Polytope of Type {4,12,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,18}*1728e
if this polytope has a name.
Group : SmallGroup(1728,46098)
Rank : 4
Schlafli Type : {4,12,18}
Number of vertices, edges, etc : 4, 24, 108, 18
Order of s0s1s2s3 : 9
Order of s0s1s2s3s2s1 : 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) :
3-fold quotients : {4,12,6}*576h
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)
(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)
(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)
(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432);;
s1 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 15)( 10, 16)( 11, 13)( 12, 14)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 31)( 26, 32)( 27, 29)( 28, 30)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)
( 49, 99)( 50,100)( 51, 97)( 52, 98)( 53,103)( 54,104)( 55,101)( 56,102)
( 57,111)( 58,112)( 59,109)( 60,110)( 61,107)( 62,108)( 63,105)( 64,106)
( 65,115)( 66,116)( 67,113)( 68,114)( 69,119)( 70,120)( 71,117)( 72,118)
( 73,127)( 74,128)( 75,125)( 76,126)( 77,123)( 78,124)( 79,121)( 80,122)
( 81,131)( 82,132)( 83,129)( 84,130)( 85,135)( 86,136)( 87,133)( 88,134)
( 89,143)( 90,144)( 91,141)( 92,142)( 93,139)( 94,140)( 95,137)( 96,138)
(145,147)(146,148)(149,151)(150,152)(153,159)(154,160)(155,157)(156,158)
(161,163)(162,164)(165,167)(166,168)(169,175)(170,176)(171,173)(172,174)
(177,179)(178,180)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)
(193,243)(194,244)(195,241)(196,242)(197,247)(198,248)(199,245)(200,246)
(201,255)(202,256)(203,253)(204,254)(205,251)(206,252)(207,249)(208,250)
(209,259)(210,260)(211,257)(212,258)(213,263)(214,264)(215,261)(216,262)
(217,271)(218,272)(219,269)(220,270)(221,267)(222,268)(223,265)(224,266)
(225,275)(226,276)(227,273)(228,274)(229,279)(230,280)(231,277)(232,278)
(233,287)(234,288)(235,285)(236,286)(237,283)(238,284)(239,281)(240,282)
(289,291)(290,292)(293,295)(294,296)(297,303)(298,304)(299,301)(300,302)
(305,307)(306,308)(309,311)(310,312)(313,319)(314,320)(315,317)(316,318)
(321,323)(322,324)(325,327)(326,328)(329,335)(330,336)(331,333)(332,334)
(337,387)(338,388)(339,385)(340,386)(341,391)(342,392)(343,389)(344,390)
(345,399)(346,400)(347,397)(348,398)(349,395)(350,396)(351,393)(352,394)
(353,403)(354,404)(355,401)(356,402)(357,407)(358,408)(359,405)(360,406)
(361,415)(362,416)(363,413)(364,414)(365,411)(366,412)(367,409)(368,410)
(369,419)(370,420)(371,417)(372,418)(373,423)(374,424)(375,421)(376,422)
(377,431)(378,432)(379,429)(380,430)(381,427)(382,428)(383,425)(384,426);;
s2 := ( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 61)( 6, 62)( 7, 64)( 8, 63)
( 9, 57)( 10, 58)( 11, 60)( 12, 59)( 13, 53)( 14, 54)( 15, 56)( 16, 55)
( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 93)( 22, 94)( 23, 96)( 24, 95)
( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)( 32, 87)
( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)( 40, 79)
( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)( 48, 71)
( 99,100)(101,109)(102,110)(103,112)(104,111)(107,108)(113,129)(114,130)
(115,132)(116,131)(117,141)(118,142)(119,144)(120,143)(121,137)(122,138)
(123,140)(124,139)(125,133)(126,134)(127,136)(128,135)(145,369)(146,370)
(147,372)(148,371)(149,381)(150,382)(151,384)(152,383)(153,377)(154,378)
(155,380)(156,379)(157,373)(158,374)(159,376)(160,375)(161,353)(162,354)
(163,356)(164,355)(165,365)(166,366)(167,368)(168,367)(169,361)(170,362)
(171,364)(172,363)(173,357)(174,358)(175,360)(176,359)(177,337)(178,338)
(179,340)(180,339)(181,349)(182,350)(183,352)(184,351)(185,345)(186,346)
(187,348)(188,347)(189,341)(190,342)(191,344)(192,343)(193,321)(194,322)
(195,324)(196,323)(197,333)(198,334)(199,336)(200,335)(201,329)(202,330)
(203,332)(204,331)(205,325)(206,326)(207,328)(208,327)(209,305)(210,306)
(211,308)(212,307)(213,317)(214,318)(215,320)(216,319)(217,313)(218,314)
(219,316)(220,315)(221,309)(222,310)(223,312)(224,311)(225,289)(226,290)
(227,292)(228,291)(229,301)(230,302)(231,304)(232,303)(233,297)(234,298)
(235,300)(236,299)(237,293)(238,294)(239,296)(240,295)(241,417)(242,418)
(243,420)(244,419)(245,429)(246,430)(247,432)(248,431)(249,425)(250,426)
(251,428)(252,427)(253,421)(254,422)(255,424)(256,423)(257,401)(258,402)
(259,404)(260,403)(261,413)(262,414)(263,416)(264,415)(265,409)(266,410)
(267,412)(268,411)(269,405)(270,406)(271,408)(272,407)(273,385)(274,386)
(275,388)(276,387)(277,397)(278,398)(279,400)(280,399)(281,393)(282,394)
(283,396)(284,395)(285,389)(286,390)(287,392)(288,391);;
s3 := ( 1,145)( 2,148)( 3,147)( 4,146)( 5,149)( 6,152)( 7,151)( 8,150)
( 9,153)( 10,156)( 11,155)( 12,154)( 13,157)( 14,160)( 15,159)( 16,158)
( 17,177)( 18,180)( 19,179)( 20,178)( 21,181)( 22,184)( 23,183)( 24,182)
( 25,185)( 26,188)( 27,187)( 28,186)( 29,189)( 30,192)( 31,191)( 32,190)
( 33,161)( 34,164)( 35,163)( 36,162)( 37,165)( 38,168)( 39,167)( 40,166)
( 41,169)( 42,172)( 43,171)( 44,170)( 45,173)( 46,176)( 47,175)( 48,174)
( 49,193)( 50,196)( 51,195)( 52,194)( 53,197)( 54,200)( 55,199)( 56,198)
( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,208)( 63,207)( 64,206)
( 65,225)( 66,228)( 67,227)( 68,226)( 69,229)( 70,232)( 71,231)( 72,230)
( 73,233)( 74,236)( 75,235)( 76,234)( 77,237)( 78,240)( 79,239)( 80,238)
( 81,209)( 82,212)( 83,211)( 84,210)( 85,213)( 86,216)( 87,215)( 88,214)
( 89,217)( 90,220)( 91,219)( 92,218)( 93,221)( 94,224)( 95,223)( 96,222)
( 97,241)( 98,244)( 99,243)(100,242)(101,245)(102,248)(103,247)(104,246)
(105,249)(106,252)(107,251)(108,250)(109,253)(110,256)(111,255)(112,254)
(113,273)(114,276)(115,275)(116,274)(117,277)(118,280)(119,279)(120,278)
(121,281)(122,284)(123,283)(124,282)(125,285)(126,288)(127,287)(128,286)
(129,257)(130,260)(131,259)(132,258)(133,261)(134,264)(135,263)(136,262)
(137,265)(138,268)(139,267)(140,266)(141,269)(142,272)(143,271)(144,270)
(289,321)(290,324)(291,323)(292,322)(293,325)(294,328)(295,327)(296,326)
(297,329)(298,332)(299,331)(300,330)(301,333)(302,336)(303,335)(304,334)
(306,308)(310,312)(314,316)(318,320)(337,369)(338,372)(339,371)(340,370)
(341,373)(342,376)(343,375)(344,374)(345,377)(346,380)(347,379)(348,378)
(349,381)(350,384)(351,383)(352,382)(354,356)(358,360)(362,364)(366,368)
(385,417)(386,420)(387,419)(388,418)(389,421)(390,424)(391,423)(392,422)
(393,425)(394,428)(395,427)(396,426)(397,429)(398,432)(399,431)(400,430)
(402,404)(406,408)(410,412)(414,416);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)
(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)
(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)
(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)
(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)
(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)
(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)
(424,432);
s1 := Sym(432)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 15)( 10, 16)( 11, 13)
( 12, 14)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 31)( 26, 32)( 27, 29)
( 28, 30)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)
( 44, 46)( 49, 99)( 50,100)( 51, 97)( 52, 98)( 53,103)( 54,104)( 55,101)
( 56,102)( 57,111)( 58,112)( 59,109)( 60,110)( 61,107)( 62,108)( 63,105)
( 64,106)( 65,115)( 66,116)( 67,113)( 68,114)( 69,119)( 70,120)( 71,117)
( 72,118)( 73,127)( 74,128)( 75,125)( 76,126)( 77,123)( 78,124)( 79,121)
( 80,122)( 81,131)( 82,132)( 83,129)( 84,130)( 85,135)( 86,136)( 87,133)
( 88,134)( 89,143)( 90,144)( 91,141)( 92,142)( 93,139)( 94,140)( 95,137)
( 96,138)(145,147)(146,148)(149,151)(150,152)(153,159)(154,160)(155,157)
(156,158)(161,163)(162,164)(165,167)(166,168)(169,175)(170,176)(171,173)
(172,174)(177,179)(178,180)(181,183)(182,184)(185,191)(186,192)(187,189)
(188,190)(193,243)(194,244)(195,241)(196,242)(197,247)(198,248)(199,245)
(200,246)(201,255)(202,256)(203,253)(204,254)(205,251)(206,252)(207,249)
(208,250)(209,259)(210,260)(211,257)(212,258)(213,263)(214,264)(215,261)
(216,262)(217,271)(218,272)(219,269)(220,270)(221,267)(222,268)(223,265)
(224,266)(225,275)(226,276)(227,273)(228,274)(229,279)(230,280)(231,277)
(232,278)(233,287)(234,288)(235,285)(236,286)(237,283)(238,284)(239,281)
(240,282)(289,291)(290,292)(293,295)(294,296)(297,303)(298,304)(299,301)
(300,302)(305,307)(306,308)(309,311)(310,312)(313,319)(314,320)(315,317)
(316,318)(321,323)(322,324)(325,327)(326,328)(329,335)(330,336)(331,333)
(332,334)(337,387)(338,388)(339,385)(340,386)(341,391)(342,392)(343,389)
(344,390)(345,399)(346,400)(347,397)(348,398)(349,395)(350,396)(351,393)
(352,394)(353,403)(354,404)(355,401)(356,402)(357,407)(358,408)(359,405)
(360,406)(361,415)(362,416)(363,413)(364,414)(365,411)(366,412)(367,409)
(368,410)(369,419)(370,420)(371,417)(372,418)(373,423)(374,424)(375,421)
(376,422)(377,431)(378,432)(379,429)(380,430)(381,427)(382,428)(383,425)
(384,426);
s2 := Sym(432)!( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 61)( 6, 62)( 7, 64)
( 8, 63)( 9, 57)( 10, 58)( 11, 60)( 12, 59)( 13, 53)( 14, 54)( 15, 56)
( 16, 55)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 93)( 22, 94)( 23, 96)
( 24, 95)( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)
( 32, 87)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)
( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)
( 48, 71)( 99,100)(101,109)(102,110)(103,112)(104,111)(107,108)(113,129)
(114,130)(115,132)(116,131)(117,141)(118,142)(119,144)(120,143)(121,137)
(122,138)(123,140)(124,139)(125,133)(126,134)(127,136)(128,135)(145,369)
(146,370)(147,372)(148,371)(149,381)(150,382)(151,384)(152,383)(153,377)
(154,378)(155,380)(156,379)(157,373)(158,374)(159,376)(160,375)(161,353)
(162,354)(163,356)(164,355)(165,365)(166,366)(167,368)(168,367)(169,361)
(170,362)(171,364)(172,363)(173,357)(174,358)(175,360)(176,359)(177,337)
(178,338)(179,340)(180,339)(181,349)(182,350)(183,352)(184,351)(185,345)
(186,346)(187,348)(188,347)(189,341)(190,342)(191,344)(192,343)(193,321)
(194,322)(195,324)(196,323)(197,333)(198,334)(199,336)(200,335)(201,329)
(202,330)(203,332)(204,331)(205,325)(206,326)(207,328)(208,327)(209,305)
(210,306)(211,308)(212,307)(213,317)(214,318)(215,320)(216,319)(217,313)
(218,314)(219,316)(220,315)(221,309)(222,310)(223,312)(224,311)(225,289)
(226,290)(227,292)(228,291)(229,301)(230,302)(231,304)(232,303)(233,297)
(234,298)(235,300)(236,299)(237,293)(238,294)(239,296)(240,295)(241,417)
(242,418)(243,420)(244,419)(245,429)(246,430)(247,432)(248,431)(249,425)
(250,426)(251,428)(252,427)(253,421)(254,422)(255,424)(256,423)(257,401)
(258,402)(259,404)(260,403)(261,413)(262,414)(263,416)(264,415)(265,409)
(266,410)(267,412)(268,411)(269,405)(270,406)(271,408)(272,407)(273,385)
(274,386)(275,388)(276,387)(277,397)(278,398)(279,400)(280,399)(281,393)
(282,394)(283,396)(284,395)(285,389)(286,390)(287,392)(288,391);
s3 := Sym(432)!( 1,145)( 2,148)( 3,147)( 4,146)( 5,149)( 6,152)( 7,151)
( 8,150)( 9,153)( 10,156)( 11,155)( 12,154)( 13,157)( 14,160)( 15,159)
( 16,158)( 17,177)( 18,180)( 19,179)( 20,178)( 21,181)( 22,184)( 23,183)
( 24,182)( 25,185)( 26,188)( 27,187)( 28,186)( 29,189)( 30,192)( 31,191)
( 32,190)( 33,161)( 34,164)( 35,163)( 36,162)( 37,165)( 38,168)( 39,167)
( 40,166)( 41,169)( 42,172)( 43,171)( 44,170)( 45,173)( 46,176)( 47,175)
( 48,174)( 49,193)( 50,196)( 51,195)( 52,194)( 53,197)( 54,200)( 55,199)
( 56,198)( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,208)( 63,207)
( 64,206)( 65,225)( 66,228)( 67,227)( 68,226)( 69,229)( 70,232)( 71,231)
( 72,230)( 73,233)( 74,236)( 75,235)( 76,234)( 77,237)( 78,240)( 79,239)
( 80,238)( 81,209)( 82,212)( 83,211)( 84,210)( 85,213)( 86,216)( 87,215)
( 88,214)( 89,217)( 90,220)( 91,219)( 92,218)( 93,221)( 94,224)( 95,223)
( 96,222)( 97,241)( 98,244)( 99,243)(100,242)(101,245)(102,248)(103,247)
(104,246)(105,249)(106,252)(107,251)(108,250)(109,253)(110,256)(111,255)
(112,254)(113,273)(114,276)(115,275)(116,274)(117,277)(118,280)(119,279)
(120,278)(121,281)(122,284)(123,283)(124,282)(125,285)(126,288)(127,287)
(128,286)(129,257)(130,260)(131,259)(132,258)(133,261)(134,264)(135,263)
(136,262)(137,265)(138,268)(139,267)(140,266)(141,269)(142,272)(143,271)
(144,270)(289,321)(290,324)(291,323)(292,322)(293,325)(294,328)(295,327)
(296,326)(297,329)(298,332)(299,331)(300,330)(301,333)(302,336)(303,335)
(304,334)(306,308)(310,312)(314,316)(318,320)(337,369)(338,372)(339,371)
(340,370)(341,373)(342,376)(343,375)(344,374)(345,377)(346,380)(347,379)
(348,378)(349,381)(350,384)(351,383)(352,382)(354,356)(358,360)(362,364)
(366,368)(385,417)(386,420)(387,419)(388,418)(389,421)(390,424)(391,423)
(392,422)(393,425)(394,428)(395,427)(396,426)(397,429)(398,432)(399,431)
(400,430)(402,404)(406,408)(410,412)(414,416);
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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3*s2*s3 >;
References : None.
to this polytope