Polytope of Type {12,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,16950)
Rank : 4
Schlafli Type : {12,6,4}
Number of vertices, edges, etc : 36, 108, 36, 4
Order of s0s1s2s3 : 12
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 : {12,6,2}*864a, {6,6,4}*864c
3-fold quotients : {12,6,4}*576b
4-fold quotients : {3,6,4}*432a, {6,6,2}*432c
6-fold quotients : {12,6,2}*288b, {6,6,4}*288c
8-fold quotients : {3,6,2}*216
9-fold quotients : {12,2,4}*192
12-fold quotients : {3,6,4}*144, {6,6,2}*144c
18-fold quotients : {12,2,2}*96, {6,2,4}*96
24-fold quotients : {3,6,2}*72
27-fold quotients : {4,2,4}*64
36-fold quotients : {3,2,4}*48, {6,2,2}*48
54-fold quotients : {2,2,4}*32, {4,2,2}*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 := ( 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)
(109,163)(110,164)(111,165)(112,169)(113,170)(114,171)(115,166)(116,167)
(117,168)(118,181)(119,182)(120,183)(121,187)(122,188)(123,189)(124,184)
(125,185)(126,186)(127,172)(128,173)(129,174)(130,178)(131,179)(132,180)
(133,175)(134,176)(135,177)(136,190)(137,191)(138,192)(139,196)(140,197)
(141,198)(142,193)(143,194)(144,195)(145,208)(146,209)(147,210)(148,214)
(149,215)(150,216)(151,211)(152,212)(153,213)(154,199)(155,200)(156,201)
(157,205)(158,206)(159,207)(160,202)(161,203)(162,204)(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)(325,379)(326,380)
(327,381)(328,385)(329,386)(330,387)(331,382)(332,383)(333,384)(334,397)
(335,398)(336,399)(337,403)(338,404)(339,405)(340,400)(341,401)(342,402)
(343,388)(344,389)(345,390)(346,394)(347,395)(348,396)(349,391)(350,392)
(351,393)(352,406)(353,407)(354,408)(355,412)(356,413)(357,414)(358,409)
(359,410)(360,411)(361,424)(362,425)(363,426)(364,430)(365,431)(366,432)
(367,427)(368,428)(369,429)(370,415)(371,416)(372,417)(373,421)(374,422)
(375,423)(376,418)(377,419)(378,420);;
s1 := ( 1,131)( 2,132)( 3,130)( 4,129)( 5,127)( 6,128)( 7,133)( 8,134)
( 9,135)( 10,122)( 11,123)( 12,121)( 13,120)( 14,118)( 15,119)( 16,124)
( 17,125)( 18,126)( 19,113)( 20,114)( 21,112)( 22,111)( 23,109)( 24,110)
( 25,115)( 26,116)( 27,117)( 28,158)( 29,159)( 30,157)( 31,156)( 32,154)
( 33,155)( 34,160)( 35,161)( 36,162)( 37,149)( 38,150)( 39,148)( 40,147)
( 41,145)( 42,146)( 43,151)( 44,152)( 45,153)( 46,140)( 47,141)( 48,139)
( 49,138)( 50,136)( 51,137)( 52,142)( 53,143)( 54,144)( 55,185)( 56,186)
( 57,184)( 58,183)( 59,181)( 60,182)( 61,187)( 62,188)( 63,189)( 64,176)
( 65,177)( 66,175)( 67,174)( 68,172)( 69,173)( 70,178)( 71,179)( 72,180)
( 73,167)( 74,168)( 75,166)( 76,165)( 77,163)( 78,164)( 79,169)( 80,170)
( 81,171)( 82,212)( 83,213)( 84,211)( 85,210)( 86,208)( 87,209)( 88,214)
( 89,215)( 90,216)( 91,203)( 92,204)( 93,202)( 94,201)( 95,199)( 96,200)
( 97,205)( 98,206)( 99,207)(100,194)(101,195)(102,193)(103,192)(104,190)
(105,191)(106,196)(107,197)(108,198)(217,347)(218,348)(219,346)(220,345)
(221,343)(222,344)(223,349)(224,350)(225,351)(226,338)(227,339)(228,337)
(229,336)(230,334)(231,335)(232,340)(233,341)(234,342)(235,329)(236,330)
(237,328)(238,327)(239,325)(240,326)(241,331)(242,332)(243,333)(244,374)
(245,375)(246,373)(247,372)(248,370)(249,371)(250,376)(251,377)(252,378)
(253,365)(254,366)(255,364)(256,363)(257,361)(258,362)(259,367)(260,368)
(261,369)(262,356)(263,357)(264,355)(265,354)(266,352)(267,353)(268,358)
(269,359)(270,360)(271,401)(272,402)(273,400)(274,399)(275,397)(276,398)
(277,403)(278,404)(279,405)(280,392)(281,393)(282,391)(283,390)(284,388)
(285,389)(286,394)(287,395)(288,396)(289,383)(290,384)(291,382)(292,381)
(293,379)(294,380)(295,385)(296,386)(297,387)(298,428)(299,429)(300,427)
(301,426)(302,424)(303,425)(304,430)(305,431)(306,432)(307,419)(308,420)
(309,418)(310,417)(311,415)(312,416)(313,421)(314,422)(315,423)(316,410)
(317,411)(318,409)(319,408)(320,406)(321,407)(322,412)(323,413)(324,414);;
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)
( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)( 68, 78)
( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)( 91,100)
( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)( 99,107)
(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)(122,132)
(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)(145,154)
(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)(153,161)
(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)(176,186)
(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)(199,208)
(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)(207,215)
(217,244)(218,246)(219,245)(220,247)(221,249)(222,248)(223,250)(224,252)
(225,251)(226,262)(227,264)(228,263)(229,265)(230,267)(231,266)(232,268)
(233,270)(234,269)(235,253)(236,255)(237,254)(238,256)(239,258)(240,257)
(241,259)(242,261)(243,260)(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)(325,352)(326,354)
(327,353)(328,355)(329,357)(330,356)(331,358)(332,360)(333,359)(334,370)
(335,372)(336,371)(337,373)(338,375)(339,374)(340,376)(341,378)(342,377)
(343,361)(344,363)(345,362)(346,364)(347,366)(348,365)(349,367)(350,369)
(351,368)(379,406)(380,408)(381,407)(382,409)(383,411)(384,410)(385,412)
(386,414)(387,413)(388,424)(389,426)(390,425)(391,427)(392,429)(393,428)
(394,430)(395,432)(396,431)(397,415)(398,417)(399,416)(400,418)(401,420)
(402,419)(403,421)(404,423)(405,422);;
s3 := ( 1,217)( 2,218)( 3,219)( 4,220)( 5,221)( 6,222)( 7,223)( 8,224)
( 9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)( 16,232)
( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)( 40,256)
( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)( 56,272)
( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)( 96,312)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)
(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)(120,336)
(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)(128,344)
(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,352)
(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)
(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)(152,368)
(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)
(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)(168,384)
(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)(176,392)
(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)(184,400)
(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)(192,408)
(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)(200,416)
(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)(208,424)
(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)(216,432);;
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, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*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 ];;
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)(109,163)(110,164)(111,165)(112,169)(113,170)(114,171)(115,166)
(116,167)(117,168)(118,181)(119,182)(120,183)(121,187)(122,188)(123,189)
(124,184)(125,185)(126,186)(127,172)(128,173)(129,174)(130,178)(131,179)
(132,180)(133,175)(134,176)(135,177)(136,190)(137,191)(138,192)(139,196)
(140,197)(141,198)(142,193)(143,194)(144,195)(145,208)(146,209)(147,210)
(148,214)(149,215)(150,216)(151,211)(152,212)(153,213)(154,199)(155,200)
(156,201)(157,205)(158,206)(159,207)(160,202)(161,203)(162,204)(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)(325,379)
(326,380)(327,381)(328,385)(329,386)(330,387)(331,382)(332,383)(333,384)
(334,397)(335,398)(336,399)(337,403)(338,404)(339,405)(340,400)(341,401)
(342,402)(343,388)(344,389)(345,390)(346,394)(347,395)(348,396)(349,391)
(350,392)(351,393)(352,406)(353,407)(354,408)(355,412)(356,413)(357,414)
(358,409)(359,410)(360,411)(361,424)(362,425)(363,426)(364,430)(365,431)
(366,432)(367,427)(368,428)(369,429)(370,415)(371,416)(372,417)(373,421)
(374,422)(375,423)(376,418)(377,419)(378,420);
s1 := Sym(432)!( 1,131)( 2,132)( 3,130)( 4,129)( 5,127)( 6,128)( 7,133)
( 8,134)( 9,135)( 10,122)( 11,123)( 12,121)( 13,120)( 14,118)( 15,119)
( 16,124)( 17,125)( 18,126)( 19,113)( 20,114)( 21,112)( 22,111)( 23,109)
( 24,110)( 25,115)( 26,116)( 27,117)( 28,158)( 29,159)( 30,157)( 31,156)
( 32,154)( 33,155)( 34,160)( 35,161)( 36,162)( 37,149)( 38,150)( 39,148)
( 40,147)( 41,145)( 42,146)( 43,151)( 44,152)( 45,153)( 46,140)( 47,141)
( 48,139)( 49,138)( 50,136)( 51,137)( 52,142)( 53,143)( 54,144)( 55,185)
( 56,186)( 57,184)( 58,183)( 59,181)( 60,182)( 61,187)( 62,188)( 63,189)
( 64,176)( 65,177)( 66,175)( 67,174)( 68,172)( 69,173)( 70,178)( 71,179)
( 72,180)( 73,167)( 74,168)( 75,166)( 76,165)( 77,163)( 78,164)( 79,169)
( 80,170)( 81,171)( 82,212)( 83,213)( 84,211)( 85,210)( 86,208)( 87,209)
( 88,214)( 89,215)( 90,216)( 91,203)( 92,204)( 93,202)( 94,201)( 95,199)
( 96,200)( 97,205)( 98,206)( 99,207)(100,194)(101,195)(102,193)(103,192)
(104,190)(105,191)(106,196)(107,197)(108,198)(217,347)(218,348)(219,346)
(220,345)(221,343)(222,344)(223,349)(224,350)(225,351)(226,338)(227,339)
(228,337)(229,336)(230,334)(231,335)(232,340)(233,341)(234,342)(235,329)
(236,330)(237,328)(238,327)(239,325)(240,326)(241,331)(242,332)(243,333)
(244,374)(245,375)(246,373)(247,372)(248,370)(249,371)(250,376)(251,377)
(252,378)(253,365)(254,366)(255,364)(256,363)(257,361)(258,362)(259,367)
(260,368)(261,369)(262,356)(263,357)(264,355)(265,354)(266,352)(267,353)
(268,358)(269,359)(270,360)(271,401)(272,402)(273,400)(274,399)(275,397)
(276,398)(277,403)(278,404)(279,405)(280,392)(281,393)(282,391)(283,390)
(284,388)(285,389)(286,394)(287,395)(288,396)(289,383)(290,384)(291,382)
(292,381)(293,379)(294,380)(295,385)(296,386)(297,387)(298,428)(299,429)
(300,427)(301,426)(302,424)(303,425)(304,430)(305,431)(306,432)(307,419)
(308,420)(309,418)(310,417)(311,415)(312,416)(313,421)(314,422)(315,423)
(316,410)(317,411)(318,409)(319,408)(320,406)(321,407)(322,412)(323,413)
(324,414);
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)( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)
( 68, 78)( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)
( 91,100)( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)
( 99,107)(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)
(122,132)(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)
(145,154)(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)
(153,161)(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)
(176,186)(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)
(199,208)(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)
(207,215)(217,244)(218,246)(219,245)(220,247)(221,249)(222,248)(223,250)
(224,252)(225,251)(226,262)(227,264)(228,263)(229,265)(230,267)(231,266)
(232,268)(233,270)(234,269)(235,253)(236,255)(237,254)(238,256)(239,258)
(240,257)(241,259)(242,261)(243,260)(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)(325,352)
(326,354)(327,353)(328,355)(329,357)(330,356)(331,358)(332,360)(333,359)
(334,370)(335,372)(336,371)(337,373)(338,375)(339,374)(340,376)(341,378)
(342,377)(343,361)(344,363)(345,362)(346,364)(347,366)(348,365)(349,367)
(350,369)(351,368)(379,406)(380,408)(381,407)(382,409)(383,411)(384,410)
(385,412)(386,414)(387,413)(388,424)(389,426)(390,425)(391,427)(392,429)
(393,428)(394,430)(395,432)(396,431)(397,415)(398,417)(399,416)(400,418)
(401,420)(402,419)(403,421)(404,423)(405,422);
s3 := Sym(432)!( 1,217)( 2,218)( 3,219)( 4,220)( 5,221)( 6,222)( 7,223)
( 8,224)( 9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)
( 16,232)( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)
( 40,256)( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)
( 56,272)( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)
( 96,312)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)
(112,328)(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)
(120,336)(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)
(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)
(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)
(144,360)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)
(152,368)(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)
(160,376)(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)
(168,384)(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)
(176,392)(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)
(184,400)(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)
(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)
(200,416)(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)
(208,424)(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)
(216,432);
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,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*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 >;
References : None.
to this polytope