Polytope of Type {4,18,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46115)
Rank : 4
Schlafli Type : {4,18,6}
Number of vertices, edges, etc : 8, 72, 108, 6
Order of s0s1s2s3 : 18
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 : {4,18,6}*864c
3-fold quotients : {4,18,2}*576, {4,6,6}*576a
4-fold quotients : {2,18,6}*432a
6-fold quotients : {4,9,2}*288, {4,18,2}*288b, {4,18,2}*288c, {4,6,6}*288d
9-fold quotients : {4,6,2}*192
12-fold quotients : {4,9,2}*144, {2,18,2}*144, {2,6,6}*144a
18-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
24-fold quotients : {2,9,2}*72
36-fold quotients : {4,3,2}*48, {2,2,6}*48, {2,6,2}*48
72-fold quotients : {2,2,3}*24, {2,3,2}*24
108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,219)( 2,220)( 3,217)( 4,218)( 5,223)( 6,224)( 7,221)( 8,222)
( 9,227)( 10,228)( 11,225)( 12,226)( 13,231)( 14,232)( 15,229)( 16,230)
( 17,235)( 18,236)( 19,233)( 20,234)( 21,239)( 22,240)( 23,237)( 24,238)
( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)( 32,246)
( 33,251)( 34,252)( 35,249)( 36,250)( 37,255)( 38,256)( 39,253)( 40,254)
( 41,259)( 42,260)( 43,257)( 44,258)( 45,263)( 46,264)( 47,261)( 48,262)
( 49,267)( 50,268)( 51,265)( 52,266)( 53,271)( 54,272)( 55,269)( 56,270)
( 57,275)( 58,276)( 59,273)( 60,274)( 61,279)( 62,280)( 63,277)( 64,278)
( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)( 72,286)
( 73,291)( 74,292)( 75,289)( 76,290)( 77,295)( 78,296)( 79,293)( 80,294)
( 81,299)( 82,300)( 83,297)( 84,298)( 85,303)( 86,304)( 87,301)( 88,302)
( 89,307)( 90,308)( 91,305)( 92,306)( 93,311)( 94,312)( 95,309)( 96,310)
( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)(104,318)
(105,323)(106,324)(107,321)(108,322)(109,327)(110,328)(111,325)(112,326)
(113,331)(114,332)(115,329)(116,330)(117,335)(118,336)(119,333)(120,334)
(121,339)(122,340)(123,337)(124,338)(125,343)(126,344)(127,341)(128,342)
(129,347)(130,348)(131,345)(132,346)(133,351)(134,352)(135,349)(136,350)
(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)(144,358)
(145,363)(146,364)(147,361)(148,362)(149,367)(150,368)(151,365)(152,366)
(153,371)(154,372)(155,369)(156,370)(157,375)(158,376)(159,373)(160,374)
(161,379)(162,380)(163,377)(164,378)(165,383)(166,384)(167,381)(168,382)
(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)(176,390)
(177,395)(178,396)(179,393)(180,394)(181,399)(182,400)(183,397)(184,398)
(185,403)(186,404)(187,401)(188,402)(189,407)(190,408)(191,405)(192,406)
(193,411)(194,412)(195,409)(196,410)(197,415)(198,416)(199,413)(200,414)
(201,419)(202,420)(203,417)(204,418)(205,423)(206,424)(207,421)(208,422)
(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)(216,430);;
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, 81)
( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 73)
( 46, 74)( 47, 76)( 48, 75)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)
( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61,105)
( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)( 68,103)( 69, 97)
( 70, 98)( 71,100)( 72, 99)(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)(145,189)(146,190)(147,192)(148,191)(149,185)(150,186)
(151,188)(152,187)(153,181)(154,182)(155,184)(156,183)(157,201)(158,202)
(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)(166,194)
(167,196)(168,195)(169,213)(170,214)(171,216)(172,215)(173,209)(174,210)
(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(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)(253,297)(254,298)(255,300)
(256,299)(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)
(264,291)(265,309)(266,310)(267,312)(268,311)(269,305)(270,306)(271,308)
(272,307)(273,301)(274,302)(275,304)(276,303)(277,321)(278,322)(279,324)
(280,323)(281,317)(282,318)(283,320)(284,319)(285,313)(286,314)(287,316)
(288,315)(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)
(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)(368,403)
(369,397)(370,398)(371,400)(372,399)(373,417)(374,418)(375,420)(376,419)
(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)(384,411)
(385,429)(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)(392,427)
(393,421)(394,422)(395,424)(396,423);;
s2 := ( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 45)( 6, 48)( 7, 47)( 8, 46)
( 9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 61)( 14, 64)( 15, 63)( 16, 62)
( 17, 69)( 18, 72)( 19, 71)( 20, 70)( 21, 65)( 22, 68)( 23, 67)( 24, 66)
( 25, 49)( 26, 52)( 27, 51)( 28, 50)( 29, 57)( 30, 60)( 31, 59)( 32, 58)
( 33, 53)( 34, 56)( 35, 55)( 36, 54)( 73, 81)( 74, 84)( 75, 83)( 76, 82)
( 78, 80)( 85,105)( 86,108)( 87,107)( 88,106)( 89,101)( 90,104)( 91,103)
( 92,102)( 93, 97)( 94,100)( 95, 99)( 96, 98)(109,145)(110,148)(111,147)
(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)
(120,150)(121,169)(122,172)(123,171)(124,170)(125,177)(126,180)(127,179)
(128,178)(129,173)(130,176)(131,175)(132,174)(133,157)(134,160)(135,159)
(136,158)(137,165)(138,168)(139,167)(140,166)(141,161)(142,164)(143,163)
(144,162)(181,189)(182,192)(183,191)(184,190)(186,188)(193,213)(194,216)
(195,215)(196,214)(197,209)(198,212)(199,211)(200,210)(201,205)(202,208)
(203,207)(204,206)(217,253)(218,256)(219,255)(220,254)(221,261)(222,264)
(223,263)(224,262)(225,257)(226,260)(227,259)(228,258)(229,277)(230,280)
(231,279)(232,278)(233,285)(234,288)(235,287)(236,286)(237,281)(238,284)
(239,283)(240,282)(241,265)(242,268)(243,267)(244,266)(245,273)(246,276)
(247,275)(248,274)(249,269)(250,272)(251,271)(252,270)(289,297)(290,300)
(291,299)(292,298)(294,296)(301,321)(302,324)(303,323)(304,322)(305,317)
(306,320)(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)(325,361)
(326,364)(327,363)(328,362)(329,369)(330,372)(331,371)(332,370)(333,365)
(334,368)(335,367)(336,366)(337,385)(338,388)(339,387)(340,386)(341,393)
(342,396)(343,395)(344,394)(345,389)(346,392)(347,391)(348,390)(349,373)
(350,376)(351,375)(352,374)(353,381)(354,384)(355,383)(356,382)(357,377)
(358,380)(359,379)(360,378)(397,405)(398,408)(399,407)(400,406)(402,404)
(409,429)(410,432)(411,431)(412,430)(413,425)(414,428)(415,427)(416,426)
(417,421)(418,424)(419,423)(420,422);;
s3 := ( 1,121)( 2,122)( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)( 8,128)
( 9,129)( 10,130)( 11,131)( 12,132)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)( 24,120)
( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)( 32,140)
( 33,141)( 34,142)( 35,143)( 36,144)( 37,157)( 38,158)( 39,159)( 40,160)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)
( 57,153)( 58,154)( 59,155)( 60,156)( 61,169)( 62,170)( 63,171)( 64,172)
( 65,173)( 66,174)( 67,175)( 68,176)( 69,177)( 70,178)( 71,179)( 72,180)
( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,201)( 82,202)( 83,203)( 84,204)( 85,181)( 86,182)( 87,183)( 88,184)
( 89,185)( 90,186)( 91,187)( 92,188)( 93,189)( 94,190)( 95,191)( 96,192)
( 97,205)( 98,206)( 99,207)(100,208)(101,209)(102,210)(103,211)(104,212)
(105,213)(106,214)(107,215)(108,216)(217,337)(218,338)(219,339)(220,340)
(221,341)(222,342)(223,343)(224,344)(225,345)(226,346)(227,347)(228,348)
(229,325)(230,326)(231,327)(232,328)(233,329)(234,330)(235,331)(236,332)
(237,333)(238,334)(239,335)(240,336)(241,349)(242,350)(243,351)(244,352)
(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)(252,360)
(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)(260,380)
(261,381)(262,382)(263,383)(264,384)(265,361)(266,362)(267,363)(268,364)
(269,365)(270,366)(271,367)(272,368)(273,369)(274,370)(275,371)(276,372)
(277,385)(278,386)(279,387)(280,388)(281,389)(282,390)(283,391)(284,392)
(285,393)(286,394)(287,395)(288,396)(289,409)(290,410)(291,411)(292,412)
(293,413)(294,414)(295,415)(296,416)(297,417)(298,418)(299,419)(300,420)
(301,397)(302,398)(303,399)(304,400)(305,401)(306,402)(307,403)(308,404)
(309,405)(310,406)(311,407)(312,408)(313,421)(314,422)(315,423)(316,424)
(317,425)(318,426)(319,427)(320,428)(321,429)(322,430)(323,431)(324,432);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1,219)( 2,220)( 3,217)( 4,218)( 5,223)( 6,224)( 7,221)
( 8,222)( 9,227)( 10,228)( 11,225)( 12,226)( 13,231)( 14,232)( 15,229)
( 16,230)( 17,235)( 18,236)( 19,233)( 20,234)( 21,239)( 22,240)( 23,237)
( 24,238)( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)
( 32,246)( 33,251)( 34,252)( 35,249)( 36,250)( 37,255)( 38,256)( 39,253)
( 40,254)( 41,259)( 42,260)( 43,257)( 44,258)( 45,263)( 46,264)( 47,261)
( 48,262)( 49,267)( 50,268)( 51,265)( 52,266)( 53,271)( 54,272)( 55,269)
( 56,270)( 57,275)( 58,276)( 59,273)( 60,274)( 61,279)( 62,280)( 63,277)
( 64,278)( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)
( 72,286)( 73,291)( 74,292)( 75,289)( 76,290)( 77,295)( 78,296)( 79,293)
( 80,294)( 81,299)( 82,300)( 83,297)( 84,298)( 85,303)( 86,304)( 87,301)
( 88,302)( 89,307)( 90,308)( 91,305)( 92,306)( 93,311)( 94,312)( 95,309)
( 96,310)( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)
(104,318)(105,323)(106,324)(107,321)(108,322)(109,327)(110,328)(111,325)
(112,326)(113,331)(114,332)(115,329)(116,330)(117,335)(118,336)(119,333)
(120,334)(121,339)(122,340)(123,337)(124,338)(125,343)(126,344)(127,341)
(128,342)(129,347)(130,348)(131,345)(132,346)(133,351)(134,352)(135,349)
(136,350)(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)
(144,358)(145,363)(146,364)(147,361)(148,362)(149,367)(150,368)(151,365)
(152,366)(153,371)(154,372)(155,369)(156,370)(157,375)(158,376)(159,373)
(160,374)(161,379)(162,380)(163,377)(164,378)(165,383)(166,384)(167,381)
(168,382)(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)
(176,390)(177,395)(178,396)(179,393)(180,394)(181,399)(182,400)(183,397)
(184,398)(185,403)(186,404)(187,401)(188,402)(189,407)(190,408)(191,405)
(192,406)(193,411)(194,412)(195,409)(196,410)(197,415)(198,416)(199,413)
(200,414)(201,419)(202,420)(203,417)(204,418)(205,423)(206,424)(207,421)
(208,422)(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)
(216,430);
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, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)( 44, 79)
( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 93)( 50, 94)( 51, 96)( 52, 95)
( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)
( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)( 68,103)
( 69, 97)( 70, 98)( 71,100)( 72, 99)(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)(145,189)(146,190)(147,192)(148,191)(149,185)
(150,186)(151,188)(152,187)(153,181)(154,182)(155,184)(156,183)(157,201)
(158,202)(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)
(166,194)(167,196)(168,195)(169,213)(170,214)(171,216)(172,215)(173,209)
(174,210)(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(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)(253,297)(254,298)
(255,300)(256,299)(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)
(263,292)(264,291)(265,309)(266,310)(267,312)(268,311)(269,305)(270,306)
(271,308)(272,307)(273,301)(274,302)(275,304)(276,303)(277,321)(278,322)
(279,324)(280,323)(281,317)(282,318)(283,320)(284,319)(285,313)(286,314)
(287,316)(288,315)(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)(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)
(368,403)(369,397)(370,398)(371,400)(372,399)(373,417)(374,418)(375,420)
(376,419)(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)
(384,411)(385,429)(386,430)(387,432)(388,431)(389,425)(390,426)(391,428)
(392,427)(393,421)(394,422)(395,424)(396,423);
s2 := Sym(432)!( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 45)( 6, 48)( 7, 47)
( 8, 46)( 9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 61)( 14, 64)( 15, 63)
( 16, 62)( 17, 69)( 18, 72)( 19, 71)( 20, 70)( 21, 65)( 22, 68)( 23, 67)
( 24, 66)( 25, 49)( 26, 52)( 27, 51)( 28, 50)( 29, 57)( 30, 60)( 31, 59)
( 32, 58)( 33, 53)( 34, 56)( 35, 55)( 36, 54)( 73, 81)( 74, 84)( 75, 83)
( 76, 82)( 78, 80)( 85,105)( 86,108)( 87,107)( 88,106)( 89,101)( 90,104)
( 91,103)( 92,102)( 93, 97)( 94,100)( 95, 99)( 96, 98)(109,145)(110,148)
(111,147)(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)
(119,151)(120,150)(121,169)(122,172)(123,171)(124,170)(125,177)(126,180)
(127,179)(128,178)(129,173)(130,176)(131,175)(132,174)(133,157)(134,160)
(135,159)(136,158)(137,165)(138,168)(139,167)(140,166)(141,161)(142,164)
(143,163)(144,162)(181,189)(182,192)(183,191)(184,190)(186,188)(193,213)
(194,216)(195,215)(196,214)(197,209)(198,212)(199,211)(200,210)(201,205)
(202,208)(203,207)(204,206)(217,253)(218,256)(219,255)(220,254)(221,261)
(222,264)(223,263)(224,262)(225,257)(226,260)(227,259)(228,258)(229,277)
(230,280)(231,279)(232,278)(233,285)(234,288)(235,287)(236,286)(237,281)
(238,284)(239,283)(240,282)(241,265)(242,268)(243,267)(244,266)(245,273)
(246,276)(247,275)(248,274)(249,269)(250,272)(251,271)(252,270)(289,297)
(290,300)(291,299)(292,298)(294,296)(301,321)(302,324)(303,323)(304,322)
(305,317)(306,320)(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)
(325,361)(326,364)(327,363)(328,362)(329,369)(330,372)(331,371)(332,370)
(333,365)(334,368)(335,367)(336,366)(337,385)(338,388)(339,387)(340,386)
(341,393)(342,396)(343,395)(344,394)(345,389)(346,392)(347,391)(348,390)
(349,373)(350,376)(351,375)(352,374)(353,381)(354,384)(355,383)(356,382)
(357,377)(358,380)(359,379)(360,378)(397,405)(398,408)(399,407)(400,406)
(402,404)(409,429)(410,432)(411,431)(412,430)(413,425)(414,428)(415,427)
(416,426)(417,421)(418,424)(419,423)(420,422);
s3 := Sym(432)!( 1,121)( 2,122)( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)
( 8,128)( 9,129)( 10,130)( 11,131)( 12,132)( 13,109)( 14,110)( 15,111)
( 16,112)( 17,113)( 18,114)( 19,115)( 20,116)( 21,117)( 22,118)( 23,119)
( 24,120)( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)
( 32,140)( 33,141)( 34,142)( 35,143)( 36,144)( 37,157)( 38,158)( 39,159)
( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)
( 48,168)( 49,145)( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)
( 56,152)( 57,153)( 58,154)( 59,155)( 60,156)( 61,169)( 62,170)( 63,171)
( 64,172)( 65,173)( 66,174)( 67,175)( 68,176)( 69,177)( 70,178)( 71,179)
( 72,180)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,181)( 86,182)( 87,183)
( 88,184)( 89,185)( 90,186)( 91,187)( 92,188)( 93,189)( 94,190)( 95,191)
( 96,192)( 97,205)( 98,206)( 99,207)(100,208)(101,209)(102,210)(103,211)
(104,212)(105,213)(106,214)(107,215)(108,216)(217,337)(218,338)(219,339)
(220,340)(221,341)(222,342)(223,343)(224,344)(225,345)(226,346)(227,347)
(228,348)(229,325)(230,326)(231,327)(232,328)(233,329)(234,330)(235,331)
(236,332)(237,333)(238,334)(239,335)(240,336)(241,349)(242,350)(243,351)
(244,352)(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)
(252,360)(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)
(260,380)(261,381)(262,382)(263,383)(264,384)(265,361)(266,362)(267,363)
(268,364)(269,365)(270,366)(271,367)(272,368)(273,369)(274,370)(275,371)
(276,372)(277,385)(278,386)(279,387)(280,388)(281,389)(282,390)(283,391)
(284,392)(285,393)(286,394)(287,395)(288,396)(289,409)(290,410)(291,411)
(292,412)(293,413)(294,414)(295,415)(296,416)(297,417)(298,418)(299,419)
(300,420)(301,397)(302,398)(303,399)(304,400)(305,401)(306,402)(307,403)
(308,404)(309,405)(310,406)(311,407)(312,408)(313,421)(314,422)(315,423)
(316,424)(317,425)(318,426)(319,427)(320,428)(321,429)(322,430)(323,431)
(324,432);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope