Polytope of Type {8,3,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,3,6}*1728
if this polytope has a name.
Group : SmallGroup(1728,30298)
Rank : 4
Schlafli Type : {8,3,6}
Number of vertices, edges, etc : 16, 72, 54, 18
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {4,3,6}*864
3-fold quotients : {8,3,6}*576
4-fold quotients : {4,3,6}*432
6-fold quotients : {4,3,6}*288
8-fold quotients : {2,3,6}*216
9-fold quotients : {8,3,2}*192
12-fold quotients : {4,3,6}*144
18-fold quotients : {4,3,2}*96
24-fold quotients : {2,3,6}*72
36-fold quotients : {4,3,2}*48
72-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)( 8,220)
( 9,229)( 10,230)( 11,232)( 12,231)( 13,226)( 14,225)( 15,227)( 16,228)
( 17,237)( 18,238)( 19,240)( 20,239)( 21,234)( 22,233)( 23,235)( 24,236)
( 25,245)( 26,246)( 27,248)( 28,247)( 29,242)( 30,241)( 31,243)( 32,244)
( 33,253)( 34,254)( 35,256)( 36,255)( 37,250)( 38,249)( 39,251)( 40,252)
( 41,261)( 42,262)( 43,264)( 44,263)( 45,258)( 46,257)( 47,259)( 48,260)
( 49,269)( 50,270)( 51,272)( 52,271)( 53,266)( 54,265)( 55,267)( 56,268)
( 57,277)( 58,278)( 59,280)( 60,279)( 61,274)( 62,273)( 63,275)( 64,276)
( 65,285)( 66,286)( 67,288)( 68,287)( 69,282)( 70,281)( 71,283)( 72,284)
( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)( 80,292)
( 81,301)( 82,302)( 83,304)( 84,303)( 85,298)( 86,297)( 87,299)( 88,300)
( 89,309)( 90,310)( 91,312)( 92,311)( 93,306)( 94,305)( 95,307)( 96,308)
( 97,317)( 98,318)( 99,320)(100,319)(101,314)(102,313)(103,315)(104,316)
(105,325)(106,326)(107,328)(108,327)(109,322)(110,321)(111,323)(112,324)
(113,333)(114,334)(115,336)(116,335)(117,330)(118,329)(119,331)(120,332)
(121,341)(122,342)(123,344)(124,343)(125,338)(126,337)(127,339)(128,340)
(129,349)(130,350)(131,352)(132,351)(133,346)(134,345)(135,347)(136,348)
(137,357)(138,358)(139,360)(140,359)(141,354)(142,353)(143,355)(144,356)
(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)(152,364)
(153,373)(154,374)(155,376)(156,375)(157,370)(158,369)(159,371)(160,372)
(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)(168,380)
(169,389)(170,390)(171,392)(172,391)(173,386)(174,385)(175,387)(176,388)
(177,397)(178,398)(179,400)(180,399)(181,394)(182,393)(183,395)(184,396)
(185,405)(186,406)(187,408)(188,407)(189,402)(190,401)(191,403)(192,404)
(193,413)(194,414)(195,416)(196,415)(197,410)(198,409)(199,411)(200,412)
(201,421)(202,422)(203,424)(204,423)(205,418)(206,417)(207,419)(208,420)
(209,429)(210,430)(211,432)(212,431)(213,426)(214,425)(215,427)(216,428);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)( 31, 53)
( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)
( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)( 47, 69)
( 48, 70)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)
( 80,150)( 81,153)( 82,154)( 83,156)( 84,155)( 85,159)( 86,160)( 87,157)
( 88,158)( 89,161)( 90,162)( 91,164)( 92,163)( 93,167)( 94,168)( 95,165)
( 96,166)( 97,193)( 98,194)( 99,196)(100,195)(101,199)(102,200)(103,197)
(104,198)(105,201)(106,202)(107,204)(108,203)(109,207)(110,208)(111,205)
(112,206)(113,209)(114,210)(115,212)(116,211)(117,215)(118,216)(119,213)
(120,214)(121,169)(122,170)(123,172)(124,171)(125,175)(126,176)(127,173)
(128,174)(129,177)(130,178)(131,180)(132,179)(133,183)(134,184)(135,181)
(136,182)(137,185)(138,186)(139,188)(140,187)(141,191)(142,192)(143,189)
(144,190)(217,218)(221,224)(222,223)(225,226)(229,232)(230,231)(233,234)
(237,240)(238,239)(241,266)(242,265)(243,267)(244,268)(245,272)(246,271)
(247,270)(248,269)(249,274)(250,273)(251,275)(252,276)(253,280)(254,279)
(255,278)(256,277)(257,282)(258,281)(259,283)(260,284)(261,288)(262,287)
(263,286)(264,285)(289,362)(290,361)(291,363)(292,364)(293,368)(294,367)
(295,366)(296,365)(297,370)(298,369)(299,371)(300,372)(301,376)(302,375)
(303,374)(304,373)(305,378)(306,377)(307,379)(308,380)(309,384)(310,383)
(311,382)(312,381)(313,410)(314,409)(315,411)(316,412)(317,416)(318,415)
(319,414)(320,413)(321,418)(322,417)(323,419)(324,420)(325,424)(326,423)
(327,422)(328,421)(329,426)(330,425)(331,427)(332,428)(333,432)(334,431)
(335,430)(336,429)(337,386)(338,385)(339,387)(340,388)(341,392)(342,391)
(343,390)(344,389)(345,394)(346,393)(347,395)(348,396)(349,400)(350,399)
(351,398)(352,397)(353,402)(354,401)(355,403)(356,404)(357,408)(358,407)
(359,406)(360,405);;
s2 := ( 1,129)( 2,130)( 3,135)( 4,136)( 5,134)( 6,133)( 7,131)( 8,132)
( 9,137)( 10,138)( 11,143)( 12,144)( 13,142)( 14,141)( 15,139)( 16,140)
( 17,121)( 18,122)( 19,127)( 20,128)( 21,126)( 22,125)( 23,123)( 24,124)
( 25, 97)( 26, 98)( 27,103)( 28,104)( 29,102)( 30,101)( 31, 99)( 32,100)
( 33,105)( 34,106)( 35,111)( 36,112)( 37,110)( 38,109)( 39,107)( 40,108)
( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)( 48,116)
( 49, 89)( 50, 90)( 51, 95)( 52, 96)( 53, 94)( 54, 93)( 55, 91)( 56, 92)
( 57, 73)( 58, 74)( 59, 79)( 60, 80)( 61, 78)( 62, 77)( 63, 75)( 64, 76)
( 65, 81)( 66, 82)( 67, 87)( 68, 88)( 69, 86)( 70, 85)( 71, 83)( 72, 84)
(145,201)(146,202)(147,207)(148,208)(149,206)(150,205)(151,203)(152,204)
(153,209)(154,210)(155,215)(156,216)(157,214)(158,213)(159,211)(160,212)
(161,193)(162,194)(163,199)(164,200)(165,198)(166,197)(167,195)(168,196)
(171,175)(172,176)(173,174)(179,183)(180,184)(181,182)(187,191)(188,192)
(189,190)(217,346)(218,345)(219,352)(220,351)(221,349)(222,350)(223,348)
(224,347)(225,354)(226,353)(227,360)(228,359)(229,357)(230,358)(231,356)
(232,355)(233,338)(234,337)(235,344)(236,343)(237,341)(238,342)(239,340)
(240,339)(241,314)(242,313)(243,320)(244,319)(245,317)(246,318)(247,316)
(248,315)(249,322)(250,321)(251,328)(252,327)(253,325)(254,326)(255,324)
(256,323)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)(263,332)
(264,331)(265,306)(266,305)(267,312)(268,311)(269,309)(270,310)(271,308)
(272,307)(273,290)(274,289)(275,296)(276,295)(277,293)(278,294)(279,292)
(280,291)(281,298)(282,297)(283,304)(284,303)(285,301)(286,302)(287,300)
(288,299)(361,418)(362,417)(363,424)(364,423)(365,421)(366,422)(367,420)
(368,419)(369,426)(370,425)(371,432)(372,431)(373,429)(374,430)(375,428)
(376,427)(377,410)(378,409)(379,416)(380,415)(381,413)(382,414)(383,412)
(384,411)(385,386)(387,392)(388,391)(393,394)(395,400)(396,399)(401,402)
(403,408)(404,407);;
s3 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)( 32, 56)
( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)( 40, 72)
( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)
(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)(112,144)
(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)(120,136)
(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)(160,168)
(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)
(177,209)(178,210)(179,211)(180,212)(181,213)(182,214)(183,215)(184,216)
(185,201)(186,202)(187,203)(188,204)(189,205)(190,206)(191,207)(192,208)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)
(249,281)(250,282)(251,283)(252,284)(253,285)(254,286)(255,287)(256,288)
(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)(264,280)
(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)(304,312)
(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)(320,344)
(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)(328,360)
(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)(336,352)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)(392,416)
(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)(400,432)
(401,417)(402,418)(403,419)(404,420)(405,421)(406,422)(407,423)(408,424);;
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, s1*s2*s1*s2*s1*s2,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1,221)( 2,222)( 3,224)( 4,223)( 5,218)( 6,217)( 7,219)
( 8,220)( 9,229)( 10,230)( 11,232)( 12,231)( 13,226)( 14,225)( 15,227)
( 16,228)( 17,237)( 18,238)( 19,240)( 20,239)( 21,234)( 22,233)( 23,235)
( 24,236)( 25,245)( 26,246)( 27,248)( 28,247)( 29,242)( 30,241)( 31,243)
( 32,244)( 33,253)( 34,254)( 35,256)( 36,255)( 37,250)( 38,249)( 39,251)
( 40,252)( 41,261)( 42,262)( 43,264)( 44,263)( 45,258)( 46,257)( 47,259)
( 48,260)( 49,269)( 50,270)( 51,272)( 52,271)( 53,266)( 54,265)( 55,267)
( 56,268)( 57,277)( 58,278)( 59,280)( 60,279)( 61,274)( 62,273)( 63,275)
( 64,276)( 65,285)( 66,286)( 67,288)( 68,287)( 69,282)( 70,281)( 71,283)
( 72,284)( 73,293)( 74,294)( 75,296)( 76,295)( 77,290)( 78,289)( 79,291)
( 80,292)( 81,301)( 82,302)( 83,304)( 84,303)( 85,298)( 86,297)( 87,299)
( 88,300)( 89,309)( 90,310)( 91,312)( 92,311)( 93,306)( 94,305)( 95,307)
( 96,308)( 97,317)( 98,318)( 99,320)(100,319)(101,314)(102,313)(103,315)
(104,316)(105,325)(106,326)(107,328)(108,327)(109,322)(110,321)(111,323)
(112,324)(113,333)(114,334)(115,336)(116,335)(117,330)(118,329)(119,331)
(120,332)(121,341)(122,342)(123,344)(124,343)(125,338)(126,337)(127,339)
(128,340)(129,349)(130,350)(131,352)(132,351)(133,346)(134,345)(135,347)
(136,348)(137,357)(138,358)(139,360)(140,359)(141,354)(142,353)(143,355)
(144,356)(145,365)(146,366)(147,368)(148,367)(149,362)(150,361)(151,363)
(152,364)(153,373)(154,374)(155,376)(156,375)(157,370)(158,369)(159,371)
(160,372)(161,381)(162,382)(163,384)(164,383)(165,378)(166,377)(167,379)
(168,380)(169,389)(170,390)(171,392)(172,391)(173,386)(174,385)(175,387)
(176,388)(177,397)(178,398)(179,400)(180,399)(181,394)(182,393)(183,395)
(184,396)(185,405)(186,406)(187,408)(188,407)(189,402)(190,401)(191,403)
(192,404)(193,413)(194,414)(195,416)(196,415)(197,410)(198,409)(199,411)
(200,412)(201,421)(202,422)(203,424)(204,423)(205,418)(206,417)(207,419)
(208,420)(209,429)(210,430)(211,432)(212,431)(213,426)(214,425)(215,427)
(216,428);
s1 := Sym(432)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)
( 31, 53)( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)
( 39, 61)( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)
( 47, 69)( 48, 70)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)
( 79,149)( 80,150)( 81,153)( 82,154)( 83,156)( 84,155)( 85,159)( 86,160)
( 87,157)( 88,158)( 89,161)( 90,162)( 91,164)( 92,163)( 93,167)( 94,168)
( 95,165)( 96,166)( 97,193)( 98,194)( 99,196)(100,195)(101,199)(102,200)
(103,197)(104,198)(105,201)(106,202)(107,204)(108,203)(109,207)(110,208)
(111,205)(112,206)(113,209)(114,210)(115,212)(116,211)(117,215)(118,216)
(119,213)(120,214)(121,169)(122,170)(123,172)(124,171)(125,175)(126,176)
(127,173)(128,174)(129,177)(130,178)(131,180)(132,179)(133,183)(134,184)
(135,181)(136,182)(137,185)(138,186)(139,188)(140,187)(141,191)(142,192)
(143,189)(144,190)(217,218)(221,224)(222,223)(225,226)(229,232)(230,231)
(233,234)(237,240)(238,239)(241,266)(242,265)(243,267)(244,268)(245,272)
(246,271)(247,270)(248,269)(249,274)(250,273)(251,275)(252,276)(253,280)
(254,279)(255,278)(256,277)(257,282)(258,281)(259,283)(260,284)(261,288)
(262,287)(263,286)(264,285)(289,362)(290,361)(291,363)(292,364)(293,368)
(294,367)(295,366)(296,365)(297,370)(298,369)(299,371)(300,372)(301,376)
(302,375)(303,374)(304,373)(305,378)(306,377)(307,379)(308,380)(309,384)
(310,383)(311,382)(312,381)(313,410)(314,409)(315,411)(316,412)(317,416)
(318,415)(319,414)(320,413)(321,418)(322,417)(323,419)(324,420)(325,424)
(326,423)(327,422)(328,421)(329,426)(330,425)(331,427)(332,428)(333,432)
(334,431)(335,430)(336,429)(337,386)(338,385)(339,387)(340,388)(341,392)
(342,391)(343,390)(344,389)(345,394)(346,393)(347,395)(348,396)(349,400)
(350,399)(351,398)(352,397)(353,402)(354,401)(355,403)(356,404)(357,408)
(358,407)(359,406)(360,405);
s2 := Sym(432)!( 1,129)( 2,130)( 3,135)( 4,136)( 5,134)( 6,133)( 7,131)
( 8,132)( 9,137)( 10,138)( 11,143)( 12,144)( 13,142)( 14,141)( 15,139)
( 16,140)( 17,121)( 18,122)( 19,127)( 20,128)( 21,126)( 22,125)( 23,123)
( 24,124)( 25, 97)( 26, 98)( 27,103)( 28,104)( 29,102)( 30,101)( 31, 99)
( 32,100)( 33,105)( 34,106)( 35,111)( 36,112)( 37,110)( 38,109)( 39,107)
( 40,108)( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)
( 48,116)( 49, 89)( 50, 90)( 51, 95)( 52, 96)( 53, 94)( 54, 93)( 55, 91)
( 56, 92)( 57, 73)( 58, 74)( 59, 79)( 60, 80)( 61, 78)( 62, 77)( 63, 75)
( 64, 76)( 65, 81)( 66, 82)( 67, 87)( 68, 88)( 69, 86)( 70, 85)( 71, 83)
( 72, 84)(145,201)(146,202)(147,207)(148,208)(149,206)(150,205)(151,203)
(152,204)(153,209)(154,210)(155,215)(156,216)(157,214)(158,213)(159,211)
(160,212)(161,193)(162,194)(163,199)(164,200)(165,198)(166,197)(167,195)
(168,196)(171,175)(172,176)(173,174)(179,183)(180,184)(181,182)(187,191)
(188,192)(189,190)(217,346)(218,345)(219,352)(220,351)(221,349)(222,350)
(223,348)(224,347)(225,354)(226,353)(227,360)(228,359)(229,357)(230,358)
(231,356)(232,355)(233,338)(234,337)(235,344)(236,343)(237,341)(238,342)
(239,340)(240,339)(241,314)(242,313)(243,320)(244,319)(245,317)(246,318)
(247,316)(248,315)(249,322)(250,321)(251,328)(252,327)(253,325)(254,326)
(255,324)(256,323)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)
(263,332)(264,331)(265,306)(266,305)(267,312)(268,311)(269,309)(270,310)
(271,308)(272,307)(273,290)(274,289)(275,296)(276,295)(277,293)(278,294)
(279,292)(280,291)(281,298)(282,297)(283,304)(284,303)(285,301)(286,302)
(287,300)(288,299)(361,418)(362,417)(363,424)(364,423)(365,421)(366,422)
(367,420)(368,419)(369,426)(370,425)(371,432)(372,431)(373,429)(374,430)
(375,428)(376,427)(377,410)(378,409)(379,416)(380,415)(381,413)(382,414)
(383,412)(384,411)(385,386)(387,392)(388,391)(393,394)(395,400)(396,399)
(401,402)(403,408)(404,407);
s3 := Sym(432)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)
( 32, 56)( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)
( 40, 72)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)
( 48, 64)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)
(104,128)(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)
(112,144)(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)
(120,136)(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)
(160,168)(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)
(176,200)(177,209)(178,210)(179,211)(180,212)(181,213)(182,214)(183,215)
(184,216)(185,201)(186,202)(187,203)(188,204)(189,205)(190,206)(191,207)
(192,208)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)
(248,272)(249,281)(250,282)(251,283)(252,284)(253,285)(254,286)(255,287)
(256,288)(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)
(264,280)(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)
(304,312)(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)
(320,344)(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)
(328,360)(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)
(336,352)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)
(392,416)(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)
(400,432)(401,417)(402,418)(403,419)(404,420)(405,421)(406,422)(407,423)
(408,424);
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,
s1*s2*s1*s2*s1*s2, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;
References : None.
to this polytope