Questions?
See the FAQ
or other info.

Polytope of Type {6,6,18}

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