Polytope of Type {8,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,6}*1728c
if this polytope has a name.
Group : SmallGroup(1728,17452)
Rank : 4
Schlafli Type : {8,6,6}
Number of vertices, edges, etc : 8, 72, 54, 18
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {8,6,3}*864a, {4,6,6}*864c
3-fold quotients : {8,6,6}*576c
4-fold quotients : {4,6,3}*432a, {2,6,6}*432a
6-fold quotients : {8,6,3}*288, {4,6,6}*288c
8-fold quotients : {2,6,3}*216
9-fold quotients : {8,2,6}*192
12-fold quotients : {4,6,3}*144, {2,6,6}*144b
18-fold quotients : {8,2,3}*96, {4,2,6}*96
24-fold quotients : {2,6,3}*72
27-fold quotients : {8,2,2}*64
36-fold quotients : {4,2,3}*48, {2,2,6}*48
54-fold quotients : {4,2,2}*32
72-fold quotients : {2,2,3}*24
108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,109)( 2,110)( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)( 8,116)
( 9,117)( 10,118)( 11,119)( 12,120)( 13,121)( 14,122)( 15,123)( 16,124)
( 17,125)( 18,126)( 19,127)( 20,128)( 21,129)( 22,130)( 23,131)( 24,132)
( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)( 32,140)
( 33,141)( 34,142)( 35,143)( 36,144)( 37,145)( 38,146)( 39,147)( 40,148)
( 41,149)( 42,150)( 43,151)( 44,152)( 45,153)( 46,154)( 47,155)( 48,156)
( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,190)( 56,191)
( 57,192)( 58,193)( 59,194)( 60,195)( 61,196)( 62,197)( 63,198)( 64,199)
( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)
( 73,208)( 74,209)( 75,210)( 76,211)( 77,212)( 78,213)( 79,214)( 80,215)
( 81,216)( 82,163)( 83,164)( 84,165)( 85,166)( 86,167)( 87,168)( 88,169)
( 89,170)( 90,171)( 91,172)( 92,173)( 93,174)( 94,175)( 95,176)( 96,177)
( 97,178)( 98,179)( 99,180)(100,181)(101,182)(102,183)(103,184)(104,185)
(105,186)(106,187)(107,188)(108,189)(217,325)(218,326)(219,327)(220,328)
(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)(228,336)
(229,337)(230,338)(231,339)(232,340)(233,341)(234,342)(235,343)(236,344)
(237,345)(238,346)(239,347)(240,348)(241,349)(242,350)(243,351)(244,352)
(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)(252,360)
(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)(260,368)
(261,369)(262,370)(263,371)(264,372)(265,373)(266,374)(267,375)(268,376)
(269,377)(270,378)(271,406)(272,407)(273,408)(274,409)(275,410)(276,411)
(277,412)(278,413)(279,414)(280,415)(281,416)(282,417)(283,418)(284,419)
(285,420)(286,421)(287,422)(288,423)(289,424)(290,425)(291,426)(292,427)
(293,428)(294,429)(295,430)(296,431)(297,432)(298,379)(299,380)(300,381)
(301,382)(302,383)(303,384)(304,385)(305,386)(306,387)(307,388)(308,389)
(309,390)(310,391)(311,392)(312,393)(313,394)(314,395)(315,396)(316,397)
(317,398)(318,399)(319,400)(320,401)(321,402)(322,403)(323,404)(324,405);;
s1 := ( 2, 3)( 5, 6)( 8, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)
( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)( 37, 46)
( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)( 45, 53)
( 55, 82)( 56, 84)( 57, 83)( 58, 85)( 59, 87)( 60, 86)( 61, 88)( 62, 90)
( 63, 89)( 64,100)( 65,102)( 66,101)( 67,103)( 68,105)( 69,104)( 70,106)
( 71,108)( 72,107)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)( 78, 95)
( 79, 97)( 80, 99)( 81, 98)(109,163)(110,165)(111,164)(112,166)(113,168)
(114,167)(115,169)(116,171)(117,170)(118,181)(119,183)(120,182)(121,184)
(122,186)(123,185)(124,187)(125,189)(126,188)(127,172)(128,174)(129,173)
(130,175)(131,177)(132,176)(133,178)(134,180)(135,179)(136,190)(137,192)
(138,191)(139,193)(140,195)(141,194)(142,196)(143,198)(144,197)(145,208)
(146,210)(147,209)(148,211)(149,213)(150,212)(151,214)(152,216)(153,215)
(154,199)(155,201)(156,200)(157,202)(158,204)(159,203)(160,205)(161,207)
(162,206)(218,219)(221,222)(224,225)(226,235)(227,237)(228,236)(229,238)
(230,240)(231,239)(232,241)(233,243)(234,242)(245,246)(248,249)(251,252)
(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)
(261,269)(271,298)(272,300)(273,299)(274,301)(275,303)(276,302)(277,304)
(278,306)(279,305)(280,316)(281,318)(282,317)(283,319)(284,321)(285,320)
(286,322)(287,324)(288,323)(289,307)(290,309)(291,308)(292,310)(293,312)
(294,311)(295,313)(296,315)(297,314)(325,379)(326,381)(327,380)(328,382)
(329,384)(330,383)(331,385)(332,387)(333,386)(334,397)(335,399)(336,398)
(337,400)(338,402)(339,401)(340,403)(341,405)(342,404)(343,388)(344,390)
(345,389)(346,391)(347,393)(348,392)(349,394)(350,396)(351,395)(352,406)
(353,408)(354,407)(355,409)(356,411)(357,410)(358,412)(359,414)(360,413)
(361,424)(362,426)(363,425)(364,427)(365,429)(366,428)(367,430)(368,432)
(369,431)(370,415)(371,417)(372,416)(373,418)(374,420)(375,419)(376,421)
(377,423)(378,422);;
s2 := ( 1, 10)( 2, 11)( 3, 12)( 4, 18)( 5, 16)( 6, 17)( 7, 14)( 8, 15)
( 9, 13)( 22, 27)( 23, 25)( 24, 26)( 28, 37)( 29, 38)( 30, 39)( 31, 45)
( 32, 43)( 33, 44)( 34, 41)( 35, 42)( 36, 40)( 49, 54)( 50, 52)( 51, 53)
( 55, 64)( 56, 65)( 57, 66)( 58, 72)( 59, 70)( 60, 71)( 61, 68)( 62, 69)
( 63, 67)( 76, 81)( 77, 79)( 78, 80)( 82, 91)( 83, 92)( 84, 93)( 85, 99)
( 86, 97)( 87, 98)( 88, 95)( 89, 96)( 90, 94)(103,108)(104,106)(105,107)
(109,118)(110,119)(111,120)(112,126)(113,124)(114,125)(115,122)(116,123)
(117,121)(130,135)(131,133)(132,134)(136,145)(137,146)(138,147)(139,153)
(140,151)(141,152)(142,149)(143,150)(144,148)(157,162)(158,160)(159,161)
(163,172)(164,173)(165,174)(166,180)(167,178)(168,179)(169,176)(170,177)
(171,175)(184,189)(185,187)(186,188)(190,199)(191,200)(192,201)(193,207)
(194,205)(195,206)(196,203)(197,204)(198,202)(211,216)(212,214)(213,215)
(217,226)(218,227)(219,228)(220,234)(221,232)(222,233)(223,230)(224,231)
(225,229)(238,243)(239,241)(240,242)(244,253)(245,254)(246,255)(247,261)
(248,259)(249,260)(250,257)(251,258)(252,256)(265,270)(266,268)(267,269)
(271,280)(272,281)(273,282)(274,288)(275,286)(276,287)(277,284)(278,285)
(279,283)(292,297)(293,295)(294,296)(298,307)(299,308)(300,309)(301,315)
(302,313)(303,314)(304,311)(305,312)(306,310)(319,324)(320,322)(321,323)
(325,334)(326,335)(327,336)(328,342)(329,340)(330,341)(331,338)(332,339)
(333,337)(346,351)(347,349)(348,350)(352,361)(353,362)(354,363)(355,369)
(356,367)(357,368)(358,365)(359,366)(360,364)(373,378)(374,376)(375,377)
(379,388)(380,389)(381,390)(382,396)(383,394)(384,395)(385,392)(386,393)
(387,391)(400,405)(401,403)(402,404)(406,415)(407,416)(408,417)(409,423)
(410,421)(411,422)(412,419)(413,420)(414,418)(427,432)(428,430)(429,431);;
s3 := ( 1,220)( 2,221)( 3,222)( 4,217)( 5,218)( 6,219)( 7,223)( 8,224)
( 9,225)( 10,238)( 11,239)( 12,240)( 13,235)( 14,236)( 15,237)( 16,241)
( 17,242)( 18,243)( 19,229)( 20,230)( 21,231)( 22,226)( 23,227)( 24,228)
( 25,232)( 26,233)( 27,234)( 28,247)( 29,248)( 30,249)( 31,244)( 32,245)
( 33,246)( 34,250)( 35,251)( 36,252)( 37,265)( 38,266)( 39,267)( 40,262)
( 41,263)( 42,264)( 43,268)( 44,269)( 45,270)( 46,256)( 47,257)( 48,258)
( 49,253)( 50,254)( 51,255)( 52,259)( 53,260)( 54,261)( 55,274)( 56,275)
( 57,276)( 58,271)( 59,272)( 60,273)( 61,277)( 62,278)( 63,279)( 64,292)
( 65,293)( 66,294)( 67,289)( 68,290)( 69,291)( 70,295)( 71,296)( 72,297)
( 73,283)( 74,284)( 75,285)( 76,280)( 77,281)( 78,282)( 79,286)( 80,287)
( 81,288)( 82,301)( 83,302)( 84,303)( 85,298)( 86,299)( 87,300)( 88,304)
( 89,305)( 90,306)( 91,319)( 92,320)( 93,321)( 94,316)( 95,317)( 96,318)
( 97,322)( 98,323)( 99,324)(100,310)(101,311)(102,312)(103,307)(104,308)
(105,309)(106,313)(107,314)(108,315)(109,328)(110,329)(111,330)(112,325)
(113,326)(114,327)(115,331)(116,332)(117,333)(118,346)(119,347)(120,348)
(121,343)(122,344)(123,345)(124,349)(125,350)(126,351)(127,337)(128,338)
(129,339)(130,334)(131,335)(132,336)(133,340)(134,341)(135,342)(136,355)
(137,356)(138,357)(139,352)(140,353)(141,354)(142,358)(143,359)(144,360)
(145,373)(146,374)(147,375)(148,370)(149,371)(150,372)(151,376)(152,377)
(153,378)(154,364)(155,365)(156,366)(157,361)(158,362)(159,363)(160,367)
(161,368)(162,369)(163,382)(164,383)(165,384)(166,379)(167,380)(168,381)
(169,385)(170,386)(171,387)(172,400)(173,401)(174,402)(175,397)(176,398)
(177,399)(178,403)(179,404)(180,405)(181,391)(182,392)(183,393)(184,388)
(185,389)(186,390)(187,394)(188,395)(189,396)(190,409)(191,410)(192,411)
(193,406)(194,407)(195,408)(196,412)(197,413)(198,414)(199,427)(200,428)
(201,429)(202,424)(203,425)(204,426)(205,430)(206,431)(207,432)(208,418)
(209,419)(210,420)(211,415)(212,416)(213,417)(214,421)(215,422)(216,423);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*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,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1,109)( 2,110)( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)
( 8,116)( 9,117)( 10,118)( 11,119)( 12,120)( 13,121)( 14,122)( 15,123)
( 16,124)( 17,125)( 18,126)( 19,127)( 20,128)( 21,129)( 22,130)( 23,131)
( 24,132)( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)
( 32,140)( 33,141)( 34,142)( 35,143)( 36,144)( 37,145)( 38,146)( 39,147)
( 40,148)( 41,149)( 42,150)( 43,151)( 44,152)( 45,153)( 46,154)( 47,155)
( 48,156)( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,190)
( 56,191)( 57,192)( 58,193)( 59,194)( 60,195)( 61,196)( 62,197)( 63,198)
( 64,199)( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)
( 72,207)( 73,208)( 74,209)( 75,210)( 76,211)( 77,212)( 78,213)( 79,214)
( 80,215)( 81,216)( 82,163)( 83,164)( 84,165)( 85,166)( 86,167)( 87,168)
( 88,169)( 89,170)( 90,171)( 91,172)( 92,173)( 93,174)( 94,175)( 95,176)
( 96,177)( 97,178)( 98,179)( 99,180)(100,181)(101,182)(102,183)(103,184)
(104,185)(105,186)(106,187)(107,188)(108,189)(217,325)(218,326)(219,327)
(220,328)(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)
(228,336)(229,337)(230,338)(231,339)(232,340)(233,341)(234,342)(235,343)
(236,344)(237,345)(238,346)(239,347)(240,348)(241,349)(242,350)(243,351)
(244,352)(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)
(252,360)(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)
(260,368)(261,369)(262,370)(263,371)(264,372)(265,373)(266,374)(267,375)
(268,376)(269,377)(270,378)(271,406)(272,407)(273,408)(274,409)(275,410)
(276,411)(277,412)(278,413)(279,414)(280,415)(281,416)(282,417)(283,418)
(284,419)(285,420)(286,421)(287,422)(288,423)(289,424)(290,425)(291,426)
(292,427)(293,428)(294,429)(295,430)(296,431)(297,432)(298,379)(299,380)
(300,381)(301,382)(302,383)(303,384)(304,385)(305,386)(306,387)(307,388)
(308,389)(309,390)(310,391)(311,392)(312,393)(313,394)(314,395)(315,396)
(316,397)(317,398)(318,399)(319,400)(320,401)(321,402)(322,403)(323,404)
(324,405);
s1 := Sym(432)!( 2, 3)( 5, 6)( 8, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)
( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)
( 37, 46)( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)
( 45, 53)( 55, 82)( 56, 84)( 57, 83)( 58, 85)( 59, 87)( 60, 86)( 61, 88)
( 62, 90)( 63, 89)( 64,100)( 65,102)( 66,101)( 67,103)( 68,105)( 69,104)
( 70,106)( 71,108)( 72,107)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)
( 78, 95)( 79, 97)( 80, 99)( 81, 98)(109,163)(110,165)(111,164)(112,166)
(113,168)(114,167)(115,169)(116,171)(117,170)(118,181)(119,183)(120,182)
(121,184)(122,186)(123,185)(124,187)(125,189)(126,188)(127,172)(128,174)
(129,173)(130,175)(131,177)(132,176)(133,178)(134,180)(135,179)(136,190)
(137,192)(138,191)(139,193)(140,195)(141,194)(142,196)(143,198)(144,197)
(145,208)(146,210)(147,209)(148,211)(149,213)(150,212)(151,214)(152,216)
(153,215)(154,199)(155,201)(156,200)(157,202)(158,204)(159,203)(160,205)
(161,207)(162,206)(218,219)(221,222)(224,225)(226,235)(227,237)(228,236)
(229,238)(230,240)(231,239)(232,241)(233,243)(234,242)(245,246)(248,249)
(251,252)(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)
(260,270)(261,269)(271,298)(272,300)(273,299)(274,301)(275,303)(276,302)
(277,304)(278,306)(279,305)(280,316)(281,318)(282,317)(283,319)(284,321)
(285,320)(286,322)(287,324)(288,323)(289,307)(290,309)(291,308)(292,310)
(293,312)(294,311)(295,313)(296,315)(297,314)(325,379)(326,381)(327,380)
(328,382)(329,384)(330,383)(331,385)(332,387)(333,386)(334,397)(335,399)
(336,398)(337,400)(338,402)(339,401)(340,403)(341,405)(342,404)(343,388)
(344,390)(345,389)(346,391)(347,393)(348,392)(349,394)(350,396)(351,395)
(352,406)(353,408)(354,407)(355,409)(356,411)(357,410)(358,412)(359,414)
(360,413)(361,424)(362,426)(363,425)(364,427)(365,429)(366,428)(367,430)
(368,432)(369,431)(370,415)(371,417)(372,416)(373,418)(374,420)(375,419)
(376,421)(377,423)(378,422);
s2 := Sym(432)!( 1, 10)( 2, 11)( 3, 12)( 4, 18)( 5, 16)( 6, 17)( 7, 14)
( 8, 15)( 9, 13)( 22, 27)( 23, 25)( 24, 26)( 28, 37)( 29, 38)( 30, 39)
( 31, 45)( 32, 43)( 33, 44)( 34, 41)( 35, 42)( 36, 40)( 49, 54)( 50, 52)
( 51, 53)( 55, 64)( 56, 65)( 57, 66)( 58, 72)( 59, 70)( 60, 71)( 61, 68)
( 62, 69)( 63, 67)( 76, 81)( 77, 79)( 78, 80)( 82, 91)( 83, 92)( 84, 93)
( 85, 99)( 86, 97)( 87, 98)( 88, 95)( 89, 96)( 90, 94)(103,108)(104,106)
(105,107)(109,118)(110,119)(111,120)(112,126)(113,124)(114,125)(115,122)
(116,123)(117,121)(130,135)(131,133)(132,134)(136,145)(137,146)(138,147)
(139,153)(140,151)(141,152)(142,149)(143,150)(144,148)(157,162)(158,160)
(159,161)(163,172)(164,173)(165,174)(166,180)(167,178)(168,179)(169,176)
(170,177)(171,175)(184,189)(185,187)(186,188)(190,199)(191,200)(192,201)
(193,207)(194,205)(195,206)(196,203)(197,204)(198,202)(211,216)(212,214)
(213,215)(217,226)(218,227)(219,228)(220,234)(221,232)(222,233)(223,230)
(224,231)(225,229)(238,243)(239,241)(240,242)(244,253)(245,254)(246,255)
(247,261)(248,259)(249,260)(250,257)(251,258)(252,256)(265,270)(266,268)
(267,269)(271,280)(272,281)(273,282)(274,288)(275,286)(276,287)(277,284)
(278,285)(279,283)(292,297)(293,295)(294,296)(298,307)(299,308)(300,309)
(301,315)(302,313)(303,314)(304,311)(305,312)(306,310)(319,324)(320,322)
(321,323)(325,334)(326,335)(327,336)(328,342)(329,340)(330,341)(331,338)
(332,339)(333,337)(346,351)(347,349)(348,350)(352,361)(353,362)(354,363)
(355,369)(356,367)(357,368)(358,365)(359,366)(360,364)(373,378)(374,376)
(375,377)(379,388)(380,389)(381,390)(382,396)(383,394)(384,395)(385,392)
(386,393)(387,391)(400,405)(401,403)(402,404)(406,415)(407,416)(408,417)
(409,423)(410,421)(411,422)(412,419)(413,420)(414,418)(427,432)(428,430)
(429,431);
s3 := Sym(432)!( 1,220)( 2,221)( 3,222)( 4,217)( 5,218)( 6,219)( 7,223)
( 8,224)( 9,225)( 10,238)( 11,239)( 12,240)( 13,235)( 14,236)( 15,237)
( 16,241)( 17,242)( 18,243)( 19,229)( 20,230)( 21,231)( 22,226)( 23,227)
( 24,228)( 25,232)( 26,233)( 27,234)( 28,247)( 29,248)( 30,249)( 31,244)
( 32,245)( 33,246)( 34,250)( 35,251)( 36,252)( 37,265)( 38,266)( 39,267)
( 40,262)( 41,263)( 42,264)( 43,268)( 44,269)( 45,270)( 46,256)( 47,257)
( 48,258)( 49,253)( 50,254)( 51,255)( 52,259)( 53,260)( 54,261)( 55,274)
( 56,275)( 57,276)( 58,271)( 59,272)( 60,273)( 61,277)( 62,278)( 63,279)
( 64,292)( 65,293)( 66,294)( 67,289)( 68,290)( 69,291)( 70,295)( 71,296)
( 72,297)( 73,283)( 74,284)( 75,285)( 76,280)( 77,281)( 78,282)( 79,286)
( 80,287)( 81,288)( 82,301)( 83,302)( 84,303)( 85,298)( 86,299)( 87,300)
( 88,304)( 89,305)( 90,306)( 91,319)( 92,320)( 93,321)( 94,316)( 95,317)
( 96,318)( 97,322)( 98,323)( 99,324)(100,310)(101,311)(102,312)(103,307)
(104,308)(105,309)(106,313)(107,314)(108,315)(109,328)(110,329)(111,330)
(112,325)(113,326)(114,327)(115,331)(116,332)(117,333)(118,346)(119,347)
(120,348)(121,343)(122,344)(123,345)(124,349)(125,350)(126,351)(127,337)
(128,338)(129,339)(130,334)(131,335)(132,336)(133,340)(134,341)(135,342)
(136,355)(137,356)(138,357)(139,352)(140,353)(141,354)(142,358)(143,359)
(144,360)(145,373)(146,374)(147,375)(148,370)(149,371)(150,372)(151,376)
(152,377)(153,378)(154,364)(155,365)(156,366)(157,361)(158,362)(159,363)
(160,367)(161,368)(162,369)(163,382)(164,383)(165,384)(166,379)(167,380)
(168,381)(169,385)(170,386)(171,387)(172,400)(173,401)(174,402)(175,397)
(176,398)(177,399)(178,403)(179,404)(180,405)(181,391)(182,392)(183,393)
(184,388)(185,389)(186,390)(187,394)(188,395)(189,396)(190,409)(191,410)
(192,411)(193,406)(194,407)(195,408)(196,412)(197,413)(198,414)(199,427)
(200,428)(201,429)(202,424)(203,425)(204,426)(205,430)(206,431)(207,432)
(208,418)(209,419)(210,420)(211,415)(212,416)(213,417)(214,421)(215,422)
(216,423);
poly := sub<Sym(432)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*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,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2 >;
References : None.
to this polytope