Polytope of Type {8,6,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,18}*1728b
if this polytope has a name.
Group : SmallGroup(1728,17171)
Rank : 4
Schlafli Type : {8,6,18}
Number of vertices, edges, etc : 8, 24, 54, 18
Order of s0s1s2s3 : 72
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 : {8,6,9}*864, {4,6,18}*864b
3-fold quotients : {8,2,18}*576, {8,6,6}*576c
4-fold quotients : {4,6,9}*432, {2,6,18}*432b
6-fold quotients : {8,2,9}*288, {4,2,18}*288, {8,6,3}*288, {4,6,6}*288c
8-fold quotients : {2,6,9}*216
9-fold quotients : {8,2,6}*192
12-fold quotients : {4,2,9}*144, {2,2,18}*144, {4,6,3}*144, {2,6,6}*144b
18-fold quotients : {8,2,3}*96, {4,2,6}*96
24-fold quotients : {2,2,9}*72, {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 := ( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)
( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)
( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)( 60, 90)
( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)( 68, 98)
( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)( 76,106)
( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(109,163)(110,164)(111,165)
(112,169)(113,170)(114,171)(115,166)(116,167)(117,168)(118,172)(119,173)
(120,174)(121,178)(122,179)(123,180)(124,175)(125,176)(126,177)(127,181)
(128,182)(129,183)(130,187)(131,188)(132,189)(133,184)(134,185)(135,186)
(136,190)(137,191)(138,192)(139,196)(140,197)(141,198)(142,193)(143,194)
(144,195)(145,199)(146,200)(147,201)(148,205)(149,206)(150,207)(151,202)
(152,203)(153,204)(154,208)(155,209)(156,210)(157,214)(158,215)(159,216)
(160,211)(161,212)(162,213)(220,223)(221,224)(222,225)(229,232)(230,233)
(231,234)(238,241)(239,242)(240,243)(247,250)(248,251)(249,252)(256,259)
(257,260)(258,261)(265,268)(266,269)(267,270)(271,298)(272,299)(273,300)
(274,304)(275,305)(276,306)(277,301)(278,302)(279,303)(280,307)(281,308)
(282,309)(283,313)(284,314)(285,315)(286,310)(287,311)(288,312)(289,316)
(290,317)(291,318)(292,322)(293,323)(294,324)(295,319)(296,320)(297,321)
(325,379)(326,380)(327,381)(328,385)(329,386)(330,387)(331,382)(332,383)
(333,384)(334,388)(335,389)(336,390)(337,394)(338,395)(339,396)(340,391)
(341,392)(342,393)(343,397)(344,398)(345,399)(346,403)(347,404)(348,405)
(349,400)(350,401)(351,402)(352,406)(353,407)(354,408)(355,412)(356,413)
(357,414)(358,409)(359,410)(360,411)(361,415)(362,416)(363,417)(364,421)
(365,422)(366,423)(367,418)(368,419)(369,420)(370,424)(371,425)(372,426)
(373,430)(374,431)(375,432)(376,427)(377,428)(378,429);;
s2 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 24)( 11, 23)( 12, 22)( 13, 21)
( 14, 20)( 15, 19)( 16, 27)( 17, 26)( 18, 25)( 28, 31)( 29, 33)( 30, 32)
( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 54)
( 44, 53)( 45, 52)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 78)( 65, 77)
( 66, 76)( 67, 75)( 68, 74)( 69, 73)( 70, 81)( 71, 80)( 72, 79)( 82, 85)
( 83, 87)( 84, 86)( 89, 90)( 91,105)( 92,104)( 93,103)( 94,102)( 95,101)
( 96,100)( 97,108)( 98,107)( 99,106)(109,112)(110,114)(111,113)(116,117)
(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,135)(125,134)
(126,133)(136,139)(137,141)(138,140)(143,144)(145,159)(146,158)(147,157)
(148,156)(149,155)(150,154)(151,162)(152,161)(153,160)(163,166)(164,168)
(165,167)(170,171)(172,186)(173,185)(174,184)(175,183)(176,182)(177,181)
(178,189)(179,188)(180,187)(190,193)(191,195)(192,194)(197,198)(199,213)
(200,212)(201,211)(202,210)(203,209)(204,208)(205,216)(206,215)(207,214)
(217,220)(218,222)(219,221)(224,225)(226,240)(227,239)(228,238)(229,237)
(230,236)(231,235)(232,243)(233,242)(234,241)(244,247)(245,249)(246,248)
(251,252)(253,267)(254,266)(255,265)(256,264)(257,263)(258,262)(259,270)
(260,269)(261,268)(271,274)(272,276)(273,275)(278,279)(280,294)(281,293)
(282,292)(283,291)(284,290)(285,289)(286,297)(287,296)(288,295)(298,301)
(299,303)(300,302)(305,306)(307,321)(308,320)(309,319)(310,318)(311,317)
(312,316)(313,324)(314,323)(315,322)(325,328)(326,330)(327,329)(332,333)
(334,348)(335,347)(336,346)(337,345)(338,344)(339,343)(340,351)(341,350)
(342,349)(352,355)(353,357)(354,356)(359,360)(361,375)(362,374)(363,373)
(364,372)(365,371)(366,370)(367,378)(368,377)(369,376)(379,382)(380,384)
(381,383)(386,387)(388,402)(389,401)(390,400)(391,399)(392,398)(393,397)
(394,405)(395,404)(396,403)(406,409)(407,411)(408,410)(413,414)(415,429)
(416,428)(417,427)(418,426)(419,425)(420,424)(421,432)(422,431)(423,430);;
s3 := ( 1,226)( 2,228)( 3,227)( 4,232)( 5,234)( 6,233)( 7,229)( 8,231)
( 9,230)( 10,217)( 11,219)( 12,218)( 13,223)( 14,225)( 15,224)( 16,220)
( 17,222)( 18,221)( 19,237)( 20,236)( 21,235)( 22,243)( 23,242)( 24,241)
( 25,240)( 26,239)( 27,238)( 28,253)( 29,255)( 30,254)( 31,259)( 32,261)
( 33,260)( 34,256)( 35,258)( 36,257)( 37,244)( 38,246)( 39,245)( 40,250)
( 41,252)( 42,251)( 43,247)( 44,249)( 45,248)( 46,264)( 47,263)( 48,262)
( 49,270)( 50,269)( 51,268)( 52,267)( 53,266)( 54,265)( 55,280)( 56,282)
( 57,281)( 58,286)( 59,288)( 60,287)( 61,283)( 62,285)( 63,284)( 64,271)
( 65,273)( 66,272)( 67,277)( 68,279)( 69,278)( 70,274)( 71,276)( 72,275)
( 73,291)( 74,290)( 75,289)( 76,297)( 77,296)( 78,295)( 79,294)( 80,293)
( 81,292)( 82,307)( 83,309)( 84,308)( 85,313)( 86,315)( 87,314)( 88,310)
( 89,312)( 90,311)( 91,298)( 92,300)( 93,299)( 94,304)( 95,306)( 96,305)
( 97,301)( 98,303)( 99,302)(100,318)(101,317)(102,316)(103,324)(104,323)
(105,322)(106,321)(107,320)(108,319)(109,334)(110,336)(111,335)(112,340)
(113,342)(114,341)(115,337)(116,339)(117,338)(118,325)(119,327)(120,326)
(121,331)(122,333)(123,332)(124,328)(125,330)(126,329)(127,345)(128,344)
(129,343)(130,351)(131,350)(132,349)(133,348)(134,347)(135,346)(136,361)
(137,363)(138,362)(139,367)(140,369)(141,368)(142,364)(143,366)(144,365)
(145,352)(146,354)(147,353)(148,358)(149,360)(150,359)(151,355)(152,357)
(153,356)(154,372)(155,371)(156,370)(157,378)(158,377)(159,376)(160,375)
(161,374)(162,373)(163,388)(164,390)(165,389)(166,394)(167,396)(168,395)
(169,391)(170,393)(171,392)(172,379)(173,381)(174,380)(175,385)(176,387)
(177,386)(178,382)(179,384)(180,383)(181,399)(182,398)(183,397)(184,405)
(185,404)(186,403)(187,402)(188,401)(189,400)(190,415)(191,417)(192,416)
(193,421)(194,423)(195,422)(196,418)(197,420)(198,419)(199,406)(200,408)
(201,407)(202,412)(203,414)(204,413)(205,409)(206,411)(207,410)(208,426)
(209,425)(210,424)(211,432)(212,431)(213,430)(214,429)(215,428)(216,427);;
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,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)
( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)
( 49, 52)( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)
( 60, 90)( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)
( 68, 98)( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)
( 76,106)( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(109,163)(110,164)
(111,165)(112,169)(113,170)(114,171)(115,166)(116,167)(117,168)(118,172)
(119,173)(120,174)(121,178)(122,179)(123,180)(124,175)(125,176)(126,177)
(127,181)(128,182)(129,183)(130,187)(131,188)(132,189)(133,184)(134,185)
(135,186)(136,190)(137,191)(138,192)(139,196)(140,197)(141,198)(142,193)
(143,194)(144,195)(145,199)(146,200)(147,201)(148,205)(149,206)(150,207)
(151,202)(152,203)(153,204)(154,208)(155,209)(156,210)(157,214)(158,215)
(159,216)(160,211)(161,212)(162,213)(220,223)(221,224)(222,225)(229,232)
(230,233)(231,234)(238,241)(239,242)(240,243)(247,250)(248,251)(249,252)
(256,259)(257,260)(258,261)(265,268)(266,269)(267,270)(271,298)(272,299)
(273,300)(274,304)(275,305)(276,306)(277,301)(278,302)(279,303)(280,307)
(281,308)(282,309)(283,313)(284,314)(285,315)(286,310)(287,311)(288,312)
(289,316)(290,317)(291,318)(292,322)(293,323)(294,324)(295,319)(296,320)
(297,321)(325,379)(326,380)(327,381)(328,385)(329,386)(330,387)(331,382)
(332,383)(333,384)(334,388)(335,389)(336,390)(337,394)(338,395)(339,396)
(340,391)(341,392)(342,393)(343,397)(344,398)(345,399)(346,403)(347,404)
(348,405)(349,400)(350,401)(351,402)(352,406)(353,407)(354,408)(355,412)
(356,413)(357,414)(358,409)(359,410)(360,411)(361,415)(362,416)(363,417)
(364,421)(365,422)(366,423)(367,418)(368,419)(369,420)(370,424)(371,425)
(372,426)(373,430)(374,431)(375,432)(376,427)(377,428)(378,429);
s2 := Sym(432)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 24)( 11, 23)( 12, 22)
( 13, 21)( 14, 20)( 15, 19)( 16, 27)( 17, 26)( 18, 25)( 28, 31)( 29, 33)
( 30, 32)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 54)( 44, 53)( 45, 52)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 78)
( 65, 77)( 66, 76)( 67, 75)( 68, 74)( 69, 73)( 70, 81)( 71, 80)( 72, 79)
( 82, 85)( 83, 87)( 84, 86)( 89, 90)( 91,105)( 92,104)( 93,103)( 94,102)
( 95,101)( 96,100)( 97,108)( 98,107)( 99,106)(109,112)(110,114)(111,113)
(116,117)(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,135)
(125,134)(126,133)(136,139)(137,141)(138,140)(143,144)(145,159)(146,158)
(147,157)(148,156)(149,155)(150,154)(151,162)(152,161)(153,160)(163,166)
(164,168)(165,167)(170,171)(172,186)(173,185)(174,184)(175,183)(176,182)
(177,181)(178,189)(179,188)(180,187)(190,193)(191,195)(192,194)(197,198)
(199,213)(200,212)(201,211)(202,210)(203,209)(204,208)(205,216)(206,215)
(207,214)(217,220)(218,222)(219,221)(224,225)(226,240)(227,239)(228,238)
(229,237)(230,236)(231,235)(232,243)(233,242)(234,241)(244,247)(245,249)
(246,248)(251,252)(253,267)(254,266)(255,265)(256,264)(257,263)(258,262)
(259,270)(260,269)(261,268)(271,274)(272,276)(273,275)(278,279)(280,294)
(281,293)(282,292)(283,291)(284,290)(285,289)(286,297)(287,296)(288,295)
(298,301)(299,303)(300,302)(305,306)(307,321)(308,320)(309,319)(310,318)
(311,317)(312,316)(313,324)(314,323)(315,322)(325,328)(326,330)(327,329)
(332,333)(334,348)(335,347)(336,346)(337,345)(338,344)(339,343)(340,351)
(341,350)(342,349)(352,355)(353,357)(354,356)(359,360)(361,375)(362,374)
(363,373)(364,372)(365,371)(366,370)(367,378)(368,377)(369,376)(379,382)
(380,384)(381,383)(386,387)(388,402)(389,401)(390,400)(391,399)(392,398)
(393,397)(394,405)(395,404)(396,403)(406,409)(407,411)(408,410)(413,414)
(415,429)(416,428)(417,427)(418,426)(419,425)(420,424)(421,432)(422,431)
(423,430);
s3 := Sym(432)!( 1,226)( 2,228)( 3,227)( 4,232)( 5,234)( 6,233)( 7,229)
( 8,231)( 9,230)( 10,217)( 11,219)( 12,218)( 13,223)( 14,225)( 15,224)
( 16,220)( 17,222)( 18,221)( 19,237)( 20,236)( 21,235)( 22,243)( 23,242)
( 24,241)( 25,240)( 26,239)( 27,238)( 28,253)( 29,255)( 30,254)( 31,259)
( 32,261)( 33,260)( 34,256)( 35,258)( 36,257)( 37,244)( 38,246)( 39,245)
( 40,250)( 41,252)( 42,251)( 43,247)( 44,249)( 45,248)( 46,264)( 47,263)
( 48,262)( 49,270)( 50,269)( 51,268)( 52,267)( 53,266)( 54,265)( 55,280)
( 56,282)( 57,281)( 58,286)( 59,288)( 60,287)( 61,283)( 62,285)( 63,284)
( 64,271)( 65,273)( 66,272)( 67,277)( 68,279)( 69,278)( 70,274)( 71,276)
( 72,275)( 73,291)( 74,290)( 75,289)( 76,297)( 77,296)( 78,295)( 79,294)
( 80,293)( 81,292)( 82,307)( 83,309)( 84,308)( 85,313)( 86,315)( 87,314)
( 88,310)( 89,312)( 90,311)( 91,298)( 92,300)( 93,299)( 94,304)( 95,306)
( 96,305)( 97,301)( 98,303)( 99,302)(100,318)(101,317)(102,316)(103,324)
(104,323)(105,322)(106,321)(107,320)(108,319)(109,334)(110,336)(111,335)
(112,340)(113,342)(114,341)(115,337)(116,339)(117,338)(118,325)(119,327)
(120,326)(121,331)(122,333)(123,332)(124,328)(125,330)(126,329)(127,345)
(128,344)(129,343)(130,351)(131,350)(132,349)(133,348)(134,347)(135,346)
(136,361)(137,363)(138,362)(139,367)(140,369)(141,368)(142,364)(143,366)
(144,365)(145,352)(146,354)(147,353)(148,358)(149,360)(150,359)(151,355)
(152,357)(153,356)(154,372)(155,371)(156,370)(157,378)(158,377)(159,376)
(160,375)(161,374)(162,373)(163,388)(164,390)(165,389)(166,394)(167,396)
(168,395)(169,391)(170,393)(171,392)(172,379)(173,381)(174,380)(175,385)
(176,387)(177,386)(178,382)(179,384)(180,383)(181,399)(182,398)(183,397)
(184,405)(185,404)(186,403)(187,402)(188,401)(189,400)(190,415)(191,417)
(192,416)(193,421)(194,423)(195,422)(196,418)(197,420)(198,419)(199,406)
(200,408)(201,407)(202,412)(203,414)(204,413)(205,409)(206,411)(207,410)
(208,426)(209,425)(210,424)(211,432)(212,431)(213,430)(214,429)(215,428)
(216,427);
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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope