Polytope of Type {18,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,12,4}*1728e
if this polytope has a name.
Group : SmallGroup(1728,46098)
Rank : 4
Schlafli Type : {18,12,4}
Number of vertices, edges, etc : 18, 108, 24, 4
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 : {6,12,4}*576h
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 17, 33)( 18, 34)( 19, 36)( 20, 35)
( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 41)( 26, 42)( 27, 44)( 28, 43)
( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 51, 52)( 55, 56)( 59, 60)( 63, 64)
( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)
( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 93)( 78, 94)( 79, 96)( 80, 95)
( 99,100)(103,104)(107,108)(111,112)(113,129)(114,130)(115,132)(116,131)
(117,133)(118,134)(119,136)(120,135)(121,137)(122,138)(123,140)(124,139)
(125,141)(126,142)(127,144)(128,143)(145,321)(146,322)(147,324)(148,323)
(149,325)(150,326)(151,328)(152,327)(153,329)(154,330)(155,332)(156,331)
(157,333)(158,334)(159,336)(160,335)(161,305)(162,306)(163,308)(164,307)
(165,309)(166,310)(167,312)(168,311)(169,313)(170,314)(171,316)(172,315)
(173,317)(174,318)(175,320)(176,319)(177,289)(178,290)(179,292)(180,291)
(181,293)(182,294)(183,296)(184,295)(185,297)(186,298)(187,300)(188,299)
(189,301)(190,302)(191,304)(192,303)(193,369)(194,370)(195,372)(196,371)
(197,373)(198,374)(199,376)(200,375)(201,377)(202,378)(203,380)(204,379)
(205,381)(206,382)(207,384)(208,383)(209,353)(210,354)(211,356)(212,355)
(213,357)(214,358)(215,360)(216,359)(217,361)(218,362)(219,364)(220,363)
(221,365)(222,366)(223,368)(224,367)(225,337)(226,338)(227,340)(228,339)
(229,341)(230,342)(231,344)(232,343)(233,345)(234,346)(235,348)(236,347)
(237,349)(238,350)(239,352)(240,351)(241,417)(242,418)(243,420)(244,419)
(245,421)(246,422)(247,424)(248,423)(249,425)(250,426)(251,428)(252,427)
(253,429)(254,430)(255,432)(256,431)(257,401)(258,402)(259,404)(260,403)
(261,405)(262,406)(263,408)(264,407)(265,409)(266,410)(267,412)(268,411)
(269,413)(270,414)(271,416)(272,415)(273,385)(274,386)(275,388)(276,387)
(277,389)(278,390)(279,392)(280,391)(281,393)(282,394)(283,396)(284,395)
(285,397)(286,398)(287,400)(288,399);;
s1 := ( 1,145)( 2,148)( 3,147)( 4,146)( 5,149)( 6,152)( 7,151)( 8,150)
( 9,157)( 10,160)( 11,159)( 12,158)( 13,153)( 14,156)( 15,155)( 16,154)
( 17,177)( 18,180)( 19,179)( 20,178)( 21,181)( 22,184)( 23,183)( 24,182)
( 25,189)( 26,192)( 27,191)( 28,190)( 29,185)( 30,188)( 31,187)( 32,186)
( 33,161)( 34,164)( 35,163)( 36,162)( 37,165)( 38,168)( 39,167)( 40,166)
( 41,173)( 42,176)( 43,175)( 44,174)( 45,169)( 46,172)( 47,171)( 48,170)
( 49,241)( 50,244)( 51,243)( 52,242)( 53,245)( 54,248)( 55,247)( 56,246)
( 57,253)( 58,256)( 59,255)( 60,254)( 61,249)( 62,252)( 63,251)( 64,250)
( 65,273)( 66,276)( 67,275)( 68,274)( 69,277)( 70,280)( 71,279)( 72,278)
( 73,285)( 74,288)( 75,287)( 76,286)( 77,281)( 78,284)( 79,283)( 80,282)
( 81,257)( 82,260)( 83,259)( 84,258)( 85,261)( 86,264)( 87,263)( 88,262)
( 89,269)( 90,272)( 91,271)( 92,270)( 93,265)( 94,268)( 95,267)( 96,266)
( 97,193)( 98,196)( 99,195)(100,194)(101,197)(102,200)(103,199)(104,198)
(105,205)(106,208)(107,207)(108,206)(109,201)(110,204)(111,203)(112,202)
(113,225)(114,228)(115,227)(116,226)(117,229)(118,232)(119,231)(120,230)
(121,237)(122,240)(123,239)(124,238)(125,233)(126,236)(127,235)(128,234)
(129,209)(130,212)(131,211)(132,210)(133,213)(134,216)(135,215)(136,214)
(137,221)(138,224)(139,223)(140,222)(141,217)(142,220)(143,219)(144,218)
(289,321)(290,324)(291,323)(292,322)(293,325)(294,328)(295,327)(296,326)
(297,333)(298,336)(299,335)(300,334)(301,329)(302,332)(303,331)(304,330)
(306,308)(310,312)(313,317)(314,320)(315,319)(316,318)(337,417)(338,420)
(339,419)(340,418)(341,421)(342,424)(343,423)(344,422)(345,429)(346,432)
(347,431)(348,430)(349,425)(350,428)(351,427)(352,426)(353,401)(354,404)
(355,403)(356,402)(357,405)(358,408)(359,407)(360,406)(361,413)(362,416)
(363,415)(364,414)(365,409)(366,412)(367,411)(368,410)(369,385)(370,388)
(371,387)(372,386)(373,389)(374,392)(375,391)(376,390)(377,397)(378,400)
(379,399)(380,398)(381,393)(382,396)(383,395)(384,394);;
s2 := ( 1, 50)( 2, 49)( 3, 52)( 4, 51)( 5, 62)( 6, 61)( 7, 64)( 8, 63)
( 9, 58)( 10, 57)( 11, 60)( 12, 59)( 13, 54)( 14, 53)( 15, 56)( 16, 55)
( 17, 66)( 18, 65)( 19, 68)( 20, 67)( 21, 78)( 22, 77)( 23, 80)( 24, 79)
( 25, 74)( 26, 73)( 27, 76)( 28, 75)( 29, 70)( 30, 69)( 31, 72)( 32, 71)
( 33, 82)( 34, 81)( 35, 84)( 36, 83)( 37, 94)( 38, 93)( 39, 96)( 40, 95)
( 41, 90)( 42, 89)( 43, 92)( 44, 91)( 45, 86)( 46, 85)( 47, 88)( 48, 87)
( 97, 98)( 99,100)(101,110)(102,109)(103,112)(104,111)(105,106)(107,108)
(113,114)(115,116)(117,126)(118,125)(119,128)(120,127)(121,122)(123,124)
(129,130)(131,132)(133,142)(134,141)(135,144)(136,143)(137,138)(139,140)
(145,194)(146,193)(147,196)(148,195)(149,206)(150,205)(151,208)(152,207)
(153,202)(154,201)(155,204)(156,203)(157,198)(158,197)(159,200)(160,199)
(161,210)(162,209)(163,212)(164,211)(165,222)(166,221)(167,224)(168,223)
(169,218)(170,217)(171,220)(172,219)(173,214)(174,213)(175,216)(176,215)
(177,226)(178,225)(179,228)(180,227)(181,238)(182,237)(183,240)(184,239)
(185,234)(186,233)(187,236)(188,235)(189,230)(190,229)(191,232)(192,231)
(241,242)(243,244)(245,254)(246,253)(247,256)(248,255)(249,250)(251,252)
(257,258)(259,260)(261,270)(262,269)(263,272)(264,271)(265,266)(267,268)
(273,274)(275,276)(277,286)(278,285)(279,288)(280,287)(281,282)(283,284)
(289,338)(290,337)(291,340)(292,339)(293,350)(294,349)(295,352)(296,351)
(297,346)(298,345)(299,348)(300,347)(301,342)(302,341)(303,344)(304,343)
(305,354)(306,353)(307,356)(308,355)(309,366)(310,365)(311,368)(312,367)
(313,362)(314,361)(315,364)(316,363)(317,358)(318,357)(319,360)(320,359)
(321,370)(322,369)(323,372)(324,371)(325,382)(326,381)(327,384)(328,383)
(329,378)(330,377)(331,380)(332,379)(333,374)(334,373)(335,376)(336,375)
(385,386)(387,388)(389,398)(390,397)(391,400)(392,399)(393,394)(395,396)
(401,402)(403,404)(405,414)(406,413)(407,416)(408,415)(409,410)(411,412)
(417,418)(419,420)(421,430)(422,429)(423,432)(424,431)(425,426)(427,428);;
s3 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 13)( 10, 14)( 11, 15)( 12, 16)
( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)( 28, 32)
( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)( 60, 64)
( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)( 76, 80)
( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
( 97,101)( 98,102)( 99,103)(100,104)(105,109)(106,110)(107,111)(108,112)
(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)
(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)
(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160)
(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)(172,176)
(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)(188,192)
(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)(204,208)
(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)(220,224)
(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)(236,240)
(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)(252,256)
(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)(268,272)
(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)(284,288)
(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)(300,304)
(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)(316,320)
(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)(332,336)
(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)(348,352)
(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)(364,368)
(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)(380,384)
(385,389)(386,390)(387,391)(388,392)(393,397)(394,398)(395,399)(396,400)
(401,405)(402,406)(403,407)(404,408)(409,413)(410,414)(411,415)(412,416)
(417,421)(418,422)(419,423)(420,424)(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, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 17, 33)( 18, 34)( 19, 36)
( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 41)( 26, 42)( 27, 44)
( 28, 43)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 51, 52)( 55, 56)( 59, 60)
( 63, 64)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)
( 72, 87)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 93)( 78, 94)( 79, 96)
( 80, 95)( 99,100)(103,104)(107,108)(111,112)(113,129)(114,130)(115,132)
(116,131)(117,133)(118,134)(119,136)(120,135)(121,137)(122,138)(123,140)
(124,139)(125,141)(126,142)(127,144)(128,143)(145,321)(146,322)(147,324)
(148,323)(149,325)(150,326)(151,328)(152,327)(153,329)(154,330)(155,332)
(156,331)(157,333)(158,334)(159,336)(160,335)(161,305)(162,306)(163,308)
(164,307)(165,309)(166,310)(167,312)(168,311)(169,313)(170,314)(171,316)
(172,315)(173,317)(174,318)(175,320)(176,319)(177,289)(178,290)(179,292)
(180,291)(181,293)(182,294)(183,296)(184,295)(185,297)(186,298)(187,300)
(188,299)(189,301)(190,302)(191,304)(192,303)(193,369)(194,370)(195,372)
(196,371)(197,373)(198,374)(199,376)(200,375)(201,377)(202,378)(203,380)
(204,379)(205,381)(206,382)(207,384)(208,383)(209,353)(210,354)(211,356)
(212,355)(213,357)(214,358)(215,360)(216,359)(217,361)(218,362)(219,364)
(220,363)(221,365)(222,366)(223,368)(224,367)(225,337)(226,338)(227,340)
(228,339)(229,341)(230,342)(231,344)(232,343)(233,345)(234,346)(235,348)
(236,347)(237,349)(238,350)(239,352)(240,351)(241,417)(242,418)(243,420)
(244,419)(245,421)(246,422)(247,424)(248,423)(249,425)(250,426)(251,428)
(252,427)(253,429)(254,430)(255,432)(256,431)(257,401)(258,402)(259,404)
(260,403)(261,405)(262,406)(263,408)(264,407)(265,409)(266,410)(267,412)
(268,411)(269,413)(270,414)(271,416)(272,415)(273,385)(274,386)(275,388)
(276,387)(277,389)(278,390)(279,392)(280,391)(281,393)(282,394)(283,396)
(284,395)(285,397)(286,398)(287,400)(288,399);
s1 := Sym(432)!( 1,145)( 2,148)( 3,147)( 4,146)( 5,149)( 6,152)( 7,151)
( 8,150)( 9,157)( 10,160)( 11,159)( 12,158)( 13,153)( 14,156)( 15,155)
( 16,154)( 17,177)( 18,180)( 19,179)( 20,178)( 21,181)( 22,184)( 23,183)
( 24,182)( 25,189)( 26,192)( 27,191)( 28,190)( 29,185)( 30,188)( 31,187)
( 32,186)( 33,161)( 34,164)( 35,163)( 36,162)( 37,165)( 38,168)( 39,167)
( 40,166)( 41,173)( 42,176)( 43,175)( 44,174)( 45,169)( 46,172)( 47,171)
( 48,170)( 49,241)( 50,244)( 51,243)( 52,242)( 53,245)( 54,248)( 55,247)
( 56,246)( 57,253)( 58,256)( 59,255)( 60,254)( 61,249)( 62,252)( 63,251)
( 64,250)( 65,273)( 66,276)( 67,275)( 68,274)( 69,277)( 70,280)( 71,279)
( 72,278)( 73,285)( 74,288)( 75,287)( 76,286)( 77,281)( 78,284)( 79,283)
( 80,282)( 81,257)( 82,260)( 83,259)( 84,258)( 85,261)( 86,264)( 87,263)
( 88,262)( 89,269)( 90,272)( 91,271)( 92,270)( 93,265)( 94,268)( 95,267)
( 96,266)( 97,193)( 98,196)( 99,195)(100,194)(101,197)(102,200)(103,199)
(104,198)(105,205)(106,208)(107,207)(108,206)(109,201)(110,204)(111,203)
(112,202)(113,225)(114,228)(115,227)(116,226)(117,229)(118,232)(119,231)
(120,230)(121,237)(122,240)(123,239)(124,238)(125,233)(126,236)(127,235)
(128,234)(129,209)(130,212)(131,211)(132,210)(133,213)(134,216)(135,215)
(136,214)(137,221)(138,224)(139,223)(140,222)(141,217)(142,220)(143,219)
(144,218)(289,321)(290,324)(291,323)(292,322)(293,325)(294,328)(295,327)
(296,326)(297,333)(298,336)(299,335)(300,334)(301,329)(302,332)(303,331)
(304,330)(306,308)(310,312)(313,317)(314,320)(315,319)(316,318)(337,417)
(338,420)(339,419)(340,418)(341,421)(342,424)(343,423)(344,422)(345,429)
(346,432)(347,431)(348,430)(349,425)(350,428)(351,427)(352,426)(353,401)
(354,404)(355,403)(356,402)(357,405)(358,408)(359,407)(360,406)(361,413)
(362,416)(363,415)(364,414)(365,409)(366,412)(367,411)(368,410)(369,385)
(370,388)(371,387)(372,386)(373,389)(374,392)(375,391)(376,390)(377,397)
(378,400)(379,399)(380,398)(381,393)(382,396)(383,395)(384,394);
s2 := Sym(432)!( 1, 50)( 2, 49)( 3, 52)( 4, 51)( 5, 62)( 6, 61)( 7, 64)
( 8, 63)( 9, 58)( 10, 57)( 11, 60)( 12, 59)( 13, 54)( 14, 53)( 15, 56)
( 16, 55)( 17, 66)( 18, 65)( 19, 68)( 20, 67)( 21, 78)( 22, 77)( 23, 80)
( 24, 79)( 25, 74)( 26, 73)( 27, 76)( 28, 75)( 29, 70)( 30, 69)( 31, 72)
( 32, 71)( 33, 82)( 34, 81)( 35, 84)( 36, 83)( 37, 94)( 38, 93)( 39, 96)
( 40, 95)( 41, 90)( 42, 89)( 43, 92)( 44, 91)( 45, 86)( 46, 85)( 47, 88)
( 48, 87)( 97, 98)( 99,100)(101,110)(102,109)(103,112)(104,111)(105,106)
(107,108)(113,114)(115,116)(117,126)(118,125)(119,128)(120,127)(121,122)
(123,124)(129,130)(131,132)(133,142)(134,141)(135,144)(136,143)(137,138)
(139,140)(145,194)(146,193)(147,196)(148,195)(149,206)(150,205)(151,208)
(152,207)(153,202)(154,201)(155,204)(156,203)(157,198)(158,197)(159,200)
(160,199)(161,210)(162,209)(163,212)(164,211)(165,222)(166,221)(167,224)
(168,223)(169,218)(170,217)(171,220)(172,219)(173,214)(174,213)(175,216)
(176,215)(177,226)(178,225)(179,228)(180,227)(181,238)(182,237)(183,240)
(184,239)(185,234)(186,233)(187,236)(188,235)(189,230)(190,229)(191,232)
(192,231)(241,242)(243,244)(245,254)(246,253)(247,256)(248,255)(249,250)
(251,252)(257,258)(259,260)(261,270)(262,269)(263,272)(264,271)(265,266)
(267,268)(273,274)(275,276)(277,286)(278,285)(279,288)(280,287)(281,282)
(283,284)(289,338)(290,337)(291,340)(292,339)(293,350)(294,349)(295,352)
(296,351)(297,346)(298,345)(299,348)(300,347)(301,342)(302,341)(303,344)
(304,343)(305,354)(306,353)(307,356)(308,355)(309,366)(310,365)(311,368)
(312,367)(313,362)(314,361)(315,364)(316,363)(317,358)(318,357)(319,360)
(320,359)(321,370)(322,369)(323,372)(324,371)(325,382)(326,381)(327,384)
(328,383)(329,378)(330,377)(331,380)(332,379)(333,374)(334,373)(335,376)
(336,375)(385,386)(387,388)(389,398)(390,397)(391,400)(392,399)(393,394)
(395,396)(401,402)(403,404)(405,414)(406,413)(407,416)(408,415)(409,410)
(411,412)(417,418)(419,420)(421,430)(422,429)(423,432)(424,431)(425,426)
(427,428);
s3 := Sym(432)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 13)( 10, 14)( 11, 15)
( 12, 16)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)
( 28, 32)( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)
( 60, 64)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)
( 76, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)( 97,101)( 98,102)( 99,103)(100,104)(105,109)(106,110)(107,111)
(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)
(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)
(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)
(156,160)(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)
(172,176)(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)
(188,192)(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)
(204,208)(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)
(220,224)(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)
(236,240)(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)
(252,256)(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)
(268,272)(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)
(284,288)(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)
(300,304)(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)
(316,320)(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)
(332,336)(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)
(348,352)(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)
(364,368)(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)
(380,384)(385,389)(386,390)(387,391)(388,392)(393,397)(394,398)(395,399)
(396,400)(401,405)(402,406)(403,407)(404,408)(409,413)(410,414)(411,415)
(412,416)(417,421)(418,422)(419,423)(420,424)(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,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope