Polytope of Type {18,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,12,4}*1728c
if this polytope has a name.
Group : SmallGroup(1728,30173)
Rank : 4
Schlafli Type : {18,12,4}
Number of vertices, edges, etc : 18, 108, 24, 4
Order of s0s1s2s3 : 36
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) :
2-fold quotients : {18,6,4}*864c
3-fold quotients : {6,12,4}*576d
6-fold quotients : {6,6,4}*288d
9-fold quotients : {2,12,4}*192b
18-fold quotients : {2,6,4}*96c
36-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 33)( 14, 34)( 15, 35)( 16, 36)
( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)
( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 69)( 50, 70)( 51, 71)( 52, 72)
( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 61)( 58, 62)( 59, 63)( 60, 64)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85,105)( 86,106)( 87,107)( 88,108)
( 89,101)( 90,102)( 91,103)( 92,104)( 93, 97)( 94, 98)( 95, 99)( 96,100)
(113,117)(114,118)(115,119)(116,120)(121,141)(122,142)(123,143)(124,144)
(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)
(149,153)(150,154)(151,155)(152,156)(157,177)(158,178)(159,179)(160,180)
(161,173)(162,174)(163,175)(164,176)(165,169)(166,170)(167,171)(168,172)
(185,189)(186,190)(187,191)(188,192)(193,213)(194,214)(195,215)(196,216)
(197,209)(198,210)(199,211)(200,212)(201,205)(202,206)(203,207)(204,208)
(221,225)(222,226)(223,227)(224,228)(229,249)(230,250)(231,251)(232,252)
(233,245)(234,246)(235,247)(236,248)(237,241)(238,242)(239,243)(240,244)
(257,261)(258,262)(259,263)(260,264)(265,285)(266,286)(267,287)(268,288)
(269,281)(270,282)(271,283)(272,284)(273,277)(274,278)(275,279)(276,280)
(293,297)(294,298)(295,299)(296,300)(301,321)(302,322)(303,323)(304,324)
(305,317)(306,318)(307,319)(308,320)(309,313)(310,314)(311,315)(312,316)
(329,333)(330,334)(331,335)(332,336)(337,357)(338,358)(339,359)(340,360)
(341,353)(342,354)(343,355)(344,356)(345,349)(346,350)(347,351)(348,352)
(365,369)(366,370)(367,371)(368,372)(373,393)(374,394)(375,395)(376,396)
(377,389)(378,390)(379,391)(380,392)(381,385)(382,386)(383,387)(384,388)
(401,405)(402,406)(403,407)(404,408)(409,429)(410,430)(411,431)(412,432)
(413,425)(414,426)(415,427)(416,428)(417,421)(418,422)(419,423)(420,424);;
s1 := ( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 21)( 6, 22)( 7, 24)( 8, 23)
( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 25, 33)( 26, 34)( 27, 36)( 28, 35)
( 31, 32)( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 93)( 42, 94)( 43, 96)
( 44, 95)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49, 73)( 50, 74)( 51, 76)
( 52, 75)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 77)( 58, 78)( 59, 80)
( 60, 79)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)
( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)(109,121)(110,122)(111,124)
(112,123)(113,129)(114,130)(115,132)(116,131)(117,125)(118,126)(119,128)
(120,127)(133,141)(134,142)(135,144)(136,143)(139,140)(145,193)(146,194)
(147,196)(148,195)(149,201)(150,202)(151,204)(152,203)(153,197)(154,198)
(155,200)(156,199)(157,181)(158,182)(159,184)(160,183)(161,189)(162,190)
(163,192)(164,191)(165,185)(166,186)(167,188)(168,187)(169,213)(170,214)
(171,216)(172,215)(173,209)(174,210)(175,212)(176,211)(177,205)(178,206)
(179,208)(180,207)(217,337)(218,338)(219,340)(220,339)(221,345)(222,346)
(223,348)(224,347)(225,341)(226,342)(227,344)(228,343)(229,325)(230,326)
(231,328)(232,327)(233,333)(234,334)(235,336)(236,335)(237,329)(238,330)
(239,332)(240,331)(241,357)(242,358)(243,360)(244,359)(245,353)(246,354)
(247,356)(248,355)(249,349)(250,350)(251,352)(252,351)(253,409)(254,410)
(255,412)(256,411)(257,417)(258,418)(259,420)(260,419)(261,413)(262,414)
(263,416)(264,415)(265,397)(266,398)(267,400)(268,399)(269,405)(270,406)
(271,408)(272,407)(273,401)(274,402)(275,404)(276,403)(277,429)(278,430)
(279,432)(280,431)(281,425)(282,426)(283,428)(284,427)(285,421)(286,422)
(287,424)(288,423)(289,373)(290,374)(291,376)(292,375)(293,381)(294,382)
(295,384)(296,383)(297,377)(298,378)(299,380)(300,379)(301,361)(302,362)
(303,364)(304,363)(305,369)(306,370)(307,372)(308,371)(309,365)(310,366)
(311,368)(312,367)(313,393)(314,394)(315,396)(316,395)(317,389)(318,390)
(319,392)(320,391)(321,385)(322,386)(323,388)(324,387);;
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)( 13,265)( 14,268)( 15,267)( 16,266)
( 17,269)( 18,272)( 19,271)( 20,270)( 21,273)( 22,276)( 23,275)( 24,274)
( 25,277)( 26,280)( 27,279)( 28,278)( 29,281)( 30,284)( 31,283)( 32,282)
( 33,285)( 34,288)( 35,287)( 36,286)( 37,217)( 38,220)( 39,219)( 40,218)
( 41,221)( 42,224)( 43,223)( 44,222)( 45,225)( 46,228)( 47,227)( 48,226)
( 49,229)( 50,232)( 51,231)( 52,230)( 53,233)( 54,236)( 55,235)( 56,234)
( 57,237)( 58,240)( 59,239)( 60,238)( 61,241)( 62,244)( 63,243)( 64,242)
( 65,245)( 66,248)( 67,247)( 68,246)( 69,249)( 70,252)( 71,251)( 72,250)
( 73,289)( 74,292)( 75,291)( 76,290)( 77,293)( 78,296)( 79,295)( 80,294)
( 81,297)( 82,300)( 83,299)( 84,298)( 85,301)( 86,304)( 87,303)( 88,302)
( 89,305)( 90,308)( 91,307)( 92,306)( 93,309)( 94,312)( 95,311)( 96,310)
( 97,313)( 98,316)( 99,315)(100,314)(101,317)(102,320)(103,319)(104,318)
(105,321)(106,324)(107,323)(108,322)(109,361)(110,364)(111,363)(112,362)
(113,365)(114,368)(115,367)(116,366)(117,369)(118,372)(119,371)(120,370)
(121,373)(122,376)(123,375)(124,374)(125,377)(126,380)(127,379)(128,378)
(129,381)(130,384)(131,383)(132,382)(133,385)(134,388)(135,387)(136,386)
(137,389)(138,392)(139,391)(140,390)(141,393)(142,396)(143,395)(144,394)
(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)(152,330)
(153,333)(154,336)(155,335)(156,334)(157,337)(158,340)(159,339)(160,338)
(161,341)(162,344)(163,343)(164,342)(165,345)(166,348)(167,347)(168,346)
(169,349)(170,352)(171,351)(172,350)(173,353)(174,356)(175,355)(176,354)
(177,357)(178,360)(179,359)(180,358)(181,397)(182,400)(183,399)(184,398)
(185,401)(186,404)(187,403)(188,402)(189,405)(190,408)(191,407)(192,406)
(193,409)(194,412)(195,411)(196,410)(197,413)(198,416)(199,415)(200,414)
(201,417)(202,420)(203,419)(204,418)(205,421)(206,424)(207,423)(208,422)
(209,425)(210,428)(211,427)(212,426)(213,429)(214,432)(215,431)(216,430);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 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)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(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)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(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*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 33)( 14, 34)( 15, 35)
( 16, 36)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)
( 24, 28)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 69)( 50, 70)( 51, 71)
( 52, 72)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 61)( 58, 62)( 59, 63)
( 60, 64)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85,105)( 86,106)( 87,107)
( 88,108)( 89,101)( 90,102)( 91,103)( 92,104)( 93, 97)( 94, 98)( 95, 99)
( 96,100)(113,117)(114,118)(115,119)(116,120)(121,141)(122,142)(123,143)
(124,144)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)
(132,136)(149,153)(150,154)(151,155)(152,156)(157,177)(158,178)(159,179)
(160,180)(161,173)(162,174)(163,175)(164,176)(165,169)(166,170)(167,171)
(168,172)(185,189)(186,190)(187,191)(188,192)(193,213)(194,214)(195,215)
(196,216)(197,209)(198,210)(199,211)(200,212)(201,205)(202,206)(203,207)
(204,208)(221,225)(222,226)(223,227)(224,228)(229,249)(230,250)(231,251)
(232,252)(233,245)(234,246)(235,247)(236,248)(237,241)(238,242)(239,243)
(240,244)(257,261)(258,262)(259,263)(260,264)(265,285)(266,286)(267,287)
(268,288)(269,281)(270,282)(271,283)(272,284)(273,277)(274,278)(275,279)
(276,280)(293,297)(294,298)(295,299)(296,300)(301,321)(302,322)(303,323)
(304,324)(305,317)(306,318)(307,319)(308,320)(309,313)(310,314)(311,315)
(312,316)(329,333)(330,334)(331,335)(332,336)(337,357)(338,358)(339,359)
(340,360)(341,353)(342,354)(343,355)(344,356)(345,349)(346,350)(347,351)
(348,352)(365,369)(366,370)(367,371)(368,372)(373,393)(374,394)(375,395)
(376,396)(377,389)(378,390)(379,391)(380,392)(381,385)(382,386)(383,387)
(384,388)(401,405)(402,406)(403,407)(404,408)(409,429)(410,430)(411,431)
(412,432)(413,425)(414,426)(415,427)(416,428)(417,421)(418,422)(419,423)
(420,424);
s1 := Sym(432)!( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 21)( 6, 22)( 7, 24)
( 8, 23)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 25, 33)( 26, 34)( 27, 36)
( 28, 35)( 31, 32)( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 93)( 42, 94)
( 43, 96)( 44, 95)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49, 73)( 50, 74)
( 51, 76)( 52, 75)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 77)( 58, 78)
( 59, 80)( 60, 79)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)
( 67,104)( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)(109,121)(110,122)
(111,124)(112,123)(113,129)(114,130)(115,132)(116,131)(117,125)(118,126)
(119,128)(120,127)(133,141)(134,142)(135,144)(136,143)(139,140)(145,193)
(146,194)(147,196)(148,195)(149,201)(150,202)(151,204)(152,203)(153,197)
(154,198)(155,200)(156,199)(157,181)(158,182)(159,184)(160,183)(161,189)
(162,190)(163,192)(164,191)(165,185)(166,186)(167,188)(168,187)(169,213)
(170,214)(171,216)(172,215)(173,209)(174,210)(175,212)(176,211)(177,205)
(178,206)(179,208)(180,207)(217,337)(218,338)(219,340)(220,339)(221,345)
(222,346)(223,348)(224,347)(225,341)(226,342)(227,344)(228,343)(229,325)
(230,326)(231,328)(232,327)(233,333)(234,334)(235,336)(236,335)(237,329)
(238,330)(239,332)(240,331)(241,357)(242,358)(243,360)(244,359)(245,353)
(246,354)(247,356)(248,355)(249,349)(250,350)(251,352)(252,351)(253,409)
(254,410)(255,412)(256,411)(257,417)(258,418)(259,420)(260,419)(261,413)
(262,414)(263,416)(264,415)(265,397)(266,398)(267,400)(268,399)(269,405)
(270,406)(271,408)(272,407)(273,401)(274,402)(275,404)(276,403)(277,429)
(278,430)(279,432)(280,431)(281,425)(282,426)(283,428)(284,427)(285,421)
(286,422)(287,424)(288,423)(289,373)(290,374)(291,376)(292,375)(293,381)
(294,382)(295,384)(296,383)(297,377)(298,378)(299,380)(300,379)(301,361)
(302,362)(303,364)(304,363)(305,369)(306,370)(307,372)(308,371)(309,365)
(310,366)(311,368)(312,367)(313,393)(314,394)(315,396)(316,395)(317,389)
(318,390)(319,392)(320,391)(321,385)(322,386)(323,388)(324,387);
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)( 13,265)( 14,268)( 15,267)
( 16,266)( 17,269)( 18,272)( 19,271)( 20,270)( 21,273)( 22,276)( 23,275)
( 24,274)( 25,277)( 26,280)( 27,279)( 28,278)( 29,281)( 30,284)( 31,283)
( 32,282)( 33,285)( 34,288)( 35,287)( 36,286)( 37,217)( 38,220)( 39,219)
( 40,218)( 41,221)( 42,224)( 43,223)( 44,222)( 45,225)( 46,228)( 47,227)
( 48,226)( 49,229)( 50,232)( 51,231)( 52,230)( 53,233)( 54,236)( 55,235)
( 56,234)( 57,237)( 58,240)( 59,239)( 60,238)( 61,241)( 62,244)( 63,243)
( 64,242)( 65,245)( 66,248)( 67,247)( 68,246)( 69,249)( 70,252)( 71,251)
( 72,250)( 73,289)( 74,292)( 75,291)( 76,290)( 77,293)( 78,296)( 79,295)
( 80,294)( 81,297)( 82,300)( 83,299)( 84,298)( 85,301)( 86,304)( 87,303)
( 88,302)( 89,305)( 90,308)( 91,307)( 92,306)( 93,309)( 94,312)( 95,311)
( 96,310)( 97,313)( 98,316)( 99,315)(100,314)(101,317)(102,320)(103,319)
(104,318)(105,321)(106,324)(107,323)(108,322)(109,361)(110,364)(111,363)
(112,362)(113,365)(114,368)(115,367)(116,366)(117,369)(118,372)(119,371)
(120,370)(121,373)(122,376)(123,375)(124,374)(125,377)(126,380)(127,379)
(128,378)(129,381)(130,384)(131,383)(132,382)(133,385)(134,388)(135,387)
(136,386)(137,389)(138,392)(139,391)(140,390)(141,393)(142,396)(143,395)
(144,394)(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)
(152,330)(153,333)(154,336)(155,335)(156,334)(157,337)(158,340)(159,339)
(160,338)(161,341)(162,344)(163,343)(164,342)(165,345)(166,348)(167,347)
(168,346)(169,349)(170,352)(171,351)(172,350)(173,353)(174,356)(175,355)
(176,354)(177,357)(178,360)(179,359)(180,358)(181,397)(182,400)(183,399)
(184,398)(185,401)(186,404)(187,403)(188,402)(189,405)(190,408)(191,407)
(192,406)(193,409)(194,412)(195,411)(196,410)(197,413)(198,416)(199,415)
(200,414)(201,417)(202,420)(203,419)(204,418)(205,421)(206,424)(207,423)
(208,422)(209,425)(210,428)(211,427)(212,426)(213,429)(214,432)(215,431)
(216,430);
s3 := Sym(432)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 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)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(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)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope