Polytope of Type {6,6,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,24}*1728a
if this polytope has a name.
Group : SmallGroup(1728,15888)
Rank : 4
Schlafli Type : {6,6,24}
Number of vertices, edges, etc : 6, 18, 72, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 6
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 : {3,6,24}*864a, {6,6,12}*864a
3-fold quotients : {6,2,24}*576
4-fold quotients : {3,6,12}*432a, {6,6,6}*432a
6-fold quotients : {3,2,24}*288, {6,2,12}*288
8-fold quotients : {3,6,6}*216a, {6,6,3}*216a
9-fold quotients : {2,2,24}*192, {6,2,8}*192
12-fold quotients : {3,2,12}*144, {6,2,6}*144
16-fold quotients : {3,6,3}*108
18-fold quotients : {3,2,8}*96, {2,2,12}*96, {6,2,4}*96
24-fold quotients : {3,2,6}*72, {6,2,3}*72
27-fold quotients : {2,2,8}*64
36-fold quotients : {3,2,4}*48, {2,2,6}*48, {6,2,2}*48
48-fold quotients : {3,2,3}*36
54-fold quotients : {2,2,4}*32
72-fold quotients : {2,2,3}*24, {3,2,2}*24
108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)
( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)( 37, 46)
( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)( 45, 53)
( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)( 68, 78)
( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)( 91,100)
( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)( 99,107)
(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)(122,132)
(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)(145,154)
(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)(153,161)
(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)(176,186)
(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)(199,208)
(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)(207,215)
(218,219)(221,222)(224,225)(226,235)(227,237)(228,236)(229,238)(230,240)
(231,239)(232,241)(233,243)(234,242)(245,246)(248,249)(251,252)(253,262)
(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)(261,269)
(272,273)(275,276)(278,279)(280,289)(281,291)(282,290)(283,292)(284,294)
(285,293)(286,295)(287,297)(288,296)(299,300)(302,303)(305,306)(307,316)
(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)(314,324)(315,323)
(326,327)(329,330)(332,333)(334,343)(335,345)(336,344)(337,346)(338,348)
(339,347)(340,349)(341,351)(342,350)(353,354)(356,357)(359,360)(361,370)
(362,372)(363,371)(364,373)(365,375)(366,374)(367,376)(368,378)(369,377)
(380,381)(383,384)(386,387)(388,397)(389,399)(390,398)(391,400)(392,402)
(393,401)(394,403)(395,405)(396,404)(407,408)(410,411)(413,414)(415,424)
(416,426)(417,425)(418,427)(419,429)(420,428)(421,430)(422,432)(423,431);;
s1 := ( 1,226)( 2,228)( 3,227)( 4,230)( 5,229)( 6,231)( 7,234)( 8,233)
( 9,232)( 10,217)( 11,219)( 12,218)( 13,221)( 14,220)( 15,222)( 16,225)
( 17,224)( 18,223)( 19,235)( 20,237)( 21,236)( 22,239)( 23,238)( 24,240)
( 25,243)( 26,242)( 27,241)( 28,253)( 29,255)( 30,254)( 31,257)( 32,256)
( 33,258)( 34,261)( 35,260)( 36,259)( 37,244)( 38,246)( 39,245)( 40,248)
( 41,247)( 42,249)( 43,252)( 44,251)( 45,250)( 46,262)( 47,264)( 48,263)
( 49,266)( 50,265)( 51,267)( 52,270)( 53,269)( 54,268)( 55,280)( 56,282)
( 57,281)( 58,284)( 59,283)( 60,285)( 61,288)( 62,287)( 63,286)( 64,271)
( 65,273)( 66,272)( 67,275)( 68,274)( 69,276)( 70,279)( 71,278)( 72,277)
( 73,289)( 74,291)( 75,290)( 76,293)( 77,292)( 78,294)( 79,297)( 80,296)
( 81,295)( 82,307)( 83,309)( 84,308)( 85,311)( 86,310)( 87,312)( 88,315)
( 89,314)( 90,313)( 91,298)( 92,300)( 93,299)( 94,302)( 95,301)( 96,303)
( 97,306)( 98,305)( 99,304)(100,316)(101,318)(102,317)(103,320)(104,319)
(105,321)(106,324)(107,323)(108,322)(109,334)(110,336)(111,335)(112,338)
(113,337)(114,339)(115,342)(116,341)(117,340)(118,325)(119,327)(120,326)
(121,329)(122,328)(123,330)(124,333)(125,332)(126,331)(127,343)(128,345)
(129,344)(130,347)(131,346)(132,348)(133,351)(134,350)(135,349)(136,361)
(137,363)(138,362)(139,365)(140,364)(141,366)(142,369)(143,368)(144,367)
(145,352)(146,354)(147,353)(148,356)(149,355)(150,357)(151,360)(152,359)
(153,358)(154,370)(155,372)(156,371)(157,374)(158,373)(159,375)(160,378)
(161,377)(162,376)(163,388)(164,390)(165,389)(166,392)(167,391)(168,393)
(169,396)(170,395)(171,394)(172,379)(173,381)(174,380)(175,383)(176,382)
(177,384)(178,387)(179,386)(180,385)(181,397)(182,399)(183,398)(184,401)
(185,400)(186,402)(187,405)(188,404)(189,403)(190,415)(191,417)(192,416)
(193,419)(194,418)(195,420)(196,423)(197,422)(198,421)(199,406)(200,408)
(201,407)(202,410)(203,409)(204,411)(205,414)(206,413)(207,412)(208,424)
(209,426)(210,425)(211,428)(212,427)(213,429)(214,432)(215,431)(216,430);;
s2 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)
( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)( 35, 36)
( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)( 53, 54)
( 55, 85)( 56, 87)( 57, 86)( 58, 82)( 59, 84)( 60, 83)( 61, 88)( 62, 90)
( 63, 89)( 64, 94)( 65, 96)( 66, 95)( 67, 91)( 68, 93)( 69, 92)( 70, 97)
( 71, 99)( 72, 98)( 73,103)( 74,105)( 75,104)( 76,100)( 77,102)( 78,101)
( 79,106)( 80,108)( 81,107)(109,166)(110,168)(111,167)(112,163)(113,165)
(114,164)(115,169)(116,171)(117,170)(118,175)(119,177)(120,176)(121,172)
(122,174)(123,173)(124,178)(125,180)(126,179)(127,184)(128,186)(129,185)
(130,181)(131,183)(132,182)(133,187)(134,189)(135,188)(136,193)(137,195)
(138,194)(139,190)(140,192)(141,191)(142,196)(143,198)(144,197)(145,202)
(146,204)(147,203)(148,199)(149,201)(150,200)(151,205)(152,207)(153,206)
(154,211)(155,213)(156,212)(157,208)(158,210)(159,209)(160,214)(161,216)
(162,215)(217,220)(218,222)(219,221)(224,225)(226,229)(227,231)(228,230)
(233,234)(235,238)(236,240)(237,239)(242,243)(244,247)(245,249)(246,248)
(251,252)(253,256)(254,258)(255,257)(260,261)(262,265)(263,267)(264,266)
(269,270)(271,301)(272,303)(273,302)(274,298)(275,300)(276,299)(277,304)
(278,306)(279,305)(280,310)(281,312)(282,311)(283,307)(284,309)(285,308)
(286,313)(287,315)(288,314)(289,319)(290,321)(291,320)(292,316)(293,318)
(294,317)(295,322)(296,324)(297,323)(325,382)(326,384)(327,383)(328,379)
(329,381)(330,380)(331,385)(332,387)(333,386)(334,391)(335,393)(336,392)
(337,388)(338,390)(339,389)(340,394)(341,396)(342,395)(343,400)(344,402)
(345,401)(346,397)(347,399)(348,398)(349,403)(350,405)(351,404)(352,409)
(353,411)(354,410)(355,406)(356,408)(357,407)(358,412)(359,414)(360,413)
(361,418)(362,420)(363,419)(364,415)(365,417)(366,416)(367,421)(368,423)
(369,422)(370,427)(371,429)(372,428)(373,424)(374,426)(375,425)(376,430)
(377,432)(378,431);;
s3 := ( 1,109)( 2,111)( 3,110)( 4,115)( 5,117)( 6,116)( 7,112)( 8,114)
( 9,113)( 10,118)( 11,120)( 12,119)( 13,124)( 14,126)( 15,125)( 16,121)
( 17,123)( 18,122)( 19,127)( 20,129)( 21,128)( 22,133)( 23,135)( 24,134)
( 25,130)( 26,132)( 27,131)( 28,136)( 29,138)( 30,137)( 31,142)( 32,144)
( 33,143)( 34,139)( 35,141)( 36,140)( 37,145)( 38,147)( 39,146)( 40,151)
( 41,153)( 42,152)( 43,148)( 44,150)( 45,149)( 46,154)( 47,156)( 48,155)
( 49,160)( 50,162)( 51,161)( 52,157)( 53,159)( 54,158)( 55,190)( 56,192)
( 57,191)( 58,196)( 59,198)( 60,197)( 61,193)( 62,195)( 63,194)( 64,199)
( 65,201)( 66,200)( 67,205)( 68,207)( 69,206)( 70,202)( 71,204)( 72,203)
( 73,208)( 74,210)( 75,209)( 76,214)( 77,216)( 78,215)( 79,211)( 80,213)
( 81,212)( 82,163)( 83,165)( 84,164)( 85,169)( 86,171)( 87,170)( 88,166)
( 89,168)( 90,167)( 91,172)( 92,174)( 93,173)( 94,178)( 95,180)( 96,179)
( 97,175)( 98,177)( 99,176)(100,181)(101,183)(102,182)(103,187)(104,189)
(105,188)(106,184)(107,186)(108,185)(217,325)(218,327)(219,326)(220,331)
(221,333)(222,332)(223,328)(224,330)(225,329)(226,334)(227,336)(228,335)
(229,340)(230,342)(231,341)(232,337)(233,339)(234,338)(235,343)(236,345)
(237,344)(238,349)(239,351)(240,350)(241,346)(242,348)(243,347)(244,352)
(245,354)(246,353)(247,358)(248,360)(249,359)(250,355)(251,357)(252,356)
(253,361)(254,363)(255,362)(256,367)(257,369)(258,368)(259,364)(260,366)
(261,365)(262,370)(263,372)(264,371)(265,376)(266,378)(267,377)(268,373)
(269,375)(270,374)(271,406)(272,408)(273,407)(274,412)(275,414)(276,413)
(277,409)(278,411)(279,410)(280,415)(281,417)(282,416)(283,421)(284,423)
(285,422)(286,418)(287,420)(288,419)(289,424)(290,426)(291,425)(292,430)
(293,432)(294,431)(295,427)(296,429)(297,428)(298,379)(299,381)(300,380)
(301,385)(302,387)(303,386)(304,382)(305,384)(306,383)(307,388)(308,390)
(309,389)(310,394)(311,396)(312,395)(313,391)(314,393)(315,392)(316,397)
(317,399)(318,398)(319,403)(320,405)(321,404)(322,400)(323,402)(324,401);;
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*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 2, 3)( 5, 6)( 8, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)
( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 29, 30)( 32, 33)( 35, 36)
( 37, 46)( 38, 48)( 39, 47)( 40, 49)( 41, 51)( 42, 50)( 43, 52)( 44, 54)
( 45, 53)( 56, 57)( 59, 60)( 62, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 76)
( 68, 78)( 69, 77)( 70, 79)( 71, 81)( 72, 80)( 83, 84)( 86, 87)( 89, 90)
( 91,100)( 92,102)( 93,101)( 94,103)( 95,105)( 96,104)( 97,106)( 98,108)
( 99,107)(110,111)(113,114)(116,117)(118,127)(119,129)(120,128)(121,130)
(122,132)(123,131)(124,133)(125,135)(126,134)(137,138)(140,141)(143,144)
(145,154)(146,156)(147,155)(148,157)(149,159)(150,158)(151,160)(152,162)
(153,161)(164,165)(167,168)(170,171)(172,181)(173,183)(174,182)(175,184)
(176,186)(177,185)(178,187)(179,189)(180,188)(191,192)(194,195)(197,198)
(199,208)(200,210)(201,209)(202,211)(203,213)(204,212)(205,214)(206,216)
(207,215)(218,219)(221,222)(224,225)(226,235)(227,237)(228,236)(229,238)
(230,240)(231,239)(232,241)(233,243)(234,242)(245,246)(248,249)(251,252)
(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)
(261,269)(272,273)(275,276)(278,279)(280,289)(281,291)(282,290)(283,292)
(284,294)(285,293)(286,295)(287,297)(288,296)(299,300)(302,303)(305,306)
(307,316)(308,318)(309,317)(310,319)(311,321)(312,320)(313,322)(314,324)
(315,323)(326,327)(329,330)(332,333)(334,343)(335,345)(336,344)(337,346)
(338,348)(339,347)(340,349)(341,351)(342,350)(353,354)(356,357)(359,360)
(361,370)(362,372)(363,371)(364,373)(365,375)(366,374)(367,376)(368,378)
(369,377)(380,381)(383,384)(386,387)(388,397)(389,399)(390,398)(391,400)
(392,402)(393,401)(394,403)(395,405)(396,404)(407,408)(410,411)(413,414)
(415,424)(416,426)(417,425)(418,427)(419,429)(420,428)(421,430)(422,432)
(423,431);
s1 := Sym(432)!( 1,226)( 2,228)( 3,227)( 4,230)( 5,229)( 6,231)( 7,234)
( 8,233)( 9,232)( 10,217)( 11,219)( 12,218)( 13,221)( 14,220)( 15,222)
( 16,225)( 17,224)( 18,223)( 19,235)( 20,237)( 21,236)( 22,239)( 23,238)
( 24,240)( 25,243)( 26,242)( 27,241)( 28,253)( 29,255)( 30,254)( 31,257)
( 32,256)( 33,258)( 34,261)( 35,260)( 36,259)( 37,244)( 38,246)( 39,245)
( 40,248)( 41,247)( 42,249)( 43,252)( 44,251)( 45,250)( 46,262)( 47,264)
( 48,263)( 49,266)( 50,265)( 51,267)( 52,270)( 53,269)( 54,268)( 55,280)
( 56,282)( 57,281)( 58,284)( 59,283)( 60,285)( 61,288)( 62,287)( 63,286)
( 64,271)( 65,273)( 66,272)( 67,275)( 68,274)( 69,276)( 70,279)( 71,278)
( 72,277)( 73,289)( 74,291)( 75,290)( 76,293)( 77,292)( 78,294)( 79,297)
( 80,296)( 81,295)( 82,307)( 83,309)( 84,308)( 85,311)( 86,310)( 87,312)
( 88,315)( 89,314)( 90,313)( 91,298)( 92,300)( 93,299)( 94,302)( 95,301)
( 96,303)( 97,306)( 98,305)( 99,304)(100,316)(101,318)(102,317)(103,320)
(104,319)(105,321)(106,324)(107,323)(108,322)(109,334)(110,336)(111,335)
(112,338)(113,337)(114,339)(115,342)(116,341)(117,340)(118,325)(119,327)
(120,326)(121,329)(122,328)(123,330)(124,333)(125,332)(126,331)(127,343)
(128,345)(129,344)(130,347)(131,346)(132,348)(133,351)(134,350)(135,349)
(136,361)(137,363)(138,362)(139,365)(140,364)(141,366)(142,369)(143,368)
(144,367)(145,352)(146,354)(147,353)(148,356)(149,355)(150,357)(151,360)
(152,359)(153,358)(154,370)(155,372)(156,371)(157,374)(158,373)(159,375)
(160,378)(161,377)(162,376)(163,388)(164,390)(165,389)(166,392)(167,391)
(168,393)(169,396)(170,395)(171,394)(172,379)(173,381)(174,380)(175,383)
(176,382)(177,384)(178,387)(179,386)(180,385)(181,397)(182,399)(183,398)
(184,401)(185,400)(186,402)(187,405)(188,404)(189,403)(190,415)(191,417)
(192,416)(193,419)(194,418)(195,420)(196,423)(197,422)(198,421)(199,406)
(200,408)(201,407)(202,410)(203,409)(204,411)(205,414)(206,413)(207,412)
(208,424)(209,426)(210,425)(211,428)(212,427)(213,429)(214,432)(215,431)
(216,430);
s2 := Sym(432)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 13)( 11, 15)( 12, 14)
( 17, 18)( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)
( 35, 36)( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)
( 53, 54)( 55, 85)( 56, 87)( 57, 86)( 58, 82)( 59, 84)( 60, 83)( 61, 88)
( 62, 90)( 63, 89)( 64, 94)( 65, 96)( 66, 95)( 67, 91)( 68, 93)( 69, 92)
( 70, 97)( 71, 99)( 72, 98)( 73,103)( 74,105)( 75,104)( 76,100)( 77,102)
( 78,101)( 79,106)( 80,108)( 81,107)(109,166)(110,168)(111,167)(112,163)
(113,165)(114,164)(115,169)(116,171)(117,170)(118,175)(119,177)(120,176)
(121,172)(122,174)(123,173)(124,178)(125,180)(126,179)(127,184)(128,186)
(129,185)(130,181)(131,183)(132,182)(133,187)(134,189)(135,188)(136,193)
(137,195)(138,194)(139,190)(140,192)(141,191)(142,196)(143,198)(144,197)
(145,202)(146,204)(147,203)(148,199)(149,201)(150,200)(151,205)(152,207)
(153,206)(154,211)(155,213)(156,212)(157,208)(158,210)(159,209)(160,214)
(161,216)(162,215)(217,220)(218,222)(219,221)(224,225)(226,229)(227,231)
(228,230)(233,234)(235,238)(236,240)(237,239)(242,243)(244,247)(245,249)
(246,248)(251,252)(253,256)(254,258)(255,257)(260,261)(262,265)(263,267)
(264,266)(269,270)(271,301)(272,303)(273,302)(274,298)(275,300)(276,299)
(277,304)(278,306)(279,305)(280,310)(281,312)(282,311)(283,307)(284,309)
(285,308)(286,313)(287,315)(288,314)(289,319)(290,321)(291,320)(292,316)
(293,318)(294,317)(295,322)(296,324)(297,323)(325,382)(326,384)(327,383)
(328,379)(329,381)(330,380)(331,385)(332,387)(333,386)(334,391)(335,393)
(336,392)(337,388)(338,390)(339,389)(340,394)(341,396)(342,395)(343,400)
(344,402)(345,401)(346,397)(347,399)(348,398)(349,403)(350,405)(351,404)
(352,409)(353,411)(354,410)(355,406)(356,408)(357,407)(358,412)(359,414)
(360,413)(361,418)(362,420)(363,419)(364,415)(365,417)(366,416)(367,421)
(368,423)(369,422)(370,427)(371,429)(372,428)(373,424)(374,426)(375,425)
(376,430)(377,432)(378,431);
s3 := Sym(432)!( 1,109)( 2,111)( 3,110)( 4,115)( 5,117)( 6,116)( 7,112)
( 8,114)( 9,113)( 10,118)( 11,120)( 12,119)( 13,124)( 14,126)( 15,125)
( 16,121)( 17,123)( 18,122)( 19,127)( 20,129)( 21,128)( 22,133)( 23,135)
( 24,134)( 25,130)( 26,132)( 27,131)( 28,136)( 29,138)( 30,137)( 31,142)
( 32,144)( 33,143)( 34,139)( 35,141)( 36,140)( 37,145)( 38,147)( 39,146)
( 40,151)( 41,153)( 42,152)( 43,148)( 44,150)( 45,149)( 46,154)( 47,156)
( 48,155)( 49,160)( 50,162)( 51,161)( 52,157)( 53,159)( 54,158)( 55,190)
( 56,192)( 57,191)( 58,196)( 59,198)( 60,197)( 61,193)( 62,195)( 63,194)
( 64,199)( 65,201)( 66,200)( 67,205)( 68,207)( 69,206)( 70,202)( 71,204)
( 72,203)( 73,208)( 74,210)( 75,209)( 76,214)( 77,216)( 78,215)( 79,211)
( 80,213)( 81,212)( 82,163)( 83,165)( 84,164)( 85,169)( 86,171)( 87,170)
( 88,166)( 89,168)( 90,167)( 91,172)( 92,174)( 93,173)( 94,178)( 95,180)
( 96,179)( 97,175)( 98,177)( 99,176)(100,181)(101,183)(102,182)(103,187)
(104,189)(105,188)(106,184)(107,186)(108,185)(217,325)(218,327)(219,326)
(220,331)(221,333)(222,332)(223,328)(224,330)(225,329)(226,334)(227,336)
(228,335)(229,340)(230,342)(231,341)(232,337)(233,339)(234,338)(235,343)
(236,345)(237,344)(238,349)(239,351)(240,350)(241,346)(242,348)(243,347)
(244,352)(245,354)(246,353)(247,358)(248,360)(249,359)(250,355)(251,357)
(252,356)(253,361)(254,363)(255,362)(256,367)(257,369)(258,368)(259,364)
(260,366)(261,365)(262,370)(263,372)(264,371)(265,376)(266,378)(267,377)
(268,373)(269,375)(270,374)(271,406)(272,408)(273,407)(274,412)(275,414)
(276,413)(277,409)(278,411)(279,410)(280,415)(281,417)(282,416)(283,421)
(284,423)(285,422)(286,418)(287,420)(288,419)(289,424)(290,426)(291,425)
(292,430)(293,432)(294,431)(295,427)(296,429)(297,428)(298,379)(299,381)
(300,380)(301,385)(302,387)(303,386)(304,382)(305,384)(306,383)(307,388)
(308,390)(309,389)(310,394)(311,396)(312,395)(313,391)(314,393)(315,392)
(316,397)(317,399)(318,398)(319,403)(320,405)(321,404)(322,400)(323,402)
(324,401);
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*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope