Polytope of Type {4,12,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,18}*1728b
if this polytope has a name.
Group : SmallGroup(1728,18104)
Rank : 4
Schlafli Type : {4,12,18}
Number of vertices, edges, etc : 4, 24, 108, 18
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 : {4,6,18}*864b, {2,12,18}*864b
3-fold quotients : {4,4,18}*576, {4,12,6}*576c
4-fold quotients : {4,6,9}*432, {2,6,18}*432b
6-fold quotients : {2,4,18}*288a, {4,2,18}*288, {4,6,6}*288c, {2,12,6}*288c
8-fold quotients : {2,6,9}*216
9-fold quotients : {4,4,6}*192
12-fold quotients : {4,2,9}*144, {2,2,18}*144, {4,6,3}*144, {2,6,6}*144b
18-fold quotients : {2,4,6}*96a, {4,2,6}*96
24-fold quotients : {2,2,9}*72, {2,6,3}*72
27-fold quotients : {4,4,2}*64
36-fold quotients : {4,2,3}*48, {2,2,6}*48
54-fold quotients : {2,4,2}*32, {4,2,2}*32
72-fold quotients : {2,2,3}*24
108-fold quotients : {2,2,2}*16
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)( 55,271)( 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);;
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)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)
( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)
( 96, 99)(103,106)(104,107)(105,108)(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)(217,244)(218,245)(219,246)(220,250)(221,251)(222,252)
(223,247)(224,248)(225,249)(226,253)(227,254)(228,255)(229,259)(230,260)
(231,261)(232,256)(233,257)(234,258)(235,262)(236,263)(237,264)(238,268)
(239,269)(240,270)(241,265)(242,266)(243,267)(271,298)(272,299)(273,300)
(274,304)(275,305)(276,306)(277,301)(278,302)(279,303)(280,307)(281,308)
(282,309)(283,313)(284,314)(285,315)(286,310)(287,311)(288,312)(289,316)
(290,317)(291,318)(292,322)(293,323)(294,324)(295,319)(296,320)(297,321)
(325,406)(326,407)(327,408)(328,412)(329,413)(330,414)(331,409)(332,410)
(333,411)(334,415)(335,416)(336,417)(337,421)(338,422)(339,423)(340,418)
(341,419)(342,420)(343,424)(344,425)(345,426)(346,430)(347,431)(348,432)
(349,427)(350,428)(351,429)(352,379)(353,380)(354,381)(355,385)(356,386)
(357,387)(358,382)(359,383)(360,384)(361,388)(362,389)(363,390)(364,394)
(365,395)(366,396)(367,391)(368,392)(369,393)(370,397)(371,398)(372,399)
(373,403)(374,404)(375,405)(376,400)(377,401)(378,402);;
s2 := ( 1,112)( 2,114)( 3,113)( 4,109)( 5,111)( 6,110)( 7,115)( 8,117)
( 9,116)( 10,132)( 11,131)( 12,130)( 13,129)( 14,128)( 15,127)( 16,135)
( 17,134)( 18,133)( 19,123)( 20,122)( 21,121)( 22,120)( 23,119)( 24,118)
( 25,126)( 26,125)( 27,124)( 28,139)( 29,141)( 30,140)( 31,136)( 32,138)
( 33,137)( 34,142)( 35,144)( 36,143)( 37,159)( 38,158)( 39,157)( 40,156)
( 41,155)( 42,154)( 43,162)( 44,161)( 45,160)( 46,150)( 47,149)( 48,148)
( 49,147)( 50,146)( 51,145)( 52,153)( 53,152)( 54,151)( 55,166)( 56,168)
( 57,167)( 58,163)( 59,165)( 60,164)( 61,169)( 62,171)( 63,170)( 64,186)
( 65,185)( 66,184)( 67,183)( 68,182)( 69,181)( 70,189)( 71,188)( 72,187)
( 73,177)( 74,176)( 75,175)( 76,174)( 77,173)( 78,172)( 79,180)( 80,179)
( 81,178)( 82,193)( 83,195)( 84,194)( 85,190)( 86,192)( 87,191)( 88,196)
( 89,198)( 90,197)( 91,213)( 92,212)( 93,211)( 94,210)( 95,209)( 96,208)
( 97,216)( 98,215)( 99,214)(100,204)(101,203)(102,202)(103,201)(104,200)
(105,199)(106,207)(107,206)(108,205)(217,328)(218,330)(219,329)(220,325)
(221,327)(222,326)(223,331)(224,333)(225,332)(226,348)(227,347)(228,346)
(229,345)(230,344)(231,343)(232,351)(233,350)(234,349)(235,339)(236,338)
(237,337)(238,336)(239,335)(240,334)(241,342)(242,341)(243,340)(244,355)
(245,357)(246,356)(247,352)(248,354)(249,353)(250,358)(251,360)(252,359)
(253,375)(254,374)(255,373)(256,372)(257,371)(258,370)(259,378)(260,377)
(261,376)(262,366)(263,365)(264,364)(265,363)(266,362)(267,361)(268,369)
(269,368)(270,367)(271,382)(272,384)(273,383)(274,379)(275,381)(276,380)
(277,385)(278,387)(279,386)(280,402)(281,401)(282,400)(283,399)(284,398)
(285,397)(286,405)(287,404)(288,403)(289,393)(290,392)(291,391)(292,390)
(293,389)(294,388)(295,396)(296,395)(297,394)(298,409)(299,411)(300,410)
(301,406)(302,408)(303,407)(304,412)(305,414)(306,413)(307,429)(308,428)
(309,427)(310,426)(311,425)(312,424)(313,432)(314,431)(315,430)(316,420)
(317,419)(318,418)(319,417)(320,416)(321,415)(322,423)(323,422)(324,421);;
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*s0*s1*s0*s1*s0*s1,
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*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 55,271)
( 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);
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)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)
( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)
( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(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)(217,244)(218,245)(219,246)(220,250)(221,251)
(222,252)(223,247)(224,248)(225,249)(226,253)(227,254)(228,255)(229,259)
(230,260)(231,261)(232,256)(233,257)(234,258)(235,262)(236,263)(237,264)
(238,268)(239,269)(240,270)(241,265)(242,266)(243,267)(271,298)(272,299)
(273,300)(274,304)(275,305)(276,306)(277,301)(278,302)(279,303)(280,307)
(281,308)(282,309)(283,313)(284,314)(285,315)(286,310)(287,311)(288,312)
(289,316)(290,317)(291,318)(292,322)(293,323)(294,324)(295,319)(296,320)
(297,321)(325,406)(326,407)(327,408)(328,412)(329,413)(330,414)(331,409)
(332,410)(333,411)(334,415)(335,416)(336,417)(337,421)(338,422)(339,423)
(340,418)(341,419)(342,420)(343,424)(344,425)(345,426)(346,430)(347,431)
(348,432)(349,427)(350,428)(351,429)(352,379)(353,380)(354,381)(355,385)
(356,386)(357,387)(358,382)(359,383)(360,384)(361,388)(362,389)(363,390)
(364,394)(365,395)(366,396)(367,391)(368,392)(369,393)(370,397)(371,398)
(372,399)(373,403)(374,404)(375,405)(376,400)(377,401)(378,402);
s2 := Sym(432)!( 1,112)( 2,114)( 3,113)( 4,109)( 5,111)( 6,110)( 7,115)
( 8,117)( 9,116)( 10,132)( 11,131)( 12,130)( 13,129)( 14,128)( 15,127)
( 16,135)( 17,134)( 18,133)( 19,123)( 20,122)( 21,121)( 22,120)( 23,119)
( 24,118)( 25,126)( 26,125)( 27,124)( 28,139)( 29,141)( 30,140)( 31,136)
( 32,138)( 33,137)( 34,142)( 35,144)( 36,143)( 37,159)( 38,158)( 39,157)
( 40,156)( 41,155)( 42,154)( 43,162)( 44,161)( 45,160)( 46,150)( 47,149)
( 48,148)( 49,147)( 50,146)( 51,145)( 52,153)( 53,152)( 54,151)( 55,166)
( 56,168)( 57,167)( 58,163)( 59,165)( 60,164)( 61,169)( 62,171)( 63,170)
( 64,186)( 65,185)( 66,184)( 67,183)( 68,182)( 69,181)( 70,189)( 71,188)
( 72,187)( 73,177)( 74,176)( 75,175)( 76,174)( 77,173)( 78,172)( 79,180)
( 80,179)( 81,178)( 82,193)( 83,195)( 84,194)( 85,190)( 86,192)( 87,191)
( 88,196)( 89,198)( 90,197)( 91,213)( 92,212)( 93,211)( 94,210)( 95,209)
( 96,208)( 97,216)( 98,215)( 99,214)(100,204)(101,203)(102,202)(103,201)
(104,200)(105,199)(106,207)(107,206)(108,205)(217,328)(218,330)(219,329)
(220,325)(221,327)(222,326)(223,331)(224,333)(225,332)(226,348)(227,347)
(228,346)(229,345)(230,344)(231,343)(232,351)(233,350)(234,349)(235,339)
(236,338)(237,337)(238,336)(239,335)(240,334)(241,342)(242,341)(243,340)
(244,355)(245,357)(246,356)(247,352)(248,354)(249,353)(250,358)(251,360)
(252,359)(253,375)(254,374)(255,373)(256,372)(257,371)(258,370)(259,378)
(260,377)(261,376)(262,366)(263,365)(264,364)(265,363)(266,362)(267,361)
(268,369)(269,368)(270,367)(271,382)(272,384)(273,383)(274,379)(275,381)
(276,380)(277,385)(278,387)(279,386)(280,402)(281,401)(282,400)(283,399)
(284,398)(285,397)(286,405)(287,404)(288,403)(289,393)(290,392)(291,391)
(292,390)(293,389)(294,388)(295,396)(296,395)(297,394)(298,409)(299,411)
(300,410)(301,406)(302,408)(303,407)(304,412)(305,414)(306,413)(307,429)
(308,428)(309,427)(310,426)(311,425)(312,424)(313,432)(314,431)(315,430)
(316,420)(317,419)(318,418)(319,417)(320,416)(321,415)(322,423)(323,422)
(324,421);
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*s0*s1*s0*s1*s0*s1, 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*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope