Polytope of Type {18,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,12,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,18104)
Rank : 4
Schlafli Type : {18,12,4}
Number of vertices, edges, etc : 18, 108, 24, 4
Order of s0s1s2s3 : 36
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 : {18,6,4}*864b, {18,12,2}*864b
3-fold quotients : {18,4,4}*576, {6,12,4}*576c
4-fold quotients : {9,6,4}*432, {18,6,2}*432b
6-fold quotients : {18,2,4}*288, {18,4,2}*288a, {6,6,4}*288c, {6,12,2}*288c
8-fold quotients : {9,6,2}*216
9-fold quotients : {6,4,4}*192
12-fold quotients : {9,2,4}*144, {18,2,2}*144, {3,6,4}*144, {6,6,2}*144c
18-fold quotients : {6,2,4}*96, {6,4,2}*96a
24-fold quotients : {9,2,2}*72, {3,6,2}*72
27-fold quotients : {2,4,4}*64
36-fold quotients : {3,2,4}*48, {6,2,2}*48
54-fold quotients : {2,2,4}*32, {2,4,2}*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 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 21)( 11, 20)( 12, 19)( 13, 27)
( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)( 43, 51)
( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)( 65, 74)
( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 83, 84)
( 85, 88)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,100)( 94,108)( 95,107)
( 96,106)( 97,105)( 98,104)( 99,103)(110,111)(112,115)(113,117)(114,116)
(118,129)(119,128)(120,127)(121,135)(122,134)(123,133)(124,132)(125,131)
(126,130)(137,138)(139,142)(140,144)(141,143)(145,156)(146,155)(147,154)
(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(164,165)(166,169)
(167,171)(168,170)(172,183)(173,182)(174,181)(175,189)(176,188)(177,187)
(178,186)(179,185)(180,184)(191,192)(193,196)(194,198)(195,197)(199,210)
(200,209)(201,208)(202,216)(203,215)(204,214)(205,213)(206,212)(207,211)
(218,219)(220,223)(221,225)(222,224)(226,237)(227,236)(228,235)(229,243)
(230,242)(231,241)(232,240)(233,239)(234,238)(245,246)(247,250)(248,252)
(249,251)(253,264)(254,263)(255,262)(256,270)(257,269)(258,268)(259,267)
(260,266)(261,265)(272,273)(274,277)(275,279)(276,278)(280,291)(281,290)
(282,289)(283,297)(284,296)(285,295)(286,294)(287,293)(288,292)(299,300)
(301,304)(302,306)(303,305)(307,318)(308,317)(309,316)(310,324)(311,323)
(312,322)(313,321)(314,320)(315,319)(326,327)(328,331)(329,333)(330,332)
(334,345)(335,344)(336,343)(337,351)(338,350)(339,349)(340,348)(341,347)
(342,346)(353,354)(355,358)(356,360)(357,359)(361,372)(362,371)(363,370)
(364,378)(365,377)(366,376)(367,375)(368,374)(369,373)(380,381)(382,385)
(383,387)(384,386)(388,399)(389,398)(390,397)(391,405)(392,404)(393,403)
(394,402)(395,401)(396,400)(407,408)(409,412)(410,414)(411,413)(415,426)
(416,425)(417,424)(418,432)(419,431)(420,430)(421,429)(422,428)(423,427);;
s1 := ( 1,229)( 2,231)( 3,230)( 4,226)( 5,228)( 6,227)( 7,232)( 8,234)
( 9,233)( 10,220)( 11,222)( 12,221)( 13,217)( 14,219)( 15,218)( 16,223)
( 17,225)( 18,224)( 19,240)( 20,239)( 21,238)( 22,237)( 23,236)( 24,235)
( 25,243)( 26,242)( 27,241)( 28,256)( 29,258)( 30,257)( 31,253)( 32,255)
( 33,254)( 34,259)( 35,261)( 36,260)( 37,247)( 38,249)( 39,248)( 40,244)
( 41,246)( 42,245)( 43,250)( 44,252)( 45,251)( 46,267)( 47,266)( 48,265)
( 49,264)( 50,263)( 51,262)( 52,270)( 53,269)( 54,268)( 55,283)( 56,285)
( 57,284)( 58,280)( 59,282)( 60,281)( 61,286)( 62,288)( 63,287)( 64,274)
( 65,276)( 66,275)( 67,271)( 68,273)( 69,272)( 70,277)( 71,279)( 72,278)
( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,289)( 79,297)( 80,296)
( 81,295)( 82,310)( 83,312)( 84,311)( 85,307)( 86,309)( 87,308)( 88,313)
( 89,315)( 90,314)( 91,301)( 92,303)( 93,302)( 94,298)( 95,300)( 96,299)
( 97,304)( 98,306)( 99,305)(100,321)(101,320)(102,319)(103,318)(104,317)
(105,316)(106,324)(107,323)(108,322)(109,337)(110,339)(111,338)(112,334)
(113,336)(114,335)(115,340)(116,342)(117,341)(118,328)(119,330)(120,329)
(121,325)(122,327)(123,326)(124,331)(125,333)(126,332)(127,348)(128,347)
(129,346)(130,345)(131,344)(132,343)(133,351)(134,350)(135,349)(136,364)
(137,366)(138,365)(139,361)(140,363)(141,362)(142,367)(143,369)(144,368)
(145,355)(146,357)(147,356)(148,352)(149,354)(150,353)(151,358)(152,360)
(153,359)(154,375)(155,374)(156,373)(157,372)(158,371)(159,370)(160,378)
(161,377)(162,376)(163,391)(164,393)(165,392)(166,388)(167,390)(168,389)
(169,394)(170,396)(171,395)(172,382)(173,384)(174,383)(175,379)(176,381)
(177,380)(178,385)(179,387)(180,386)(181,402)(182,401)(183,400)(184,399)
(185,398)(186,397)(187,405)(188,404)(189,403)(190,418)(191,420)(192,419)
(193,415)(194,417)(195,416)(196,421)(197,423)(198,422)(199,409)(200,411)
(201,410)(202,406)(203,408)(204,407)(205,412)(206,414)(207,413)(208,429)
(209,428)(210,427)(211,426)(212,425)(213,424)(214,432)(215,431)(216,430);;
s2 := ( 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)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)
( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)
( 96, 99)(103,106)(104,107)(105,108)(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)(217,244)(218,245)(219,246)(220,250)(221,251)(222,252)
(223,247)(224,248)(225,249)(226,253)(227,254)(228,255)(229,259)(230,260)
(231,261)(232,256)(233,257)(234,258)(235,262)(236,263)(237,264)(238,268)
(239,269)(240,270)(241,265)(242,266)(243,267)(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)
(325,406)(326,407)(327,408)(328,412)(329,413)(330,414)(331,409)(332,410)
(333,411)(334,415)(335,416)(336,417)(337,421)(338,422)(339,423)(340,418)
(341,419)(342,420)(343,424)(344,425)(345,426)(346,430)(347,431)(348,432)
(349,427)(350,428)(351,429)(352,379)(353,380)(354,381)(355,385)(356,386)
(357,387)(358,382)(359,383)(360,384)(361,388)(362,389)(363,390)(364,394)
(365,395)(366,396)(367,391)(368,392)(369,393)(370,397)(371,398)(372,399)
(373,403)(374,404)(375,405)(376,400)(377,401)(378,402);;
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)( 55,163)( 56,164)
( 57,165)( 58,166)( 59,167)( 60,168)( 61,169)( 62,170)( 63,171)( 64,172)
( 65,173)( 66,174)( 67,175)( 68,176)( 69,177)( 70,178)( 71,179)( 72,180)
( 73,181)( 74,182)( 75,183)( 76,184)( 77,185)( 78,186)( 79,187)( 80,188)
( 81,189)( 82,190)( 83,191)( 84,192)( 85,193)( 86,194)( 87,195)( 88,196)
( 89,197)( 90,198)( 91,199)( 92,200)( 93,201)( 94,202)( 95,203)( 96,204)
( 97,205)( 98,206)( 99,207)(100,208)(101,209)(102,210)(103,211)(104,212)
(105,213)(106,214)(107,215)(108,216)(217,325)(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)(271,379)(272,380)(273,381)(274,382)(275,383)(276,384)
(277,385)(278,386)(279,387)(280,388)(281,389)(282,390)(283,391)(284,392)
(285,393)(286,394)(287,395)(288,396)(289,397)(290,398)(291,399)(292,400)
(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)(300,408)
(301,409)(302,410)(303,411)(304,412)(305,413)(306,414)(307,415)(308,416)
(309,417)(310,418)(311,419)(312,420)(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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 21)( 11, 20)( 12, 19)
( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)
( 32, 36)( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)
( 43, 51)( 44, 50)( 45, 49)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 75)
( 65, 74)( 66, 73)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)
( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 91,102)( 92,101)( 93,100)( 94,108)
( 95,107)( 96,106)( 97,105)( 98,104)( 99,103)(110,111)(112,115)(113,117)
(114,116)(118,129)(119,128)(120,127)(121,135)(122,134)(123,133)(124,132)
(125,131)(126,130)(137,138)(139,142)(140,144)(141,143)(145,156)(146,155)
(147,154)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(164,165)
(166,169)(167,171)(168,170)(172,183)(173,182)(174,181)(175,189)(176,188)
(177,187)(178,186)(179,185)(180,184)(191,192)(193,196)(194,198)(195,197)
(199,210)(200,209)(201,208)(202,216)(203,215)(204,214)(205,213)(206,212)
(207,211)(218,219)(220,223)(221,225)(222,224)(226,237)(227,236)(228,235)
(229,243)(230,242)(231,241)(232,240)(233,239)(234,238)(245,246)(247,250)
(248,252)(249,251)(253,264)(254,263)(255,262)(256,270)(257,269)(258,268)
(259,267)(260,266)(261,265)(272,273)(274,277)(275,279)(276,278)(280,291)
(281,290)(282,289)(283,297)(284,296)(285,295)(286,294)(287,293)(288,292)
(299,300)(301,304)(302,306)(303,305)(307,318)(308,317)(309,316)(310,324)
(311,323)(312,322)(313,321)(314,320)(315,319)(326,327)(328,331)(329,333)
(330,332)(334,345)(335,344)(336,343)(337,351)(338,350)(339,349)(340,348)
(341,347)(342,346)(353,354)(355,358)(356,360)(357,359)(361,372)(362,371)
(363,370)(364,378)(365,377)(366,376)(367,375)(368,374)(369,373)(380,381)
(382,385)(383,387)(384,386)(388,399)(389,398)(390,397)(391,405)(392,404)
(393,403)(394,402)(395,401)(396,400)(407,408)(409,412)(410,414)(411,413)
(415,426)(416,425)(417,424)(418,432)(419,431)(420,430)(421,429)(422,428)
(423,427);
s1 := Sym(432)!( 1,229)( 2,231)( 3,230)( 4,226)( 5,228)( 6,227)( 7,232)
( 8,234)( 9,233)( 10,220)( 11,222)( 12,221)( 13,217)( 14,219)( 15,218)
( 16,223)( 17,225)( 18,224)( 19,240)( 20,239)( 21,238)( 22,237)( 23,236)
( 24,235)( 25,243)( 26,242)( 27,241)( 28,256)( 29,258)( 30,257)( 31,253)
( 32,255)( 33,254)( 34,259)( 35,261)( 36,260)( 37,247)( 38,249)( 39,248)
( 40,244)( 41,246)( 42,245)( 43,250)( 44,252)( 45,251)( 46,267)( 47,266)
( 48,265)( 49,264)( 50,263)( 51,262)( 52,270)( 53,269)( 54,268)( 55,283)
( 56,285)( 57,284)( 58,280)( 59,282)( 60,281)( 61,286)( 62,288)( 63,287)
( 64,274)( 65,276)( 66,275)( 67,271)( 68,273)( 69,272)( 70,277)( 71,279)
( 72,278)( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,289)( 79,297)
( 80,296)( 81,295)( 82,310)( 83,312)( 84,311)( 85,307)( 86,309)( 87,308)
( 88,313)( 89,315)( 90,314)( 91,301)( 92,303)( 93,302)( 94,298)( 95,300)
( 96,299)( 97,304)( 98,306)( 99,305)(100,321)(101,320)(102,319)(103,318)
(104,317)(105,316)(106,324)(107,323)(108,322)(109,337)(110,339)(111,338)
(112,334)(113,336)(114,335)(115,340)(116,342)(117,341)(118,328)(119,330)
(120,329)(121,325)(122,327)(123,326)(124,331)(125,333)(126,332)(127,348)
(128,347)(129,346)(130,345)(131,344)(132,343)(133,351)(134,350)(135,349)
(136,364)(137,366)(138,365)(139,361)(140,363)(141,362)(142,367)(143,369)
(144,368)(145,355)(146,357)(147,356)(148,352)(149,354)(150,353)(151,358)
(152,360)(153,359)(154,375)(155,374)(156,373)(157,372)(158,371)(159,370)
(160,378)(161,377)(162,376)(163,391)(164,393)(165,392)(166,388)(167,390)
(168,389)(169,394)(170,396)(171,395)(172,382)(173,384)(174,383)(175,379)
(176,381)(177,380)(178,385)(179,387)(180,386)(181,402)(182,401)(183,400)
(184,399)(185,398)(186,397)(187,405)(188,404)(189,403)(190,418)(191,420)
(192,419)(193,415)(194,417)(195,416)(196,421)(197,423)(198,422)(199,409)
(200,411)(201,410)(202,406)(203,408)(204,407)(205,412)(206,414)(207,413)
(208,429)(209,428)(210,427)(211,426)(212,425)(213,424)(214,432)(215,431)
(216,430);
s2 := 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)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)
( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)
( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(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)(217,244)(218,245)(219,246)(220,250)(221,251)
(222,252)(223,247)(224,248)(225,249)(226,253)(227,254)(228,255)(229,259)
(230,260)(231,261)(232,256)(233,257)(234,258)(235,262)(236,263)(237,264)
(238,268)(239,269)(240,270)(241,265)(242,266)(243,267)(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)(325,406)(326,407)(327,408)(328,412)(329,413)(330,414)(331,409)
(332,410)(333,411)(334,415)(335,416)(336,417)(337,421)(338,422)(339,423)
(340,418)(341,419)(342,420)(343,424)(344,425)(345,426)(346,430)(347,431)
(348,432)(349,427)(350,428)(351,429)(352,379)(353,380)(354,381)(355,385)
(356,386)(357,387)(358,382)(359,383)(360,384)(361,388)(362,389)(363,390)
(364,394)(365,395)(366,396)(367,391)(368,392)(369,393)(370,397)(371,398)
(372,399)(373,403)(374,404)(375,405)(376,400)(377,401)(378,402);
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)( 55,163)
( 56,164)( 57,165)( 58,166)( 59,167)( 60,168)( 61,169)( 62,170)( 63,171)
( 64,172)( 65,173)( 66,174)( 67,175)( 68,176)( 69,177)( 70,178)( 71,179)
( 72,180)( 73,181)( 74,182)( 75,183)( 76,184)( 77,185)( 78,186)( 79,187)
( 80,188)( 81,189)( 82,190)( 83,191)( 84,192)( 85,193)( 86,194)( 87,195)
( 88,196)( 89,197)( 90,198)( 91,199)( 92,200)( 93,201)( 94,202)( 95,203)
( 96,204)( 97,205)( 98,206)( 99,207)(100,208)(101,209)(102,210)(103,211)
(104,212)(105,213)(106,214)(107,215)(108,216)(217,325)(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)(271,379)(272,380)(273,381)(274,382)(275,383)
(276,384)(277,385)(278,386)(279,387)(280,388)(281,389)(282,390)(283,391)
(284,392)(285,393)(286,394)(287,395)(288,396)(289,397)(290,398)(291,399)
(292,400)(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)
(300,408)(301,409)(302,410)(303,411)(304,412)(305,413)(306,414)(307,415)
(308,416)(309,417)(310,418)(311,419)(312,420)(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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope