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