,300)(205,301)(206,302)(207,306)(208,307)(209,308)
(210,321)(211,322)(212,323)(213,318)(214,319)(215,320)(216,324)(217,325)
(218,326);
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)( 57,300)
( 58,302)( 59,301)( 60,306)( 61,308)( 62,307)( 63,303)( 64,305)( 65,304)
( 66,309)( 67,311)( 68,310)( 69,315)( 70,317)( 71,316)( 72,312)( 73,314)
( 74,313)( 75,318)( 76,320)( 77,319)( 78,324)( 79,326)( 80,325)( 81,321)
( 82,323)( 83,322)( 84,273)( 85,275)( 86,274)( 87,279)( 88,281)( 89,280)
( 90,276)( 91,278)( 92,277)( 93,282)( 94,284)( 95,283)( 96,288)( 97,290)
( 98,289)( 99,285)(100,287)(101,286)(102,291)(103,293)(104,292)(105,297)
(106,299)(107,298)(108,294)(109,296)(110,295)(111,381)(112,383)(113,382)
(114,387)(115,389)(116,388)(117,384)(118,386)(119,385)(120,390)(121,392)
(122,391)(123,396)(124,398)(125,397)(126,393)(127,395)(128,394)(129,399)
(130,401)(131,400)(132,405)(133,407)(134,406)(135,402)(136,404)(137,403)
(138,408)(139,410)(140,409)(141,414)(142,416)(143,415)(144,411)(145,413)
(146,412)(147,417)(148,419)(149,418)(150,423)(151,425)(152,424)(153,420)
(154,422)(155,421)(156,426)(157,428)(158,427)(159,432)(160,434)(161,433)
(162,429)(163,431)(164,430)(165,327)(166,329)(167,328)(168,333)(169,335)
(170,334)(171,330)(172,332)(173,331)(174,336)(175,338)(176,337)(177,342)
(178,344)(179,343)(180,339)(181,341)(182,340)(183,345)(184,347)(185,346)
(186,351)(187,353)(188,352)(189,348)(190,350)(191,349)(192,354)(193,356)
(194,355)(195,360)(196,362)(197,361)(198,357)(199,359)(200,358)(201,363)
(202,365)(203,364)(204,369)(205,371)(206,370)(207,366)(208,368)(209,367)
(210,372)(211,374)(212,373)(213,378)(214,380)(215,379)(216,375)(217,377)
(218,376);
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, 85)( 58, 84)( 59, 86)( 60, 88)( 61, 87)
( 62, 89)( 63, 91)( 64, 90)( 65, 92)( 66, 94)( 67, 93)( 68, 95)( 69, 97)
( 70, 96)( 71, 98)( 72,100)( 73, 99)( 74,101)( 75,103)( 76,102)( 77,104)
( 78,106)( 79,105)( 80,107)( 81,109)( 82,108)( 83,110)(111,166)(112,165)
(113,167)(114,169)(115,168)(116,170)(117,172)(118,171)(119,173)(120,175)
(121,174)(122,176)(123,178)(124,177)(125,179)(126,181)(127,180)(128,182)
(129,184)(130,183)(131,185)(132,187)(133,186)(134,188)(135,190)(136,189)
(137,191)(138,193)(139,192)(140,194)(141,196)(142,195)(143,197)(144,199)
(145,198)(146,200)(147,202)(148,201)(149,203)(150,205)(151,204)(152,206)
(153,208)(154,207)(155,209)(156,211)(157,210)(158,212)(159,214)(160,213)
(161,215)(162,217)(163,216)(164,218)(219,274)(220,273)(221,275)(222,277)
(223,276)(224,278)(225,280)(226,279)(227,281)(228,283)(229,282)(230,284)
(231,286)(232,285)(233,287)(234,289)(235,288)(236,290)(237,292)(238,291)
(239,293)(240,295)(241,294)(242,296)(243,298)(244,297)(245,299)(246,301)
(247,300)(248,302)(249,304)(250,303)(251,305)(252,307)(253,306)(254,308)
(255,310)(256,309)(257,311)(258,313)(259,312)(260,314)(261,316)(262,315)
(263,317)(264,319)(265,318)(266,320)(267,322)(268,321)(269,323)(270,325)
(271,324)(272,326)(327,355)(328,354)(329,356)(330,358)(331,357)(332,359)
(333,361)(334,360)(335,362)(336,364)(337,363)(338,365)(339,367)(340,366)
(341,368)(342,370)(343,369)(344,371)(345,373)(346,372)(347,374)(348,376)
(349,375)(350,377)(351,379)(352,378)(353,380)(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, s1*s2*s1*s2*s1*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*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*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