Polytope of Type {9,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,6,4}*1728a
if this polytope has a name.
Group : SmallGroup(1728,30216)
Rank : 4
Schlafli Type : {9,6,4}
Number of vertices, edges, etc : 36, 108, 48, 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 : {9,6,2}*864
3-fold quotients : {3,6,4}*576a
4-fold quotients : {9,6,4}*432
6-fold quotients : {3,6,2}*288
8-fold quotients : {9,6,2}*216
9-fold quotients : {3,6,4}*192
12-fold quotients : {9,2,4}*144, {3,6,4}*144
18-fold quotients : {3,6,2}*96
24-fold quotients : {9,2,2}*72, {3,6,2}*72
36-fold quotients : {3,2,4}*48, {3,3,2}*48
72-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)
( 44, 83)( 45, 77)( 46, 78)( 47, 80)( 48, 79)( 49,105)( 50,106)( 51,108)
( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)( 59,100)
( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)( 67, 92)
( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)(111,112)(113,117)(114,118)
(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,181)(146,182)
(147,184)(148,183)(149,189)(150,190)(151,192)(152,191)(153,185)(154,186)
(155,188)(156,187)(157,213)(158,214)(159,216)(160,215)(161,209)(162,210)
(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)(170,202)
(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)(178,194)
(179,196)(180,195)(219,220)(221,225)(222,226)(223,228)(224,227)(229,249)
(230,250)(231,252)(232,251)(233,245)(234,246)(235,248)(236,247)(237,241)
(238,242)(239,244)(240,243)(253,289)(254,290)(255,292)(256,291)(257,297)
(258,298)(259,300)(260,299)(261,293)(262,294)(263,296)(264,295)(265,321)
(266,322)(267,324)(268,323)(269,317)(270,318)(271,320)(272,319)(273,313)
(274,314)(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)(281,305)
(282,306)(283,308)(284,307)(285,301)(286,302)(287,304)(288,303)(327,328)
(329,333)(330,334)(331,336)(332,335)(337,357)(338,358)(339,360)(340,359)
(341,353)(342,354)(343,356)(344,355)(345,349)(346,350)(347,352)(348,351)
(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)(368,407)
(369,401)(370,402)(371,404)(372,403)(373,429)(374,430)(375,432)(376,431)
(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)(384,423)
(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)
(393,409)(394,410)(395,412)(396,411);;
s1 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 57)( 6, 60)( 7, 59)( 8, 58)
( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 37)( 14, 40)( 15, 39)( 16, 38)
( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 41)( 22, 44)( 23, 43)( 24, 42)
( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)( 32, 66)
( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 73, 85)( 74, 88)( 75, 87)( 76, 86)
( 77, 93)( 78, 96)( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)
( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,157)(110,160)(111,159)
(112,158)(113,165)(114,168)(115,167)(116,166)(117,161)(118,164)(119,163)
(120,162)(121,145)(122,148)(123,147)(124,146)(125,153)(126,156)(127,155)
(128,154)(129,149)(130,152)(131,151)(132,150)(133,177)(134,180)(135,179)
(136,178)(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)(143,171)
(144,170)(181,193)(182,196)(183,195)(184,194)(185,201)(186,204)(187,203)
(188,202)(189,197)(190,200)(191,199)(192,198)(205,213)(206,216)(207,215)
(208,214)(210,212)(217,265)(218,268)(219,267)(220,266)(221,273)(222,276)
(223,275)(224,274)(225,269)(226,272)(227,271)(228,270)(229,253)(230,256)
(231,255)(232,254)(233,261)(234,264)(235,263)(236,262)(237,257)(238,260)
(239,259)(240,258)(241,285)(242,288)(243,287)(244,286)(245,281)(246,284)
(247,283)(248,282)(249,277)(250,280)(251,279)(252,278)(289,301)(290,304)
(291,303)(292,302)(293,309)(294,312)(295,311)(296,310)(297,305)(298,308)
(299,307)(300,306)(313,321)(314,324)(315,323)(316,322)(318,320)(325,373)
(326,376)(327,375)(328,374)(329,381)(330,384)(331,383)(332,382)(333,377)
(334,380)(335,379)(336,378)(337,361)(338,364)(339,363)(340,362)(341,369)
(342,372)(343,371)(344,370)(345,365)(346,368)(347,367)(348,366)(349,393)
(350,396)(351,395)(352,394)(353,389)(354,392)(355,391)(356,390)(357,385)
(358,388)(359,387)(360,386)(397,409)(398,412)(399,411)(400,410)(401,417)
(402,420)(403,419)(404,418)(405,413)(406,416)(407,415)(408,414)(421,429)
(422,432)(423,431)(424,430)(426,428);;
s2 := ( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)
( 33, 34)( 37, 74)( 38, 73)( 39, 75)( 40, 76)( 41, 78)( 42, 77)( 43, 79)
( 44, 80)( 45, 82)( 46, 81)( 47, 83)( 48, 84)( 49, 86)( 50, 85)( 51, 87)
( 52, 88)( 53, 90)( 54, 89)( 55, 91)( 56, 92)( 57, 94)( 58, 93)( 59, 95)
( 60, 96)( 61, 98)( 62, 97)( 63, 99)( 64,100)( 65,102)( 66,101)( 67,103)
( 68,104)( 69,106)( 70,105)( 71,107)( 72,108)(109,110)(113,114)(117,118)
(121,122)(125,126)(129,130)(133,134)(137,138)(141,142)(145,182)(146,181)
(147,183)(148,184)(149,186)(150,185)(151,187)(152,188)(153,190)(154,189)
(155,191)(156,192)(157,194)(158,193)(159,195)(160,196)(161,198)(162,197)
(163,199)(164,200)(165,202)(166,201)(167,203)(168,204)(169,206)(170,205)
(171,207)(172,208)(173,210)(174,209)(175,211)(176,212)(177,214)(178,213)
(179,215)(180,216)(217,326)(218,325)(219,327)(220,328)(221,330)(222,329)
(223,331)(224,332)(225,334)(226,333)(227,335)(228,336)(229,338)(230,337)
(231,339)(232,340)(233,342)(234,341)(235,343)(236,344)(237,346)(238,345)
(239,347)(240,348)(241,350)(242,349)(243,351)(244,352)(245,354)(246,353)
(247,355)(248,356)(249,358)(250,357)(251,359)(252,360)(253,398)(254,397)
(255,399)(256,400)(257,402)(258,401)(259,403)(260,404)(261,406)(262,405)
(263,407)(264,408)(265,410)(266,409)(267,411)(268,412)(269,414)(270,413)
(271,415)(272,416)(273,418)(274,417)(275,419)(276,420)(277,422)(278,421)
(279,423)(280,424)(281,426)(282,425)(283,427)(284,428)(285,430)(286,429)
(287,431)(288,432)(289,362)(290,361)(291,363)(292,364)(293,366)(294,365)
(295,367)(296,368)(297,370)(298,369)(299,371)(300,372)(301,374)(302,373)
(303,375)(304,376)(305,378)(306,377)(307,379)(308,380)(309,382)(310,381)
(311,383)(312,384)(313,386)(314,385)(315,387)(316,388)(317,390)(318,389)
(319,391)(320,392)(321,394)(322,393)(323,395)(324,396);;
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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)
( 43, 84)( 44, 83)( 45, 77)( 46, 78)( 47, 80)( 48, 79)( 49,105)( 50,106)
( 51,108)( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)
( 59,100)( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)
( 67, 92)( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)(111,112)(113,117)
(114,118)(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)
(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,181)
(146,182)(147,184)(148,183)(149,189)(150,190)(151,192)(152,191)(153,185)
(154,186)(155,188)(156,187)(157,213)(158,214)(159,216)(160,215)(161,209)
(162,210)(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)
(170,202)(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)
(178,194)(179,196)(180,195)(219,220)(221,225)(222,226)(223,228)(224,227)
(229,249)(230,250)(231,252)(232,251)(233,245)(234,246)(235,248)(236,247)
(237,241)(238,242)(239,244)(240,243)(253,289)(254,290)(255,292)(256,291)
(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)(263,296)(264,295)
(265,321)(266,322)(267,324)(268,323)(269,317)(270,318)(271,320)(272,319)
(273,313)(274,314)(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)
(281,305)(282,306)(283,308)(284,307)(285,301)(286,302)(287,304)(288,303)
(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)(338,358)(339,360)
(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)(346,350)(347,352)
(348,351)(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)
(368,407)(369,401)(370,402)(371,404)(372,403)(373,429)(374,430)(375,432)
(376,431)(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)
(384,423)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)
(392,415)(393,409)(394,410)(395,412)(396,411);
s1 := Sym(432)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 57)( 6, 60)( 7, 59)
( 8, 58)( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 37)( 14, 40)( 15, 39)
( 16, 38)( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 41)( 22, 44)( 23, 43)
( 24, 42)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 65)( 30, 68)( 31, 67)
( 32, 66)( 33, 61)( 34, 64)( 35, 63)( 36, 62)( 73, 85)( 74, 88)( 75, 87)
( 76, 86)( 77, 93)( 78, 96)( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)
( 84, 90)( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,157)(110,160)
(111,159)(112,158)(113,165)(114,168)(115,167)(116,166)(117,161)(118,164)
(119,163)(120,162)(121,145)(122,148)(123,147)(124,146)(125,153)(126,156)
(127,155)(128,154)(129,149)(130,152)(131,151)(132,150)(133,177)(134,180)
(135,179)(136,178)(137,173)(138,176)(139,175)(140,174)(141,169)(142,172)
(143,171)(144,170)(181,193)(182,196)(183,195)(184,194)(185,201)(186,204)
(187,203)(188,202)(189,197)(190,200)(191,199)(192,198)(205,213)(206,216)
(207,215)(208,214)(210,212)(217,265)(218,268)(219,267)(220,266)(221,273)
(222,276)(223,275)(224,274)(225,269)(226,272)(227,271)(228,270)(229,253)
(230,256)(231,255)(232,254)(233,261)(234,264)(235,263)(236,262)(237,257)
(238,260)(239,259)(240,258)(241,285)(242,288)(243,287)(244,286)(245,281)
(246,284)(247,283)(248,282)(249,277)(250,280)(251,279)(252,278)(289,301)
(290,304)(291,303)(292,302)(293,309)(294,312)(295,311)(296,310)(297,305)
(298,308)(299,307)(300,306)(313,321)(314,324)(315,323)(316,322)(318,320)
(325,373)(326,376)(327,375)(328,374)(329,381)(330,384)(331,383)(332,382)
(333,377)(334,380)(335,379)(336,378)(337,361)(338,364)(339,363)(340,362)
(341,369)(342,372)(343,371)(344,370)(345,365)(346,368)(347,367)(348,366)
(349,393)(350,396)(351,395)(352,394)(353,389)(354,392)(355,391)(356,390)
(357,385)(358,388)(359,387)(360,386)(397,409)(398,412)(399,411)(400,410)
(401,417)(402,420)(403,419)(404,418)(405,413)(406,416)(407,415)(408,414)
(421,429)(422,432)(423,431)(424,430)(426,428);
s2 := Sym(432)!( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)
( 29, 30)( 33, 34)( 37, 74)( 38, 73)( 39, 75)( 40, 76)( 41, 78)( 42, 77)
( 43, 79)( 44, 80)( 45, 82)( 46, 81)( 47, 83)( 48, 84)( 49, 86)( 50, 85)
( 51, 87)( 52, 88)( 53, 90)( 54, 89)( 55, 91)( 56, 92)( 57, 94)( 58, 93)
( 59, 95)( 60, 96)( 61, 98)( 62, 97)( 63, 99)( 64,100)( 65,102)( 66,101)
( 67,103)( 68,104)( 69,106)( 70,105)( 71,107)( 72,108)(109,110)(113,114)
(117,118)(121,122)(125,126)(129,130)(133,134)(137,138)(141,142)(145,182)
(146,181)(147,183)(148,184)(149,186)(150,185)(151,187)(152,188)(153,190)
(154,189)(155,191)(156,192)(157,194)(158,193)(159,195)(160,196)(161,198)
(162,197)(163,199)(164,200)(165,202)(166,201)(167,203)(168,204)(169,206)
(170,205)(171,207)(172,208)(173,210)(174,209)(175,211)(176,212)(177,214)
(178,213)(179,215)(180,216)(217,326)(218,325)(219,327)(220,328)(221,330)
(222,329)(223,331)(224,332)(225,334)(226,333)(227,335)(228,336)(229,338)
(230,337)(231,339)(232,340)(233,342)(234,341)(235,343)(236,344)(237,346)
(238,345)(239,347)(240,348)(241,350)(242,349)(243,351)(244,352)(245,354)
(246,353)(247,355)(248,356)(249,358)(250,357)(251,359)(252,360)(253,398)
(254,397)(255,399)(256,400)(257,402)(258,401)(259,403)(260,404)(261,406)
(262,405)(263,407)(264,408)(265,410)(266,409)(267,411)(268,412)(269,414)
(270,413)(271,415)(272,416)(273,418)(274,417)(275,419)(276,420)(277,422)
(278,421)(279,423)(280,424)(281,426)(282,425)(283,427)(284,428)(285,430)
(286,429)(287,431)(288,432)(289,362)(290,361)(291,363)(292,364)(293,366)
(294,365)(295,367)(296,368)(297,370)(298,369)(299,371)(300,372)(301,374)
(302,373)(303,375)(304,376)(305,378)(306,377)(307,379)(308,380)(309,382)
(310,381)(311,383)(312,384)(313,386)(314,385)(315,387)(316,388)(317,390)
(318,389)(319,391)(320,392)(321,394)(322,393)(323,395)(324,396);
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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope