Polytope of Type {4,6,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 5
Schlafli Type : {4,6,6,6}
Number of vertices, edges, etc : 4, 12, 18, 18, 6
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Universal
Non-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 : {4,3,6,6}*864a, {4,6,6,3}*864b
3-fold quotients : {4,6,2,6}*576c
4-fold quotients : {4,3,6,3}*432
6-fold quotients : {4,3,2,6}*288, {4,6,2,3}*288c
9-fold quotients : {4,6,2,2}*192c
12-fold quotients : {4,3,2,3}*144
18-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432);;
s1 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 73)
( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 77)
( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 93)
( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 97)
( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)
( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)(116,119)
(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)
(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)
(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)(158,194)
(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)(166,198)
(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)(174,214)
(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(219,220)(221,225)
(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)(236,239)
(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)(255,292)
(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)(263,296)
(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)(271,312)
(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)(279,316)
(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)(287,320)
(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)(341,345)
(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)(356,359)
(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)(368,407)
(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)(376,411)
(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)(384,415)
(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)(392,431)
(393,425)(394,426)(395,428)(396,427);;
s2 := ( 1,253)( 2,256)( 3,255)( 4,254)( 5,261)( 6,264)( 7,263)( 8,262)
( 9,257)( 10,260)( 11,259)( 12,258)( 13,269)( 14,272)( 15,271)( 16,270)
( 17,265)( 18,268)( 19,267)( 20,266)( 21,273)( 22,276)( 23,275)( 24,274)
( 25,285)( 26,288)( 27,287)( 28,286)( 29,281)( 30,284)( 31,283)( 32,282)
( 33,277)( 34,280)( 35,279)( 36,278)( 37,217)( 38,220)( 39,219)( 40,218)
( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)( 48,222)
( 49,233)( 50,236)( 51,235)( 52,234)( 53,229)( 54,232)( 55,231)( 56,230)
( 57,237)( 58,240)( 59,239)( 60,238)( 61,249)( 62,252)( 63,251)( 64,250)
( 65,245)( 66,248)( 67,247)( 68,246)( 69,241)( 70,244)( 71,243)( 72,242)
( 73,289)( 74,292)( 75,291)( 76,290)( 77,297)( 78,300)( 79,299)( 80,298)
( 81,293)( 82,296)( 83,295)( 84,294)( 85,305)( 86,308)( 87,307)( 88,306)
( 89,301)( 90,304)( 91,303)( 92,302)( 93,309)( 94,312)( 95,311)( 96,310)
( 97,321)( 98,324)( 99,323)(100,322)(101,317)(102,320)(103,319)(104,318)
(105,313)(106,316)(107,315)(108,314)(109,361)(110,364)(111,363)(112,362)
(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)(120,366)
(121,377)(122,380)(123,379)(124,378)(125,373)(126,376)(127,375)(128,374)
(129,381)(130,384)(131,383)(132,382)(133,393)(134,396)(135,395)(136,394)
(137,389)(138,392)(139,391)(140,390)(141,385)(142,388)(143,387)(144,386)
(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)(152,334)
(153,329)(154,332)(155,331)(156,330)(157,341)(158,344)(159,343)(160,342)
(161,337)(162,340)(163,339)(164,338)(165,345)(166,348)(167,347)(168,346)
(169,357)(170,360)(171,359)(172,358)(173,353)(174,356)(175,355)(176,354)
(177,349)(178,352)(179,351)(180,350)(181,397)(182,400)(183,399)(184,398)
(185,405)(186,408)(187,407)(188,406)(189,401)(190,404)(191,403)(192,402)
(193,413)(194,416)(195,415)(196,414)(197,409)(198,412)(199,411)(200,410)
(201,417)(202,420)(203,419)(204,418)(205,429)(206,432)(207,431)(208,430)
(209,425)(210,428)(211,427)(212,426)(213,421)(214,424)(215,423)(216,422);;
s3 := ( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 21)( 6, 22)( 7, 23)( 8, 24)
( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 29, 33)( 30, 34)( 31, 35)( 32, 36)
( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)( 44, 60)
( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)( 80, 96)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)(101,105)(102,106)(103,107)(104,108)
(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)(116,132)
(117,125)(118,126)(119,127)(120,128)(137,141)(138,142)(139,143)(140,144)
(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)(152,168)
(153,161)(154,162)(155,163)(156,164)(173,177)(174,178)(175,179)(176,180)
(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)(188,204)
(189,197)(190,198)(191,199)(192,200)(209,213)(210,214)(211,215)(212,216)
(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)(224,240)
(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)(248,252)
(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)(260,276)
(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)(284,288)
(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)(296,312)
(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)(320,324)
(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)(332,348)
(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)(356,360)
(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)(368,384)
(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)(392,396)
(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)(404,420)
(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)(428,432);;
s4 := ( 1,109)( 2,110)( 3,111)( 4,112)( 5,117)( 6,118)( 7,119)( 8,120)
( 9,113)( 10,114)( 11,115)( 12,116)( 13,133)( 14,134)( 15,135)( 16,136)
( 17,141)( 18,142)( 19,143)( 20,144)( 21,137)( 22,138)( 23,139)( 24,140)
( 25,121)( 26,122)( 27,123)( 28,124)( 29,129)( 30,130)( 31,131)( 32,132)
( 33,125)( 34,126)( 35,127)( 36,128)( 37,145)( 38,146)( 39,147)( 40,148)
( 41,153)( 42,154)( 43,155)( 44,156)( 45,149)( 46,150)( 47,151)( 48,152)
( 49,169)( 50,170)( 51,171)( 52,172)( 53,177)( 54,178)( 55,179)( 56,180)
( 57,173)( 58,174)( 59,175)( 60,176)( 61,157)( 62,158)( 63,159)( 64,160)
( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)( 72,164)
( 73,181)( 74,182)( 75,183)( 76,184)( 77,189)( 78,190)( 79,191)( 80,192)
( 81,185)( 82,186)( 83,187)( 84,188)( 85,205)( 86,206)( 87,207)( 88,208)
( 89,213)( 90,214)( 91,215)( 92,216)( 93,209)( 94,210)( 95,211)( 96,212)
( 97,193)( 98,194)( 99,195)(100,196)(101,201)(102,202)(103,203)(104,204)
(105,197)(106,198)(107,199)(108,200)(217,325)(218,326)(219,327)(220,328)
(221,333)(222,334)(223,335)(224,336)(225,329)(226,330)(227,331)(228,332)
(229,349)(230,350)(231,351)(232,352)(233,357)(234,358)(235,359)(236,360)
(237,353)(238,354)(239,355)(240,356)(241,337)(242,338)(243,339)(244,340)
(245,345)(246,346)(247,347)(248,348)(249,341)(250,342)(251,343)(252,344)
(253,361)(254,362)(255,363)(256,364)(257,369)(258,370)(259,371)(260,372)
(261,365)(262,366)(263,367)(264,368)(265,385)(266,386)(267,387)(268,388)
(269,393)(270,394)(271,395)(272,396)(273,389)(274,390)(275,391)(276,392)
(277,373)(278,374)(279,375)(280,376)(281,381)(282,382)(283,383)(284,384)
(285,377)(286,378)(287,379)(288,380)(289,397)(290,398)(291,399)(292,400)
(293,405)(294,406)(295,407)(296,408)(297,401)(298,402)(299,403)(300,404)
(301,421)(302,422)(303,423)(304,424)(305,429)(306,430)(307,431)(308,432)
(309,425)(310,426)(311,427)(312,428)(313,409)(314,410)(315,411)(316,412)
(317,417)(318,418)(319,419)(320,420)(321,413)(322,414)(323,415)(324,416);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432);
s1 := Sym(432)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)
( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)
( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)
( 45, 77)( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)
( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)
( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)
( 69,101)( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)
(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)
(138,142)(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)
(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)
(158,194)(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)
(166,198)(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)
(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(219,220)
(221,225)(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)
(236,239)(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)
(255,292)(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)
(263,296)(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)
(271,312)(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)
(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)
(287,320)(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)
(341,345)(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)
(356,359)(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)
(368,407)(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)
(376,411)(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)
(384,415)(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)
(392,431)(393,425)(394,426)(395,428)(396,427);
s2 := Sym(432)!( 1,253)( 2,256)( 3,255)( 4,254)( 5,261)( 6,264)( 7,263)
( 8,262)( 9,257)( 10,260)( 11,259)( 12,258)( 13,269)( 14,272)( 15,271)
( 16,270)( 17,265)( 18,268)( 19,267)( 20,266)( 21,273)( 22,276)( 23,275)
( 24,274)( 25,285)( 26,288)( 27,287)( 28,286)( 29,281)( 30,284)( 31,283)
( 32,282)( 33,277)( 34,280)( 35,279)( 36,278)( 37,217)( 38,220)( 39,219)
( 40,218)( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)
( 48,222)( 49,233)( 50,236)( 51,235)( 52,234)( 53,229)( 54,232)( 55,231)
( 56,230)( 57,237)( 58,240)( 59,239)( 60,238)( 61,249)( 62,252)( 63,251)
( 64,250)( 65,245)( 66,248)( 67,247)( 68,246)( 69,241)( 70,244)( 71,243)
( 72,242)( 73,289)( 74,292)( 75,291)( 76,290)( 77,297)( 78,300)( 79,299)
( 80,298)( 81,293)( 82,296)( 83,295)( 84,294)( 85,305)( 86,308)( 87,307)
( 88,306)( 89,301)( 90,304)( 91,303)( 92,302)( 93,309)( 94,312)( 95,311)
( 96,310)( 97,321)( 98,324)( 99,323)(100,322)(101,317)(102,320)(103,319)
(104,318)(105,313)(106,316)(107,315)(108,314)(109,361)(110,364)(111,363)
(112,362)(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)
(120,366)(121,377)(122,380)(123,379)(124,378)(125,373)(126,376)(127,375)
(128,374)(129,381)(130,384)(131,383)(132,382)(133,393)(134,396)(135,395)
(136,394)(137,389)(138,392)(139,391)(140,390)(141,385)(142,388)(143,387)
(144,386)(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)
(152,334)(153,329)(154,332)(155,331)(156,330)(157,341)(158,344)(159,343)
(160,342)(161,337)(162,340)(163,339)(164,338)(165,345)(166,348)(167,347)
(168,346)(169,357)(170,360)(171,359)(172,358)(173,353)(174,356)(175,355)
(176,354)(177,349)(178,352)(179,351)(180,350)(181,397)(182,400)(183,399)
(184,398)(185,405)(186,408)(187,407)(188,406)(189,401)(190,404)(191,403)
(192,402)(193,413)(194,416)(195,415)(196,414)(197,409)(198,412)(199,411)
(200,410)(201,417)(202,420)(203,419)(204,418)(205,429)(206,432)(207,431)
(208,430)(209,425)(210,428)(211,427)(212,426)(213,421)(214,424)(215,423)
(216,422);
s3 := Sym(432)!( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 21)( 6, 22)( 7, 23)
( 8, 24)( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 29, 33)( 30, 34)( 31, 35)
( 32, 36)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)
( 44, 60)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)
( 80, 96)( 81, 89)( 82, 90)( 83, 91)( 84, 92)(101,105)(102,106)(103,107)
(104,108)(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)
(116,132)(117,125)(118,126)(119,127)(120,128)(137,141)(138,142)(139,143)
(140,144)(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)
(152,168)(153,161)(154,162)(155,163)(156,164)(173,177)(174,178)(175,179)
(176,180)(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)
(188,204)(189,197)(190,198)(191,199)(192,200)(209,213)(210,214)(211,215)
(212,216)(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)
(224,240)(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)
(248,252)(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)
(260,276)(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)
(284,288)(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)
(296,312)(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)
(320,324)(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)
(332,348)(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)
(356,360)(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)
(368,384)(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)
(392,396)(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)
(404,420)(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)
(428,432);
s4 := Sym(432)!( 1,109)( 2,110)( 3,111)( 4,112)( 5,117)( 6,118)( 7,119)
( 8,120)( 9,113)( 10,114)( 11,115)( 12,116)( 13,133)( 14,134)( 15,135)
( 16,136)( 17,141)( 18,142)( 19,143)( 20,144)( 21,137)( 22,138)( 23,139)
( 24,140)( 25,121)( 26,122)( 27,123)( 28,124)( 29,129)( 30,130)( 31,131)
( 32,132)( 33,125)( 34,126)( 35,127)( 36,128)( 37,145)( 38,146)( 39,147)
( 40,148)( 41,153)( 42,154)( 43,155)( 44,156)( 45,149)( 46,150)( 47,151)
( 48,152)( 49,169)( 50,170)( 51,171)( 52,172)( 53,177)( 54,178)( 55,179)
( 56,180)( 57,173)( 58,174)( 59,175)( 60,176)( 61,157)( 62,158)( 63,159)
( 64,160)( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)
( 72,164)( 73,181)( 74,182)( 75,183)( 76,184)( 77,189)( 78,190)( 79,191)
( 80,192)( 81,185)( 82,186)( 83,187)( 84,188)( 85,205)( 86,206)( 87,207)
( 88,208)( 89,213)( 90,214)( 91,215)( 92,216)( 93,209)( 94,210)( 95,211)
( 96,212)( 97,193)( 98,194)( 99,195)(100,196)(101,201)(102,202)(103,203)
(104,204)(105,197)(106,198)(107,199)(108,200)(217,325)(218,326)(219,327)
(220,328)(221,333)(222,334)(223,335)(224,336)(225,329)(226,330)(227,331)
(228,332)(229,349)(230,350)(231,351)(232,352)(233,357)(234,358)(235,359)
(236,360)(237,353)(238,354)(239,355)(240,356)(241,337)(242,338)(243,339)
(244,340)(245,345)(246,346)(247,347)(248,348)(249,341)(250,342)(251,343)
(252,344)(253,361)(254,362)(255,363)(256,364)(257,369)(258,370)(259,371)
(260,372)(261,365)(262,366)(263,367)(264,368)(265,385)(266,386)(267,387)
(268,388)(269,393)(270,394)(271,395)(272,396)(273,389)(274,390)(275,391)
(276,392)(277,373)(278,374)(279,375)(280,376)(281,381)(282,382)(283,383)
(284,384)(285,377)(286,378)(287,379)(288,380)(289,397)(290,398)(291,399)
(292,400)(293,405)(294,406)(295,407)(296,408)(297,401)(298,402)(299,403)
(300,404)(301,421)(302,422)(303,423)(304,424)(305,429)(306,430)(307,431)
(308,432)(309,425)(310,426)(311,427)(312,428)(313,409)(314,410)(315,411)
(316,412)(317,417)(318,418)(319,419)(320,420)(321,413)(322,414)(323,415)
(324,416);
poly := sub<Sym(432)|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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope