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Polytope of Type {4,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,6}*1728f
if this polytope has a name.
Group : SmallGroup(1728,30242)
Rank : 4
Schlafli Type : {4,12,6}
Number of vertices, edges, etc : 4, 72, 108, 18
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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 : {4,6,6}*864d
   3-fold quotients : {4,12,6}*576g
   4-fold quotients : {4,3,6}*432
   6-fold quotients : {4,6,6}*288e
   9-fold quotients : {4,12,2}*192c
   12-fold quotients : {4,3,6}*144
   18-fold quotients : {4,6,2}*96c
   36-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,111)(  2,112)(  3,109)(  4,110)(  5,115)(  6,116)(  7,113)(  8,114)
(  9,119)( 10,120)( 11,117)( 12,118)( 13,123)( 14,124)( 15,121)( 16,122)
( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)( 22,132)( 23,129)( 24,130)
( 25,135)( 26,136)( 27,133)( 28,134)( 29,139)( 30,140)( 31,137)( 32,138)
( 33,143)( 34,144)( 35,141)( 36,142)( 37,147)( 38,148)( 39,145)( 40,146)
( 41,151)( 42,152)( 43,149)( 44,150)( 45,155)( 46,156)( 47,153)( 48,154)
( 49,159)( 50,160)( 51,157)( 52,158)( 53,163)( 54,164)( 55,161)( 56,162)
( 57,167)( 58,168)( 59,165)( 60,166)( 61,171)( 62,172)( 63,169)( 64,170)
( 65,175)( 66,176)( 67,173)( 68,174)( 69,179)( 70,180)( 71,177)( 72,178)
( 73,183)( 74,184)( 75,181)( 76,182)( 77,187)( 78,188)( 79,185)( 80,186)
( 81,191)( 82,192)( 83,189)( 84,190)( 85,195)( 86,196)( 87,193)( 88,194)
( 89,199)( 90,200)( 91,197)( 92,198)( 93,203)( 94,204)( 95,201)( 96,202)
( 97,207)( 98,208)( 99,205)(100,206)(101,211)(102,212)(103,209)(104,210)
(105,215)(106,216)(107,213)(108,214)(217,327)(218,328)(219,325)(220,326)
(221,331)(222,332)(223,329)(224,330)(225,335)(226,336)(227,333)(228,334)
(229,339)(230,340)(231,337)(232,338)(233,343)(234,344)(235,341)(236,342)
(237,347)(238,348)(239,345)(240,346)(241,351)(242,352)(243,349)(244,350)
(245,355)(246,356)(247,353)(248,354)(249,359)(250,360)(251,357)(252,358)
(253,363)(254,364)(255,361)(256,362)(257,367)(258,368)(259,365)(260,366)
(261,371)(262,372)(263,369)(264,370)(265,375)(266,376)(267,373)(268,374)
(269,379)(270,380)(271,377)(272,378)(273,383)(274,384)(275,381)(276,382)
(277,387)(278,388)(279,385)(280,386)(281,391)(282,392)(283,389)(284,390)
(285,395)(286,396)(287,393)(288,394)(289,399)(290,400)(291,397)(292,398)
(293,403)(294,404)(295,401)(296,402)(297,407)(298,408)(299,405)(300,406)
(301,411)(302,412)(303,409)(304,410)(305,415)(306,416)(307,413)(308,414)
(309,419)(310,420)(311,417)(312,418)(313,423)(314,424)(315,421)(316,422)
(317,427)(318,428)(319,425)(320,426)(321,431)(322,432)(323,429)(324,430);;
s1 := (  3,  4)(  7,  8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)
( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 37, 73)
( 38, 74)( 39, 76)( 40, 75)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 81)
( 46, 82)( 47, 84)( 48, 83)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)
( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)( 60,107)( 61, 85)
( 62, 86)( 63, 88)( 64, 87)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 93)
( 70, 94)( 71, 96)( 72, 95)(111,112)(115,116)(119,120)(121,133)(122,134)
(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)(129,141)(130,142)
(131,144)(132,143)(145,181)(146,182)(147,184)(148,183)(149,185)(150,186)
(151,188)(152,187)(153,189)(154,190)(155,192)(156,191)(157,205)(158,206)
(159,208)(160,207)(161,209)(162,210)(163,212)(164,211)(165,213)(166,214)
(167,216)(168,215)(169,193)(170,194)(171,196)(172,195)(173,197)(174,198)
(175,200)(176,199)(177,201)(178,202)(179,204)(180,203)(217,325)(218,326)
(219,328)(220,327)(221,329)(222,330)(223,332)(224,331)(225,333)(226,334)
(227,336)(228,335)(229,349)(230,350)(231,352)(232,351)(233,353)(234,354)
(235,356)(236,355)(237,357)(238,358)(239,360)(240,359)(241,337)(242,338)
(243,340)(244,339)(245,341)(246,342)(247,344)(248,343)(249,345)(250,346)
(251,348)(252,347)(253,397)(254,398)(255,400)(256,399)(257,401)(258,402)
(259,404)(260,403)(261,405)(262,406)(263,408)(264,407)(265,421)(266,422)
(267,424)(268,423)(269,425)(270,426)(271,428)(272,427)(273,429)(274,430)
(275,432)(276,431)(277,409)(278,410)(279,412)(280,411)(281,413)(282,414)
(283,416)(284,415)(285,417)(286,418)(287,420)(288,419)(289,361)(290,362)
(291,364)(292,363)(293,365)(294,366)(295,368)(296,367)(297,369)(298,370)
(299,372)(300,371)(301,385)(302,386)(303,388)(304,387)(305,389)(306,390)
(307,392)(308,391)(309,393)(310,394)(311,396)(312,395)(313,373)(314,374)
(315,376)(316,375)(317,377)(318,378)(319,380)(320,379)(321,381)(322,382)
(323,384)(324,383);;
s2 := (  1,281)(  2,284)(  3,283)(  4,282)(  5,285)(  6,288)(  7,287)(  8,286)
(  9,277)( 10,280)( 11,279)( 12,278)( 13,265)( 14,268)( 15,267)( 16,266)
( 17,269)( 18,272)( 19,271)( 20,270)( 21,273)( 22,276)( 23,275)( 24,274)
( 25,261)( 26,264)( 27,263)( 28,262)( 29,253)( 30,256)( 31,255)( 32,254)
( 33,257)( 34,260)( 35,259)( 36,258)( 37,245)( 38,248)( 39,247)( 40,246)
( 41,249)( 42,252)( 43,251)( 44,250)( 45,241)( 46,244)( 47,243)( 48,242)
( 49,229)( 50,232)( 51,231)( 52,230)( 53,233)( 54,236)( 55,235)( 56,234)
( 57,237)( 58,240)( 59,239)( 60,238)( 61,225)( 62,228)( 63,227)( 64,226)
( 65,217)( 66,220)( 67,219)( 68,218)( 69,221)( 70,224)( 71,223)( 72,222)
( 73,317)( 74,320)( 75,319)( 76,318)( 77,321)( 78,324)( 79,323)( 80,322)
( 81,313)( 82,316)( 83,315)( 84,314)( 85,301)( 86,304)( 87,303)( 88,302)
( 89,305)( 90,308)( 91,307)( 92,306)( 93,309)( 94,312)( 95,311)( 96,310)
( 97,297)( 98,300)( 99,299)(100,298)(101,289)(102,292)(103,291)(104,290)
(105,293)(106,296)(107,295)(108,294)(109,389)(110,392)(111,391)(112,390)
(113,393)(114,396)(115,395)(116,394)(117,385)(118,388)(119,387)(120,386)
(121,373)(122,376)(123,375)(124,374)(125,377)(126,380)(127,379)(128,378)
(129,381)(130,384)(131,383)(132,382)(133,369)(134,372)(135,371)(136,370)
(137,361)(138,364)(139,363)(140,362)(141,365)(142,368)(143,367)(144,366)
(145,353)(146,356)(147,355)(148,354)(149,357)(150,360)(151,359)(152,358)
(153,349)(154,352)(155,351)(156,350)(157,337)(158,340)(159,339)(160,338)
(161,341)(162,344)(163,343)(164,342)(165,345)(166,348)(167,347)(168,346)
(169,333)(170,336)(171,335)(172,334)(173,325)(174,328)(175,327)(176,326)
(177,329)(178,332)(179,331)(180,330)(181,425)(182,428)(183,427)(184,426)
(185,429)(186,432)(187,431)(188,430)(189,421)(190,424)(191,423)(192,422)
(193,409)(194,412)(195,411)(196,410)(197,413)(198,416)(199,415)(200,414)
(201,417)(202,420)(203,419)(204,418)(205,405)(206,408)(207,407)(208,406)
(209,397)(210,400)(211,399)(212,398)(213,401)(214,404)(215,403)(216,402);;
s3 := (  5,  9)(  6, 10)(  7, 11)(  8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)
( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)
( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)
( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)
(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)
(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)
(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)
(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)
(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)
(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212)
(221,225)(222,226)(223,227)(224,228)(229,241)(230,242)(231,243)(232,244)
(233,249)(234,250)(235,251)(236,252)(237,245)(238,246)(239,247)(240,248)
(257,261)(258,262)(259,263)(260,264)(265,277)(266,278)(267,279)(268,280)
(269,285)(270,286)(271,287)(272,288)(273,281)(274,282)(275,283)(276,284)
(293,297)(294,298)(295,299)(296,300)(301,313)(302,314)(303,315)(304,316)
(305,321)(306,322)(307,323)(308,324)(309,317)(310,318)(311,319)(312,320)
(329,333)(330,334)(331,335)(332,336)(337,349)(338,350)(339,351)(340,352)
(341,357)(342,358)(343,359)(344,360)(345,353)(346,354)(347,355)(348,356)
(365,369)(366,370)(367,371)(368,372)(373,385)(374,386)(375,387)(376,388)
(377,393)(378,394)(379,395)(380,396)(381,389)(382,390)(383,391)(384,392)
(401,405)(402,406)(403,407)(404,408)(409,421)(410,422)(411,423)(412,424)
(413,429)(414,430)(415,431)(416,432)(417,425)(418,426)(419,427)(420,428);;
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1, 
s1*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(432)!(  1,111)(  2,112)(  3,109)(  4,110)(  5,115)(  6,116)(  7,113)
(  8,114)(  9,119)( 10,120)( 11,117)( 12,118)( 13,123)( 14,124)( 15,121)
( 16,122)( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)( 22,132)( 23,129)
( 24,130)( 25,135)( 26,136)( 27,133)( 28,134)( 29,139)( 30,140)( 31,137)
( 32,138)( 33,143)( 34,144)( 35,141)( 36,142)( 37,147)( 38,148)( 39,145)
( 40,146)( 41,151)( 42,152)( 43,149)( 44,150)( 45,155)( 46,156)( 47,153)
( 48,154)( 49,159)( 50,160)( 51,157)( 52,158)( 53,163)( 54,164)( 55,161)
( 56,162)( 57,167)( 58,168)( 59,165)( 60,166)( 61,171)( 62,172)( 63,169)
( 64,170)( 65,175)( 66,176)( 67,173)( 68,174)( 69,179)( 70,180)( 71,177)
( 72,178)( 73,183)( 74,184)( 75,181)( 76,182)( 77,187)( 78,188)( 79,185)
( 80,186)( 81,191)( 82,192)( 83,189)( 84,190)( 85,195)( 86,196)( 87,193)
( 88,194)( 89,199)( 90,200)( 91,197)( 92,198)( 93,203)( 94,204)( 95,201)
( 96,202)( 97,207)( 98,208)( 99,205)(100,206)(101,211)(102,212)(103,209)
(104,210)(105,215)(106,216)(107,213)(108,214)(217,327)(218,328)(219,325)
(220,326)(221,331)(222,332)(223,329)(224,330)(225,335)(226,336)(227,333)
(228,334)(229,339)(230,340)(231,337)(232,338)(233,343)(234,344)(235,341)
(236,342)(237,347)(238,348)(239,345)(240,346)(241,351)(242,352)(243,349)
(244,350)(245,355)(246,356)(247,353)(248,354)(249,359)(250,360)(251,357)
(252,358)(253,363)(254,364)(255,361)(256,362)(257,367)(258,368)(259,365)
(260,366)(261,371)(262,372)(263,369)(264,370)(265,375)(266,376)(267,373)
(268,374)(269,379)(270,380)(271,377)(272,378)(273,383)(274,384)(275,381)
(276,382)(277,387)(278,388)(279,385)(280,386)(281,391)(282,392)(283,389)
(284,390)(285,395)(286,396)(287,393)(288,394)(289,399)(290,400)(291,397)
(292,398)(293,403)(294,404)(295,401)(296,402)(297,407)(298,408)(299,405)
(300,406)(301,411)(302,412)(303,409)(304,410)(305,415)(306,416)(307,413)
(308,414)(309,419)(310,420)(311,417)(312,418)(313,423)(314,424)(315,421)
(316,422)(317,427)(318,428)(319,425)(320,426)(321,431)(322,432)(323,429)
(324,430);
s1 := Sym(432)!(  3,  4)(  7,  8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)
( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 77)( 42, 78)( 43, 80)( 44, 79)
( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 97)( 50, 98)( 51,100)( 52, 99)
( 53,101)( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)( 60,107)
( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 89)( 66, 90)( 67, 92)( 68, 91)
( 69, 93)( 70, 94)( 71, 96)( 72, 95)(111,112)(115,116)(119,120)(121,133)
(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)(129,141)
(130,142)(131,144)(132,143)(145,181)(146,182)(147,184)(148,183)(149,185)
(150,186)(151,188)(152,187)(153,189)(154,190)(155,192)(156,191)(157,205)
(158,206)(159,208)(160,207)(161,209)(162,210)(163,212)(164,211)(165,213)
(166,214)(167,216)(168,215)(169,193)(170,194)(171,196)(172,195)(173,197)
(174,198)(175,200)(176,199)(177,201)(178,202)(179,204)(180,203)(217,325)
(218,326)(219,328)(220,327)(221,329)(222,330)(223,332)(224,331)(225,333)
(226,334)(227,336)(228,335)(229,349)(230,350)(231,352)(232,351)(233,353)
(234,354)(235,356)(236,355)(237,357)(238,358)(239,360)(240,359)(241,337)
(242,338)(243,340)(244,339)(245,341)(246,342)(247,344)(248,343)(249,345)
(250,346)(251,348)(252,347)(253,397)(254,398)(255,400)(256,399)(257,401)
(258,402)(259,404)(260,403)(261,405)(262,406)(263,408)(264,407)(265,421)
(266,422)(267,424)(268,423)(269,425)(270,426)(271,428)(272,427)(273,429)
(274,430)(275,432)(276,431)(277,409)(278,410)(279,412)(280,411)(281,413)
(282,414)(283,416)(284,415)(285,417)(286,418)(287,420)(288,419)(289,361)
(290,362)(291,364)(292,363)(293,365)(294,366)(295,368)(296,367)(297,369)
(298,370)(299,372)(300,371)(301,385)(302,386)(303,388)(304,387)(305,389)
(306,390)(307,392)(308,391)(309,393)(310,394)(311,396)(312,395)(313,373)
(314,374)(315,376)(316,375)(317,377)(318,378)(319,380)(320,379)(321,381)
(322,382)(323,384)(324,383);
s2 := Sym(432)!(  1,281)(  2,284)(  3,283)(  4,282)(  5,285)(  6,288)(  7,287)
(  8,286)(  9,277)( 10,280)( 11,279)( 12,278)( 13,265)( 14,268)( 15,267)
( 16,266)( 17,269)( 18,272)( 19,271)( 20,270)( 21,273)( 22,276)( 23,275)
( 24,274)( 25,261)( 26,264)( 27,263)( 28,262)( 29,253)( 30,256)( 31,255)
( 32,254)( 33,257)( 34,260)( 35,259)( 36,258)( 37,245)( 38,248)( 39,247)
( 40,246)( 41,249)( 42,252)( 43,251)( 44,250)( 45,241)( 46,244)( 47,243)
( 48,242)( 49,229)( 50,232)( 51,231)( 52,230)( 53,233)( 54,236)( 55,235)
( 56,234)( 57,237)( 58,240)( 59,239)( 60,238)( 61,225)( 62,228)( 63,227)
( 64,226)( 65,217)( 66,220)( 67,219)( 68,218)( 69,221)( 70,224)( 71,223)
( 72,222)( 73,317)( 74,320)( 75,319)( 76,318)( 77,321)( 78,324)( 79,323)
( 80,322)( 81,313)( 82,316)( 83,315)( 84,314)( 85,301)( 86,304)( 87,303)
( 88,302)( 89,305)( 90,308)( 91,307)( 92,306)( 93,309)( 94,312)( 95,311)
( 96,310)( 97,297)( 98,300)( 99,299)(100,298)(101,289)(102,292)(103,291)
(104,290)(105,293)(106,296)(107,295)(108,294)(109,389)(110,392)(111,391)
(112,390)(113,393)(114,396)(115,395)(116,394)(117,385)(118,388)(119,387)
(120,386)(121,373)(122,376)(123,375)(124,374)(125,377)(126,380)(127,379)
(128,378)(129,381)(130,384)(131,383)(132,382)(133,369)(134,372)(135,371)
(136,370)(137,361)(138,364)(139,363)(140,362)(141,365)(142,368)(143,367)
(144,366)(145,353)(146,356)(147,355)(148,354)(149,357)(150,360)(151,359)
(152,358)(153,349)(154,352)(155,351)(156,350)(157,337)(158,340)(159,339)
(160,338)(161,341)(162,344)(163,343)(164,342)(165,345)(166,348)(167,347)
(168,346)(169,333)(170,336)(171,335)(172,334)(173,325)(174,328)(175,327)
(176,326)(177,329)(178,332)(179,331)(180,330)(181,425)(182,428)(183,427)
(184,426)(185,429)(186,432)(187,431)(188,430)(189,421)(190,424)(191,423)
(192,422)(193,409)(194,412)(195,411)(196,410)(197,413)(198,416)(199,415)
(200,414)(201,417)(202,420)(203,419)(204,418)(205,405)(206,408)(207,407)
(208,406)(209,397)(210,400)(211,399)(212,398)(213,401)(214,404)(215,403)
(216,402);
s3 := Sym(432)!(  5,  9)(  6, 10)(  7, 11)(  8, 12)( 13, 25)( 14, 26)( 15, 27)
( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)
( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)
( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)
( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)
( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)
(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)
(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)
(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)
(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)
(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)
(204,212)(221,225)(222,226)(223,227)(224,228)(229,241)(230,242)(231,243)
(232,244)(233,249)(234,250)(235,251)(236,252)(237,245)(238,246)(239,247)
(240,248)(257,261)(258,262)(259,263)(260,264)(265,277)(266,278)(267,279)
(268,280)(269,285)(270,286)(271,287)(272,288)(273,281)(274,282)(275,283)
(276,284)(293,297)(294,298)(295,299)(296,300)(301,313)(302,314)(303,315)
(304,316)(305,321)(306,322)(307,323)(308,324)(309,317)(310,318)(311,319)
(312,320)(329,333)(330,334)(331,335)(332,336)(337,349)(338,350)(339,351)
(340,352)(341,357)(342,358)(343,359)(344,360)(345,353)(346,354)(347,355)
(348,356)(365,369)(366,370)(367,371)(368,372)(373,385)(374,386)(375,387)
(376,388)(377,393)(378,394)(379,395)(380,396)(381,389)(382,390)(383,391)
(384,392)(401,405)(402,406)(403,407)(404,408)(409,421)(410,422)(411,423)
(412,424)(413,429)(414,430)(415,431)(416,432)(417,425)(418,426)(419,427)
(420,428);
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1, 
s1*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2 >; 
 
References : None.
to this polytope