Polytope of Type {16,6,9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,6,9}*1728
if this polytope has a name.
Group : SmallGroup(1728,5288)
Rank : 4
Schlafli Type : {16,6,9}
Number of vertices, edges, etc : 16, 48, 27, 9
Order of s0s1s2s3 : 144
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 : {8,6,9}*864
3-fold quotients : {16,2,9}*576, {16,6,3}*576
4-fold quotients : {4,6,9}*432
6-fold quotients : {8,2,9}*288, {8,6,3}*288
8-fold quotients : {2,6,9}*216
9-fold quotients : {16,2,3}*192
12-fold quotients : {4,2,9}*144, {4,6,3}*144
18-fold quotients : {8,2,3}*96
24-fold quotients : {2,2,9}*72, {2,6,3}*72
36-fold quotients : {4,2,3}*48
72-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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)( 55,298)( 56,299)
( 57,300)( 58,301)( 59,302)( 60,303)( 61,304)( 62,305)( 63,306)( 64,307)
( 65,308)( 66,309)( 67,310)( 68,311)( 69,312)( 70,313)( 71,314)( 72,315)
( 73,316)( 74,317)( 75,318)( 76,319)( 77,320)( 78,321)( 79,322)( 80,323)
( 81,324)( 82,271)( 83,272)( 84,273)( 85,274)( 86,275)( 87,276)( 88,277)
( 89,278)( 90,279)( 91,280)( 92,281)( 93,282)( 94,283)( 95,284)( 96,285)
( 97,286)( 98,287)( 99,288)(100,289)(101,290)(102,291)(103,292)(104,293)
(105,294)(106,295)(107,296)(108,297)(109,379)(110,380)(111,381)(112,382)
(113,383)(114,384)(115,385)(116,386)(117,387)(118,388)(119,389)(120,390)
(121,391)(122,392)(123,393)(124,394)(125,395)(126,396)(127,397)(128,398)
(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)
(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)(144,414)
(145,415)(146,416)(147,417)(148,418)(149,419)(150,420)(151,421)(152,422)
(153,423)(154,424)(155,425)(156,426)(157,427)(158,428)(159,429)(160,430)
(161,431)(162,432)(163,325)(164,326)(165,327)(166,328)(167,329)(168,330)
(169,331)(170,332)(171,333)(172,334)(173,335)(174,336)(175,337)(176,338)
(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,345)(184,346)
(185,347)(186,348)(187,349)(188,350)(189,351)(190,352)(191,353)(192,354)
(193,355)(194,356)(195,357)(196,358)(197,359)(198,360)(199,361)(200,362)
(201,363)(202,364)(203,365)(204,366)(205,367)(206,368)(207,369)(208,370)
(209,371)(210,372)(211,373)(212,374)(213,375)(214,376)(215,377)(216,378);;
s1 := ( 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)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)( 60, 90)
( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)( 68, 98)
( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)( 76,106)
( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(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)(217,325)(218,326)(219,327)(220,331)(221,332)
(222,333)(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)(229,340)
(230,341)(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)(237,345)
(238,349)(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)(245,353)
(246,354)(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)(253,361)
(254,362)(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)(261,366)
(262,370)(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)(269,374)
(270,375)(271,406)(272,407)(273,408)(274,412)(275,413)(276,414)(277,409)
(278,410)(279,411)(280,415)(281,416)(282,417)(283,421)(284,422)(285,423)
(286,418)(287,419)(288,420)(289,424)(290,425)(291,426)(292,430)(293,431)
(294,432)(295,427)(296,428)(297,429)(298,379)(299,380)(300,381)(301,385)
(302,386)(303,387)(304,382)(305,383)(306,384)(307,388)(308,389)(309,390)
(310,394)(311,395)(312,396)(313,391)(314,392)(315,393)(316,397)(317,398)
(318,399)(319,403)(320,404)(321,405)(322,400)(323,401)(324,402);;
s2 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 24)( 11, 23)( 12, 22)( 13, 21)
( 14, 20)( 15, 19)( 16, 27)( 17, 26)( 18, 25)( 28, 31)( 29, 33)( 30, 32)
( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 54)
( 44, 53)( 45, 52)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 78)( 65, 77)
( 66, 76)( 67, 75)( 68, 74)( 69, 73)( 70, 81)( 71, 80)( 72, 79)( 82, 85)
( 83, 87)( 84, 86)( 89, 90)( 91,105)( 92,104)( 93,103)( 94,102)( 95,101)
( 96,100)( 97,108)( 98,107)( 99,106)(109,112)(110,114)(111,113)(116,117)
(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,135)(125,134)
(126,133)(136,139)(137,141)(138,140)(143,144)(145,159)(146,158)(147,157)
(148,156)(149,155)(150,154)(151,162)(152,161)(153,160)(163,166)(164,168)
(165,167)(170,171)(172,186)(173,185)(174,184)(175,183)(176,182)(177,181)
(178,189)(179,188)(180,187)(190,193)(191,195)(192,194)(197,198)(199,213)
(200,212)(201,211)(202,210)(203,209)(204,208)(205,216)(206,215)(207,214)
(217,220)(218,222)(219,221)(224,225)(226,240)(227,239)(228,238)(229,237)
(230,236)(231,235)(232,243)(233,242)(234,241)(244,247)(245,249)(246,248)
(251,252)(253,267)(254,266)(255,265)(256,264)(257,263)(258,262)(259,270)
(260,269)(261,268)(271,274)(272,276)(273,275)(278,279)(280,294)(281,293)
(282,292)(283,291)(284,290)(285,289)(286,297)(287,296)(288,295)(298,301)
(299,303)(300,302)(305,306)(307,321)(308,320)(309,319)(310,318)(311,317)
(312,316)(313,324)(314,323)(315,322)(325,328)(326,330)(327,329)(332,333)
(334,348)(335,347)(336,346)(337,345)(338,344)(339,343)(340,351)(341,350)
(342,349)(352,355)(353,357)(354,356)(359,360)(361,375)(362,374)(363,373)
(364,372)(365,371)(366,370)(367,378)(368,377)(369,376)(379,382)(380,384)
(381,383)(386,387)(388,402)(389,401)(390,400)(391,399)(392,398)(393,397)
(394,405)(395,404)(396,403)(406,409)(407,411)(408,410)(413,414)(415,429)
(416,428)(417,427)(418,426)(419,425)(420,424)(421,432)(422,431)(423,430);;
s3 := ( 1, 10)( 2, 12)( 3, 11)( 4, 16)( 5, 18)( 6, 17)( 7, 13)( 8, 15)
( 9, 14)( 19, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 37)( 29, 39)( 30, 38)
( 31, 43)( 32, 45)( 33, 44)( 34, 40)( 35, 42)( 36, 41)( 46, 48)( 49, 54)
( 50, 53)( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)( 60, 71)
( 61, 67)( 62, 69)( 63, 68)( 73, 75)( 76, 81)( 77, 80)( 78, 79)( 82, 91)
( 83, 93)( 84, 92)( 85, 97)( 86, 99)( 87, 98)( 88, 94)( 89, 96)( 90, 95)
(100,102)(103,108)(104,107)(105,106)(109,118)(110,120)(111,119)(112,124)
(113,126)(114,125)(115,121)(116,123)(117,122)(127,129)(130,135)(131,134)
(132,133)(136,145)(137,147)(138,146)(139,151)(140,153)(141,152)(142,148)
(143,150)(144,149)(154,156)(157,162)(158,161)(159,160)(163,172)(164,174)
(165,173)(166,178)(167,180)(168,179)(169,175)(170,177)(171,176)(181,183)
(184,189)(185,188)(186,187)(190,199)(191,201)(192,200)(193,205)(194,207)
(195,206)(196,202)(197,204)(198,203)(208,210)(211,216)(212,215)(213,214)
(217,226)(218,228)(219,227)(220,232)(221,234)(222,233)(223,229)(224,231)
(225,230)(235,237)(238,243)(239,242)(240,241)(244,253)(245,255)(246,254)
(247,259)(248,261)(249,260)(250,256)(251,258)(252,257)(262,264)(265,270)
(266,269)(267,268)(271,280)(272,282)(273,281)(274,286)(275,288)(276,287)
(277,283)(278,285)(279,284)(289,291)(292,297)(293,296)(294,295)(298,307)
(299,309)(300,308)(301,313)(302,315)(303,314)(304,310)(305,312)(306,311)
(316,318)(319,324)(320,323)(321,322)(325,334)(326,336)(327,335)(328,340)
(329,342)(330,341)(331,337)(332,339)(333,338)(343,345)(346,351)(347,350)
(348,349)(352,361)(353,363)(354,362)(355,367)(356,369)(357,368)(358,364)
(359,366)(360,365)(370,372)(373,378)(374,377)(375,376)(379,388)(380,390)
(381,389)(382,394)(383,396)(384,395)(385,391)(386,393)(387,392)(397,399)
(400,405)(401,404)(402,403)(406,415)(407,417)(408,416)(409,421)(410,423)
(411,422)(412,418)(413,420)(414,419)(424,426)(427,432)(428,431)(429,430);;
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*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)!( 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)( 55,298)
( 56,299)( 57,300)( 58,301)( 59,302)( 60,303)( 61,304)( 62,305)( 63,306)
( 64,307)( 65,308)( 66,309)( 67,310)( 68,311)( 69,312)( 70,313)( 71,314)
( 72,315)( 73,316)( 74,317)( 75,318)( 76,319)( 77,320)( 78,321)( 79,322)
( 80,323)( 81,324)( 82,271)( 83,272)( 84,273)( 85,274)( 86,275)( 87,276)
( 88,277)( 89,278)( 90,279)( 91,280)( 92,281)( 93,282)( 94,283)( 95,284)
( 96,285)( 97,286)( 98,287)( 99,288)(100,289)(101,290)(102,291)(103,292)
(104,293)(105,294)(106,295)(107,296)(108,297)(109,379)(110,380)(111,381)
(112,382)(113,383)(114,384)(115,385)(116,386)(117,387)(118,388)(119,389)
(120,390)(121,391)(122,392)(123,393)(124,394)(125,395)(126,396)(127,397)
(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)
(136,406)(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)
(144,414)(145,415)(146,416)(147,417)(148,418)(149,419)(150,420)(151,421)
(152,422)(153,423)(154,424)(155,425)(156,426)(157,427)(158,428)(159,429)
(160,430)(161,431)(162,432)(163,325)(164,326)(165,327)(166,328)(167,329)
(168,330)(169,331)(170,332)(171,333)(172,334)(173,335)(174,336)(175,337)
(176,338)(177,339)(178,340)(179,341)(180,342)(181,343)(182,344)(183,345)
(184,346)(185,347)(186,348)(187,349)(188,350)(189,351)(190,352)(191,353)
(192,354)(193,355)(194,356)(195,357)(196,358)(197,359)(198,360)(199,361)
(200,362)(201,363)(202,364)(203,365)(204,366)(205,367)(206,368)(207,369)
(208,370)(209,371)(210,372)(211,373)(212,374)(213,375)(214,376)(215,377)
(216,378);
s1 := 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)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)
( 60, 90)( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)
( 68, 98)( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)
( 76,106)( 77,107)( 78,108)( 79,103)( 80,104)( 81,105)(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)(217,325)(218,326)(219,327)(220,331)
(221,332)(222,333)(223,328)(224,329)(225,330)(226,334)(227,335)(228,336)
(229,340)(230,341)(231,342)(232,337)(233,338)(234,339)(235,343)(236,344)
(237,345)(238,349)(239,350)(240,351)(241,346)(242,347)(243,348)(244,352)
(245,353)(246,354)(247,358)(248,359)(249,360)(250,355)(251,356)(252,357)
(253,361)(254,362)(255,363)(256,367)(257,368)(258,369)(259,364)(260,365)
(261,366)(262,370)(263,371)(264,372)(265,376)(266,377)(267,378)(268,373)
(269,374)(270,375)(271,406)(272,407)(273,408)(274,412)(275,413)(276,414)
(277,409)(278,410)(279,411)(280,415)(281,416)(282,417)(283,421)(284,422)
(285,423)(286,418)(287,419)(288,420)(289,424)(290,425)(291,426)(292,430)
(293,431)(294,432)(295,427)(296,428)(297,429)(298,379)(299,380)(300,381)
(301,385)(302,386)(303,387)(304,382)(305,383)(306,384)(307,388)(308,389)
(309,390)(310,394)(311,395)(312,396)(313,391)(314,392)(315,393)(316,397)
(317,398)(318,399)(319,403)(320,404)(321,405)(322,400)(323,401)(324,402);
s2 := Sym(432)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 24)( 11, 23)( 12, 22)
( 13, 21)( 14, 20)( 15, 19)( 16, 27)( 17, 26)( 18, 25)( 28, 31)( 29, 33)
( 30, 32)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 54)( 44, 53)( 45, 52)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 78)
( 65, 77)( 66, 76)( 67, 75)( 68, 74)( 69, 73)( 70, 81)( 71, 80)( 72, 79)
( 82, 85)( 83, 87)( 84, 86)( 89, 90)( 91,105)( 92,104)( 93,103)( 94,102)
( 95,101)( 96,100)( 97,108)( 98,107)( 99,106)(109,112)(110,114)(111,113)
(116,117)(118,132)(119,131)(120,130)(121,129)(122,128)(123,127)(124,135)
(125,134)(126,133)(136,139)(137,141)(138,140)(143,144)(145,159)(146,158)
(147,157)(148,156)(149,155)(150,154)(151,162)(152,161)(153,160)(163,166)
(164,168)(165,167)(170,171)(172,186)(173,185)(174,184)(175,183)(176,182)
(177,181)(178,189)(179,188)(180,187)(190,193)(191,195)(192,194)(197,198)
(199,213)(200,212)(201,211)(202,210)(203,209)(204,208)(205,216)(206,215)
(207,214)(217,220)(218,222)(219,221)(224,225)(226,240)(227,239)(228,238)
(229,237)(230,236)(231,235)(232,243)(233,242)(234,241)(244,247)(245,249)
(246,248)(251,252)(253,267)(254,266)(255,265)(256,264)(257,263)(258,262)
(259,270)(260,269)(261,268)(271,274)(272,276)(273,275)(278,279)(280,294)
(281,293)(282,292)(283,291)(284,290)(285,289)(286,297)(287,296)(288,295)
(298,301)(299,303)(300,302)(305,306)(307,321)(308,320)(309,319)(310,318)
(311,317)(312,316)(313,324)(314,323)(315,322)(325,328)(326,330)(327,329)
(332,333)(334,348)(335,347)(336,346)(337,345)(338,344)(339,343)(340,351)
(341,350)(342,349)(352,355)(353,357)(354,356)(359,360)(361,375)(362,374)
(363,373)(364,372)(365,371)(366,370)(367,378)(368,377)(369,376)(379,382)
(380,384)(381,383)(386,387)(388,402)(389,401)(390,400)(391,399)(392,398)
(393,397)(394,405)(395,404)(396,403)(406,409)(407,411)(408,410)(413,414)
(415,429)(416,428)(417,427)(418,426)(419,425)(420,424)(421,432)(422,431)
(423,430);
s3 := Sym(432)!( 1, 10)( 2, 12)( 3, 11)( 4, 16)( 5, 18)( 6, 17)( 7, 13)
( 8, 15)( 9, 14)( 19, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 37)( 29, 39)
( 30, 38)( 31, 43)( 32, 45)( 33, 44)( 34, 40)( 35, 42)( 36, 41)( 46, 48)
( 49, 54)( 50, 53)( 51, 52)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)
( 60, 71)( 61, 67)( 62, 69)( 63, 68)( 73, 75)( 76, 81)( 77, 80)( 78, 79)
( 82, 91)( 83, 93)( 84, 92)( 85, 97)( 86, 99)( 87, 98)( 88, 94)( 89, 96)
( 90, 95)(100,102)(103,108)(104,107)(105,106)(109,118)(110,120)(111,119)
(112,124)(113,126)(114,125)(115,121)(116,123)(117,122)(127,129)(130,135)
(131,134)(132,133)(136,145)(137,147)(138,146)(139,151)(140,153)(141,152)
(142,148)(143,150)(144,149)(154,156)(157,162)(158,161)(159,160)(163,172)
(164,174)(165,173)(166,178)(167,180)(168,179)(169,175)(170,177)(171,176)
(181,183)(184,189)(185,188)(186,187)(190,199)(191,201)(192,200)(193,205)
(194,207)(195,206)(196,202)(197,204)(198,203)(208,210)(211,216)(212,215)
(213,214)(217,226)(218,228)(219,227)(220,232)(221,234)(222,233)(223,229)
(224,231)(225,230)(235,237)(238,243)(239,242)(240,241)(244,253)(245,255)
(246,254)(247,259)(248,261)(249,260)(250,256)(251,258)(252,257)(262,264)
(265,270)(266,269)(267,268)(271,280)(272,282)(273,281)(274,286)(275,288)
(276,287)(277,283)(278,285)(279,284)(289,291)(292,297)(293,296)(294,295)
(298,307)(299,309)(300,308)(301,313)(302,315)(303,314)(304,310)(305,312)
(306,311)(316,318)(319,324)(320,323)(321,322)(325,334)(326,336)(327,335)
(328,340)(329,342)(330,341)(331,337)(332,339)(333,338)(343,345)(346,351)
(347,350)(348,349)(352,361)(353,363)(354,362)(355,367)(356,369)(357,368)
(358,364)(359,366)(360,365)(370,372)(373,378)(374,377)(375,376)(379,388)
(380,390)(381,389)(382,394)(383,396)(384,395)(385,391)(386,393)(387,392)
(397,399)(400,405)(401,404)(402,403)(406,415)(407,417)(408,416)(409,421)
(410,423)(411,422)(412,418)(413,420)(414,419)(424,426)(427,432)(428,431)
(429,430);
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*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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