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Polytope of Type {6,6,8}

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