Polytope of Type {4,6,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,18}*1728
if this polytope has a name.
Group : SmallGroup(1728,46114)
Rank : 4
Schlafli Type : {4,6,18}
Number of vertices, edges, etc : 8, 24, 108, 18
Order of s0s1s2s3 : 18
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}*864c
3-fold quotients : {4,6,6}*576a
4-fold quotients : {2,6,18}*432a
6-fold quotients : {4,6,6}*288d
9-fold quotients : {4,6,2}*192
12-fold quotients : {2,2,18}*144, {2,6,6}*144a
18-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
24-fold quotients : {2,2,9}*72
36-fold quotients : {4,3,2}*48, {2,2,6}*48, {2,6,2}*48
72-fold quotients : {2,2,3}*24, {2,3,2}*24
108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,219)( 2,220)( 3,217)( 4,218)( 5,223)( 6,224)( 7,221)( 8,222)
( 9,227)( 10,228)( 11,225)( 12,226)( 13,231)( 14,232)( 15,229)( 16,230)
( 17,235)( 18,236)( 19,233)( 20,234)( 21,239)( 22,240)( 23,237)( 24,238)
( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)( 32,246)
( 33,251)( 34,252)( 35,249)( 36,250)( 37,255)( 38,256)( 39,253)( 40,254)
( 41,259)( 42,260)( 43,257)( 44,258)( 45,263)( 46,264)( 47,261)( 48,262)
( 49,267)( 50,268)( 51,265)( 52,266)( 53,271)( 54,272)( 55,269)( 56,270)
( 57,275)( 58,276)( 59,273)( 60,274)( 61,279)( 62,280)( 63,277)( 64,278)
( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)( 72,286)
( 73,291)( 74,292)( 75,289)( 76,290)( 77,295)( 78,296)( 79,293)( 80,294)
( 81,299)( 82,300)( 83,297)( 84,298)( 85,303)( 86,304)( 87,301)( 88,302)
( 89,307)( 90,308)( 91,305)( 92,306)( 93,311)( 94,312)( 95,309)( 96,310)
( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)(104,318)
(105,323)(106,324)(107,321)(108,322)(109,327)(110,328)(111,325)(112,326)
(113,331)(114,332)(115,329)(116,330)(117,335)(118,336)(119,333)(120,334)
(121,339)(122,340)(123,337)(124,338)(125,343)(126,344)(127,341)(128,342)
(129,347)(130,348)(131,345)(132,346)(133,351)(134,352)(135,349)(136,350)
(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)(144,358)
(145,363)(146,364)(147,361)(148,362)(149,367)(150,368)(151,365)(152,366)
(153,371)(154,372)(155,369)(156,370)(157,375)(158,376)(159,373)(160,374)
(161,379)(162,380)(163,377)(164,378)(165,383)(166,384)(167,381)(168,382)
(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)(176,390)
(177,395)(178,396)(179,393)(180,394)(181,399)(182,400)(183,397)(184,398)
(185,403)(186,404)(187,401)(188,402)(189,407)(190,408)(191,405)(192,406)
(193,411)(194,412)(195,409)(196,410)(197,415)(198,416)(199,413)(200,414)
(201,419)(202,420)(203,417)(204,418)(205,423)(206,424)(207,421)(208,422)
(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)(216,430);;
s1 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 77)( 42, 78)( 43, 80)
( 44, 79)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 85)( 50, 86)( 51, 88)
( 52, 87)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 93)( 58, 94)( 59, 96)
( 60, 95)( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,101)( 66,102)( 67,104)
( 68,103)( 69,105)( 70,106)( 71,108)( 72,107)(111,112)(115,116)(119,120)
(123,124)(127,128)(131,132)(135,136)(139,140)(143,144)(145,181)(146,182)
(147,184)(148,183)(149,185)(150,186)(151,188)(152,187)(153,189)(154,190)
(155,192)(156,191)(157,193)(158,194)(159,196)(160,195)(161,197)(162,198)
(163,200)(164,199)(165,201)(166,202)(167,204)(168,203)(169,205)(170,206)
(171,208)(172,207)(173,209)(174,210)(175,212)(176,211)(177,213)(178,214)
(179,216)(180,215)(219,220)(223,224)(227,228)(231,232)(235,236)(239,240)
(243,244)(247,248)(251,252)(253,289)(254,290)(255,292)(256,291)(257,293)
(258,294)(259,296)(260,295)(261,297)(262,298)(263,300)(264,299)(265,301)
(266,302)(267,304)(268,303)(269,305)(270,306)(271,308)(272,307)(273,309)
(274,310)(275,312)(276,311)(277,313)(278,314)(279,316)(280,315)(281,317)
(282,318)(283,320)(284,319)(285,321)(286,322)(287,324)(288,323)(327,328)
(331,332)(335,336)(339,340)(343,344)(347,348)(351,352)(355,356)(359,360)
(361,397)(362,398)(363,400)(364,399)(365,401)(366,402)(367,404)(368,403)
(369,405)(370,406)(371,408)(372,407)(373,409)(374,410)(375,412)(376,411)
(377,413)(378,414)(379,416)(380,415)(381,417)(382,418)(383,420)(384,419)
(385,421)(386,422)(387,424)(388,423)(389,425)(390,426)(391,428)(392,427)
(393,429)(394,430)(395,432)(396,431);;
s2 := ( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 45)( 6, 48)( 7, 47)( 8, 46)
( 9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 69)( 14, 72)( 15, 71)( 16, 70)
( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 61)( 22, 64)( 23, 63)( 24, 62)
( 25, 57)( 26, 60)( 27, 59)( 28, 58)( 29, 53)( 30, 56)( 31, 55)( 32, 54)
( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 74, 76)( 77, 81)( 78, 84)( 79, 83)
( 80, 82)( 85,105)( 86,108)( 87,107)( 88,106)( 89,101)( 90,104)( 91,103)
( 92,102)( 93, 97)( 94,100)( 95, 99)( 96, 98)(109,145)(110,148)(111,147)
(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)(119,151)
(120,150)(121,177)(122,180)(123,179)(124,178)(125,173)(126,176)(127,175)
(128,174)(129,169)(130,172)(131,171)(132,170)(133,165)(134,168)(135,167)
(136,166)(137,161)(138,164)(139,163)(140,162)(141,157)(142,160)(143,159)
(144,158)(182,184)(185,189)(186,192)(187,191)(188,190)(193,213)(194,216)
(195,215)(196,214)(197,209)(198,212)(199,211)(200,210)(201,205)(202,208)
(203,207)(204,206)(217,253)(218,256)(219,255)(220,254)(221,261)(222,264)
(223,263)(224,262)(225,257)(226,260)(227,259)(228,258)(229,285)(230,288)
(231,287)(232,286)(233,281)(234,284)(235,283)(236,282)(237,277)(238,280)
(239,279)(240,278)(241,273)(242,276)(243,275)(244,274)(245,269)(246,272)
(247,271)(248,270)(249,265)(250,268)(251,267)(252,266)(290,292)(293,297)
(294,300)(295,299)(296,298)(301,321)(302,324)(303,323)(304,322)(305,317)
(306,320)(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)(325,361)
(326,364)(327,363)(328,362)(329,369)(330,372)(331,371)(332,370)(333,365)
(334,368)(335,367)(336,366)(337,393)(338,396)(339,395)(340,394)(341,389)
(342,392)(343,391)(344,390)(345,385)(346,388)(347,387)(348,386)(349,381)
(350,384)(351,383)(352,382)(353,377)(354,380)(355,379)(356,378)(357,373)
(358,376)(359,375)(360,374)(398,400)(401,405)(402,408)(403,407)(404,406)
(409,429)(410,432)(411,431)(412,430)(413,425)(414,428)(415,427)(416,426)
(417,421)(418,424)(419,423)(420,422);;
s3 := ( 1,121)( 2,122)( 3,123)( 4,124)( 5,129)( 6,130)( 7,131)( 8,132)
( 9,125)( 10,126)( 11,127)( 12,128)( 13,109)( 14,110)( 15,111)( 16,112)
( 17,117)( 18,118)( 19,119)( 20,120)( 21,113)( 22,114)( 23,115)( 24,116)
( 25,141)( 26,142)( 27,143)( 28,144)( 29,137)( 30,138)( 31,139)( 32,140)
( 33,133)( 34,134)( 35,135)( 36,136)( 37,157)( 38,158)( 39,159)( 40,160)
( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)( 48,164)
( 49,145)( 50,146)( 51,147)( 52,148)( 53,153)( 54,154)( 55,155)( 56,156)
( 57,149)( 58,150)( 59,151)( 60,152)( 61,177)( 62,178)( 63,179)( 64,180)
( 65,173)( 66,174)( 67,175)( 68,176)( 69,169)( 70,170)( 71,171)( 72,172)
( 73,193)( 74,194)( 75,195)( 76,196)( 77,201)( 78,202)( 79,203)( 80,204)
( 81,197)( 82,198)( 83,199)( 84,200)( 85,181)( 86,182)( 87,183)( 88,184)
( 89,189)( 90,190)( 91,191)( 92,192)( 93,185)( 94,186)( 95,187)( 96,188)
( 97,213)( 98,214)( 99,215)(100,216)(101,209)(102,210)(103,211)(104,212)
(105,205)(106,206)(107,207)(108,208)(217,337)(218,338)(219,339)(220,340)
(221,345)(222,346)(223,347)(224,348)(225,341)(226,342)(227,343)(228,344)
(229,325)(230,326)(231,327)(232,328)(233,333)(234,334)(235,335)(236,336)
(237,329)(238,330)(239,331)(240,332)(241,357)(242,358)(243,359)(244,360)
(245,353)(246,354)(247,355)(248,356)(249,349)(250,350)(251,351)(252,352)
(253,373)(254,374)(255,375)(256,376)(257,381)(258,382)(259,383)(260,384)
(261,377)(262,378)(263,379)(264,380)(265,361)(266,362)(267,363)(268,364)
(269,369)(270,370)(271,371)(272,372)(273,365)(274,366)(275,367)(276,368)
(277,393)(278,394)(279,395)(280,396)(281,389)(282,390)(283,391)(284,392)
(285,385)(286,386)(287,387)(288,388)(289,409)(290,410)(291,411)(292,412)
(293,417)(294,418)(295,419)(296,420)(297,413)(298,414)(299,415)(300,416)
(301,397)(302,398)(303,399)(304,400)(305,405)(306,406)(307,407)(308,408)
(309,401)(310,402)(311,403)(312,404)(313,429)(314,430)(315,431)(316,432)
(317,425)(318,426)(319,427)(320,428)(321,421)(322,422)(323,423)(324,424);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
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)!( 1,219)( 2,220)( 3,217)( 4,218)( 5,223)( 6,224)( 7,221)
( 8,222)( 9,227)( 10,228)( 11,225)( 12,226)( 13,231)( 14,232)( 15,229)
( 16,230)( 17,235)( 18,236)( 19,233)( 20,234)( 21,239)( 22,240)( 23,237)
( 24,238)( 25,243)( 26,244)( 27,241)( 28,242)( 29,247)( 30,248)( 31,245)
( 32,246)( 33,251)( 34,252)( 35,249)( 36,250)( 37,255)( 38,256)( 39,253)
( 40,254)( 41,259)( 42,260)( 43,257)( 44,258)( 45,263)( 46,264)( 47,261)
( 48,262)( 49,267)( 50,268)( 51,265)( 52,266)( 53,271)( 54,272)( 55,269)
( 56,270)( 57,275)( 58,276)( 59,273)( 60,274)( 61,279)( 62,280)( 63,277)
( 64,278)( 65,283)( 66,284)( 67,281)( 68,282)( 69,287)( 70,288)( 71,285)
( 72,286)( 73,291)( 74,292)( 75,289)( 76,290)( 77,295)( 78,296)( 79,293)
( 80,294)( 81,299)( 82,300)( 83,297)( 84,298)( 85,303)( 86,304)( 87,301)
( 88,302)( 89,307)( 90,308)( 91,305)( 92,306)( 93,311)( 94,312)( 95,309)
( 96,310)( 97,315)( 98,316)( 99,313)(100,314)(101,319)(102,320)(103,317)
(104,318)(105,323)(106,324)(107,321)(108,322)(109,327)(110,328)(111,325)
(112,326)(113,331)(114,332)(115,329)(116,330)(117,335)(118,336)(119,333)
(120,334)(121,339)(122,340)(123,337)(124,338)(125,343)(126,344)(127,341)
(128,342)(129,347)(130,348)(131,345)(132,346)(133,351)(134,352)(135,349)
(136,350)(137,355)(138,356)(139,353)(140,354)(141,359)(142,360)(143,357)
(144,358)(145,363)(146,364)(147,361)(148,362)(149,367)(150,368)(151,365)
(152,366)(153,371)(154,372)(155,369)(156,370)(157,375)(158,376)(159,373)
(160,374)(161,379)(162,380)(163,377)(164,378)(165,383)(166,384)(167,381)
(168,382)(169,387)(170,388)(171,385)(172,386)(173,391)(174,392)(175,389)
(176,390)(177,395)(178,396)(179,393)(180,394)(181,399)(182,400)(183,397)
(184,398)(185,403)(186,404)(187,401)(188,402)(189,407)(190,408)(191,405)
(192,406)(193,411)(194,412)(195,409)(196,410)(197,415)(198,416)(199,413)
(200,414)(201,419)(202,420)(203,417)(204,418)(205,423)(206,424)(207,421)
(208,422)(209,427)(210,428)(211,425)(212,426)(213,431)(214,432)(215,429)
(216,430);
s1 := Sym(432)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 77)( 42, 78)
( 43, 80)( 44, 79)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 85)( 50, 86)
( 51, 88)( 52, 87)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 93)( 58, 94)
( 59, 96)( 60, 95)( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,101)( 66,102)
( 67,104)( 68,103)( 69,105)( 70,106)( 71,108)( 72,107)(111,112)(115,116)
(119,120)(123,124)(127,128)(131,132)(135,136)(139,140)(143,144)(145,181)
(146,182)(147,184)(148,183)(149,185)(150,186)(151,188)(152,187)(153,189)
(154,190)(155,192)(156,191)(157,193)(158,194)(159,196)(160,195)(161,197)
(162,198)(163,200)(164,199)(165,201)(166,202)(167,204)(168,203)(169,205)
(170,206)(171,208)(172,207)(173,209)(174,210)(175,212)(176,211)(177,213)
(178,214)(179,216)(180,215)(219,220)(223,224)(227,228)(231,232)(235,236)
(239,240)(243,244)(247,248)(251,252)(253,289)(254,290)(255,292)(256,291)
(257,293)(258,294)(259,296)(260,295)(261,297)(262,298)(263,300)(264,299)
(265,301)(266,302)(267,304)(268,303)(269,305)(270,306)(271,308)(272,307)
(273,309)(274,310)(275,312)(276,311)(277,313)(278,314)(279,316)(280,315)
(281,317)(282,318)(283,320)(284,319)(285,321)(286,322)(287,324)(288,323)
(327,328)(331,332)(335,336)(339,340)(343,344)(347,348)(351,352)(355,356)
(359,360)(361,397)(362,398)(363,400)(364,399)(365,401)(366,402)(367,404)
(368,403)(369,405)(370,406)(371,408)(372,407)(373,409)(374,410)(375,412)
(376,411)(377,413)(378,414)(379,416)(380,415)(381,417)(382,418)(383,420)
(384,419)(385,421)(386,422)(387,424)(388,423)(389,425)(390,426)(391,428)
(392,427)(393,429)(394,430)(395,432)(396,431);
s2 := Sym(432)!( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 45)( 6, 48)( 7, 47)
( 8, 46)( 9, 41)( 10, 44)( 11, 43)( 12, 42)( 13, 69)( 14, 72)( 15, 71)
( 16, 70)( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 61)( 22, 64)( 23, 63)
( 24, 62)( 25, 57)( 26, 60)( 27, 59)( 28, 58)( 29, 53)( 30, 56)( 31, 55)
( 32, 54)( 33, 49)( 34, 52)( 35, 51)( 36, 50)( 74, 76)( 77, 81)( 78, 84)
( 79, 83)( 80, 82)( 85,105)( 86,108)( 87,107)( 88,106)( 89,101)( 90,104)
( 91,103)( 92,102)( 93, 97)( 94,100)( 95, 99)( 96, 98)(109,145)(110,148)
(111,147)(112,146)(113,153)(114,156)(115,155)(116,154)(117,149)(118,152)
(119,151)(120,150)(121,177)(122,180)(123,179)(124,178)(125,173)(126,176)
(127,175)(128,174)(129,169)(130,172)(131,171)(132,170)(133,165)(134,168)
(135,167)(136,166)(137,161)(138,164)(139,163)(140,162)(141,157)(142,160)
(143,159)(144,158)(182,184)(185,189)(186,192)(187,191)(188,190)(193,213)
(194,216)(195,215)(196,214)(197,209)(198,212)(199,211)(200,210)(201,205)
(202,208)(203,207)(204,206)(217,253)(218,256)(219,255)(220,254)(221,261)
(222,264)(223,263)(224,262)(225,257)(226,260)(227,259)(228,258)(229,285)
(230,288)(231,287)(232,286)(233,281)(234,284)(235,283)(236,282)(237,277)
(238,280)(239,279)(240,278)(241,273)(242,276)(243,275)(244,274)(245,269)
(246,272)(247,271)(248,270)(249,265)(250,268)(251,267)(252,266)(290,292)
(293,297)(294,300)(295,299)(296,298)(301,321)(302,324)(303,323)(304,322)
(305,317)(306,320)(307,319)(308,318)(309,313)(310,316)(311,315)(312,314)
(325,361)(326,364)(327,363)(328,362)(329,369)(330,372)(331,371)(332,370)
(333,365)(334,368)(335,367)(336,366)(337,393)(338,396)(339,395)(340,394)
(341,389)(342,392)(343,391)(344,390)(345,385)(346,388)(347,387)(348,386)
(349,381)(350,384)(351,383)(352,382)(353,377)(354,380)(355,379)(356,378)
(357,373)(358,376)(359,375)(360,374)(398,400)(401,405)(402,408)(403,407)
(404,406)(409,429)(410,432)(411,431)(412,430)(413,425)(414,428)(415,427)
(416,426)(417,421)(418,424)(419,423)(420,422);
s3 := Sym(432)!( 1,121)( 2,122)( 3,123)( 4,124)( 5,129)( 6,130)( 7,131)
( 8,132)( 9,125)( 10,126)( 11,127)( 12,128)( 13,109)( 14,110)( 15,111)
( 16,112)( 17,117)( 18,118)( 19,119)( 20,120)( 21,113)( 22,114)( 23,115)
( 24,116)( 25,141)( 26,142)( 27,143)( 28,144)( 29,137)( 30,138)( 31,139)
( 32,140)( 33,133)( 34,134)( 35,135)( 36,136)( 37,157)( 38,158)( 39,159)
( 40,160)( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)
( 48,164)( 49,145)( 50,146)( 51,147)( 52,148)( 53,153)( 54,154)( 55,155)
( 56,156)( 57,149)( 58,150)( 59,151)( 60,152)( 61,177)( 62,178)( 63,179)
( 64,180)( 65,173)( 66,174)( 67,175)( 68,176)( 69,169)( 70,170)( 71,171)
( 72,172)( 73,193)( 74,194)( 75,195)( 76,196)( 77,201)( 78,202)( 79,203)
( 80,204)( 81,197)( 82,198)( 83,199)( 84,200)( 85,181)( 86,182)( 87,183)
( 88,184)( 89,189)( 90,190)( 91,191)( 92,192)( 93,185)( 94,186)( 95,187)
( 96,188)( 97,213)( 98,214)( 99,215)(100,216)(101,209)(102,210)(103,211)
(104,212)(105,205)(106,206)(107,207)(108,208)(217,337)(218,338)(219,339)
(220,340)(221,345)(222,346)(223,347)(224,348)(225,341)(226,342)(227,343)
(228,344)(229,325)(230,326)(231,327)(232,328)(233,333)(234,334)(235,335)
(236,336)(237,329)(238,330)(239,331)(240,332)(241,357)(242,358)(243,359)
(244,360)(245,353)(246,354)(247,355)(248,356)(249,349)(250,350)(251,351)
(252,352)(253,373)(254,374)(255,375)(256,376)(257,381)(258,382)(259,383)
(260,384)(261,377)(262,378)(263,379)(264,380)(265,361)(266,362)(267,363)
(268,364)(269,369)(270,370)(271,371)(272,372)(273,365)(274,366)(275,367)
(276,368)(277,393)(278,394)(279,395)(280,396)(281,389)(282,390)(283,391)
(284,392)(285,385)(286,386)(287,387)(288,388)(289,409)(290,410)(291,411)
(292,412)(293,417)(294,418)(295,419)(296,420)(297,413)(298,414)(299,415)
(300,416)(301,397)(302,398)(303,399)(304,400)(305,405)(306,406)(307,407)
(308,408)(309,401)(310,402)(311,403)(312,404)(313,429)(314,430)(315,431)
(316,432)(317,425)(318,426)(319,427)(320,428)(321,421)(322,422)(323,423)
(324,424);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
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