Polytope of Type {4,18,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18,12}*1728e
if this polytope has a name.
Group : SmallGroup(1728,46118)
Rank : 4
Schlafli Type : {4,18,12}
Number of vertices, edges, etc : 4, 36, 108, 12
Order of s0s1s2s3 : 9
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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) :
3-fold quotients : {4,18,4}*576e, {4,6,12}*576f
6-fold quotients : {4,9,4}*288
9-fold quotients : {4,6,4}*192e
18-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)
(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)
(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)
(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)( 55, 56)
( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)( 68, 83)
( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)( 76, 95)
( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 99,100)(103,104)(105,109)(106,110)
(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,133)(118,134)
(119,136)(120,135)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(145,321)(146,322)(147,324)(148,323)(149,325)(150,326)
(151,328)(152,327)(153,333)(154,334)(155,336)(156,335)(157,329)(158,330)
(159,332)(160,331)(161,305)(162,306)(163,308)(164,307)(165,309)(166,310)
(167,312)(168,311)(169,317)(170,318)(171,320)(172,319)(173,313)(174,314)
(175,316)(176,315)(177,289)(178,290)(179,292)(180,291)(181,293)(182,294)
(183,296)(184,295)(185,301)(186,302)(187,304)(188,303)(189,297)(190,298)
(191,300)(192,299)(193,369)(194,370)(195,372)(196,371)(197,373)(198,374)
(199,376)(200,375)(201,381)(202,382)(203,384)(204,383)(205,377)(206,378)
(207,380)(208,379)(209,353)(210,354)(211,356)(212,355)(213,357)(214,358)
(215,360)(216,359)(217,365)(218,366)(219,368)(220,367)(221,361)(222,362)
(223,364)(224,363)(225,337)(226,338)(227,340)(228,339)(229,341)(230,342)
(231,344)(232,343)(233,349)(234,350)(235,352)(236,351)(237,345)(238,346)
(239,348)(240,347)(241,417)(242,418)(243,420)(244,419)(245,421)(246,422)
(247,424)(248,423)(249,429)(250,430)(251,432)(252,431)(253,425)(254,426)
(255,428)(256,427)(257,401)(258,402)(259,404)(260,403)(261,405)(262,406)
(263,408)(264,407)(265,413)(266,414)(267,416)(268,415)(269,409)(270,410)
(271,412)(272,411)(273,385)(274,386)(275,388)(276,387)(277,389)(278,390)
(279,392)(280,391)(281,397)(282,398)(283,400)(284,399)(285,393)(286,394)
(287,396)(288,395);;
s2 := ( 1,145)( 2,148)( 3,147)( 4,146)( 5,157)( 6,160)( 7,159)( 8,158)
( 9,153)( 10,156)( 11,155)( 12,154)( 13,149)( 14,152)( 15,151)( 16,150)
( 17,177)( 18,180)( 19,179)( 20,178)( 21,189)( 22,192)( 23,191)( 24,190)
( 25,185)( 26,188)( 27,187)( 28,186)( 29,181)( 30,184)( 31,183)( 32,182)
( 33,161)( 34,164)( 35,163)( 36,162)( 37,173)( 38,176)( 39,175)( 40,174)
( 41,169)( 42,172)( 43,171)( 44,170)( 45,165)( 46,168)( 47,167)( 48,166)
( 49,241)( 50,244)( 51,243)( 52,242)( 53,253)( 54,256)( 55,255)( 56,254)
( 57,249)( 58,252)( 59,251)( 60,250)( 61,245)( 62,248)( 63,247)( 64,246)
( 65,273)( 66,276)( 67,275)( 68,274)( 69,285)( 70,288)( 71,287)( 72,286)
( 73,281)( 74,284)( 75,283)( 76,282)( 77,277)( 78,280)( 79,279)( 80,278)
( 81,257)( 82,260)( 83,259)( 84,258)( 85,269)( 86,272)( 87,271)( 88,270)
( 89,265)( 90,268)( 91,267)( 92,266)( 93,261)( 94,264)( 95,263)( 96,262)
( 97,193)( 98,196)( 99,195)(100,194)(101,205)(102,208)(103,207)(104,206)
(105,201)(106,204)(107,203)(108,202)(109,197)(110,200)(111,199)(112,198)
(113,225)(114,228)(115,227)(116,226)(117,237)(118,240)(119,239)(120,238)
(121,233)(122,236)(123,235)(124,234)(125,229)(126,232)(127,231)(128,230)
(129,209)(130,212)(131,211)(132,210)(133,221)(134,224)(135,223)(136,222)
(137,217)(138,220)(139,219)(140,218)(141,213)(142,216)(143,215)(144,214)
(289,321)(290,324)(291,323)(292,322)(293,333)(294,336)(295,335)(296,334)
(297,329)(298,332)(299,331)(300,330)(301,325)(302,328)(303,327)(304,326)
(306,308)(309,317)(310,320)(311,319)(312,318)(314,316)(337,417)(338,420)
(339,419)(340,418)(341,429)(342,432)(343,431)(344,430)(345,425)(346,428)
(347,427)(348,426)(349,421)(350,424)(351,423)(352,422)(353,401)(354,404)
(355,403)(356,402)(357,413)(358,416)(359,415)(360,414)(361,409)(362,412)
(363,411)(364,410)(365,405)(366,408)(367,407)(368,406)(369,385)(370,388)
(371,387)(372,386)(373,397)(374,400)(375,399)(376,398)(377,393)(378,396)
(379,395)(380,394)(381,389)(382,392)(383,391)(384,390);;
s3 := ( 1, 50)( 2, 49)( 3, 52)( 4, 51)( 5, 54)( 6, 53)( 7, 56)( 8, 55)
( 9, 58)( 10, 57)( 11, 60)( 12, 59)( 13, 62)( 14, 61)( 15, 64)( 16, 63)
( 17, 66)( 18, 65)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 72)( 24, 71)
( 25, 74)( 26, 73)( 27, 76)( 28, 75)( 29, 78)( 30, 77)( 31, 80)( 32, 79)
( 33, 82)( 34, 81)( 35, 84)( 36, 83)( 37, 86)( 38, 85)( 39, 88)( 40, 87)
( 41, 90)( 42, 89)( 43, 92)( 44, 91)( 45, 94)( 46, 93)( 47, 96)( 48, 95)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,194)(146,193)(147,196)(148,195)(149,198)(150,197)(151,200)(152,199)
(153,202)(154,201)(155,204)(156,203)(157,206)(158,205)(159,208)(160,207)
(161,210)(162,209)(163,212)(164,211)(165,214)(166,213)(167,216)(168,215)
(169,218)(170,217)(171,220)(172,219)(173,222)(174,221)(175,224)(176,223)
(177,226)(178,225)(179,228)(180,227)(181,230)(182,229)(183,232)(184,231)
(185,234)(186,233)(187,236)(188,235)(189,238)(190,237)(191,240)(192,239)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,338)(290,337)(291,340)(292,339)(293,342)(294,341)(295,344)(296,343)
(297,346)(298,345)(299,348)(300,347)(301,350)(302,349)(303,352)(304,351)
(305,354)(306,353)(307,356)(308,355)(309,358)(310,357)(311,360)(312,359)
(313,362)(314,361)(315,364)(316,363)(317,366)(318,365)(319,368)(320,367)
(321,370)(322,369)(323,372)(324,371)(325,374)(326,373)(327,376)(328,375)
(329,378)(330,377)(331,380)(332,379)(333,382)(334,381)(335,384)(336,383)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432);;
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*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)
(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)
(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)
(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)
(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)
(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)
(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)
(424,432);
s1 := Sym(432)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 51, 52)
( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 65, 81)( 66, 82)( 67, 84)
( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 93)( 74, 94)( 75, 96)
( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 99,100)(103,104)(105,109)
(106,110)(107,112)(108,111)(113,129)(114,130)(115,132)(116,131)(117,133)
(118,134)(119,136)(120,135)(121,141)(122,142)(123,144)(124,143)(125,137)
(126,138)(127,140)(128,139)(145,321)(146,322)(147,324)(148,323)(149,325)
(150,326)(151,328)(152,327)(153,333)(154,334)(155,336)(156,335)(157,329)
(158,330)(159,332)(160,331)(161,305)(162,306)(163,308)(164,307)(165,309)
(166,310)(167,312)(168,311)(169,317)(170,318)(171,320)(172,319)(173,313)
(174,314)(175,316)(176,315)(177,289)(178,290)(179,292)(180,291)(181,293)
(182,294)(183,296)(184,295)(185,301)(186,302)(187,304)(188,303)(189,297)
(190,298)(191,300)(192,299)(193,369)(194,370)(195,372)(196,371)(197,373)
(198,374)(199,376)(200,375)(201,381)(202,382)(203,384)(204,383)(205,377)
(206,378)(207,380)(208,379)(209,353)(210,354)(211,356)(212,355)(213,357)
(214,358)(215,360)(216,359)(217,365)(218,366)(219,368)(220,367)(221,361)
(222,362)(223,364)(224,363)(225,337)(226,338)(227,340)(228,339)(229,341)
(230,342)(231,344)(232,343)(233,349)(234,350)(235,352)(236,351)(237,345)
(238,346)(239,348)(240,347)(241,417)(242,418)(243,420)(244,419)(245,421)
(246,422)(247,424)(248,423)(249,429)(250,430)(251,432)(252,431)(253,425)
(254,426)(255,428)(256,427)(257,401)(258,402)(259,404)(260,403)(261,405)
(262,406)(263,408)(264,407)(265,413)(266,414)(267,416)(268,415)(269,409)
(270,410)(271,412)(272,411)(273,385)(274,386)(275,388)(276,387)(277,389)
(278,390)(279,392)(280,391)(281,397)(282,398)(283,400)(284,399)(285,393)
(286,394)(287,396)(288,395);
s2 := Sym(432)!( 1,145)( 2,148)( 3,147)( 4,146)( 5,157)( 6,160)( 7,159)
( 8,158)( 9,153)( 10,156)( 11,155)( 12,154)( 13,149)( 14,152)( 15,151)
( 16,150)( 17,177)( 18,180)( 19,179)( 20,178)( 21,189)( 22,192)( 23,191)
( 24,190)( 25,185)( 26,188)( 27,187)( 28,186)( 29,181)( 30,184)( 31,183)
( 32,182)( 33,161)( 34,164)( 35,163)( 36,162)( 37,173)( 38,176)( 39,175)
( 40,174)( 41,169)( 42,172)( 43,171)( 44,170)( 45,165)( 46,168)( 47,167)
( 48,166)( 49,241)( 50,244)( 51,243)( 52,242)( 53,253)( 54,256)( 55,255)
( 56,254)( 57,249)( 58,252)( 59,251)( 60,250)( 61,245)( 62,248)( 63,247)
( 64,246)( 65,273)( 66,276)( 67,275)( 68,274)( 69,285)( 70,288)( 71,287)
( 72,286)( 73,281)( 74,284)( 75,283)( 76,282)( 77,277)( 78,280)( 79,279)
( 80,278)( 81,257)( 82,260)( 83,259)( 84,258)( 85,269)( 86,272)( 87,271)
( 88,270)( 89,265)( 90,268)( 91,267)( 92,266)( 93,261)( 94,264)( 95,263)
( 96,262)( 97,193)( 98,196)( 99,195)(100,194)(101,205)(102,208)(103,207)
(104,206)(105,201)(106,204)(107,203)(108,202)(109,197)(110,200)(111,199)
(112,198)(113,225)(114,228)(115,227)(116,226)(117,237)(118,240)(119,239)
(120,238)(121,233)(122,236)(123,235)(124,234)(125,229)(126,232)(127,231)
(128,230)(129,209)(130,212)(131,211)(132,210)(133,221)(134,224)(135,223)
(136,222)(137,217)(138,220)(139,219)(140,218)(141,213)(142,216)(143,215)
(144,214)(289,321)(290,324)(291,323)(292,322)(293,333)(294,336)(295,335)
(296,334)(297,329)(298,332)(299,331)(300,330)(301,325)(302,328)(303,327)
(304,326)(306,308)(309,317)(310,320)(311,319)(312,318)(314,316)(337,417)
(338,420)(339,419)(340,418)(341,429)(342,432)(343,431)(344,430)(345,425)
(346,428)(347,427)(348,426)(349,421)(350,424)(351,423)(352,422)(353,401)
(354,404)(355,403)(356,402)(357,413)(358,416)(359,415)(360,414)(361,409)
(362,412)(363,411)(364,410)(365,405)(366,408)(367,407)(368,406)(369,385)
(370,388)(371,387)(372,386)(373,397)(374,400)(375,399)(376,398)(377,393)
(378,396)(379,395)(380,394)(381,389)(382,392)(383,391)(384,390);
s3 := Sym(432)!( 1, 50)( 2, 49)( 3, 52)( 4, 51)( 5, 54)( 6, 53)( 7, 56)
( 8, 55)( 9, 58)( 10, 57)( 11, 60)( 12, 59)( 13, 62)( 14, 61)( 15, 64)
( 16, 63)( 17, 66)( 18, 65)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 72)
( 24, 71)( 25, 74)( 26, 73)( 27, 76)( 28, 75)( 29, 78)( 30, 77)( 31, 80)
( 32, 79)( 33, 82)( 34, 81)( 35, 84)( 36, 83)( 37, 86)( 38, 85)( 39, 88)
( 40, 87)( 41, 90)( 42, 89)( 43, 92)( 44, 91)( 45, 94)( 46, 93)( 47, 96)
( 48, 95)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,194)(146,193)(147,196)(148,195)(149,198)(150,197)(151,200)
(152,199)(153,202)(154,201)(155,204)(156,203)(157,206)(158,205)(159,208)
(160,207)(161,210)(162,209)(163,212)(164,211)(165,214)(166,213)(167,216)
(168,215)(169,218)(170,217)(171,220)(172,219)(173,222)(174,221)(175,224)
(176,223)(177,226)(178,225)(179,228)(180,227)(181,230)(182,229)(183,232)
(184,231)(185,234)(186,233)(187,236)(188,235)(189,238)(190,237)(191,240)
(192,239)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,338)(290,337)(291,340)(292,339)(293,342)(294,341)(295,344)
(296,343)(297,346)(298,345)(299,348)(300,347)(301,350)(302,349)(303,352)
(304,351)(305,354)(306,353)(307,356)(308,355)(309,358)(310,357)(311,360)
(312,359)(313,362)(314,361)(315,364)(316,363)(317,366)(318,365)(319,368)
(320,367)(321,370)(322,369)(323,372)(324,371)(325,374)(326,373)(327,376)
(328,375)(329,378)(330,377)(331,380)(332,379)(333,382)(334,381)(335,384)
(336,383)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432);
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*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope