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