Polytope of Type {6,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 4
Schlafli Type : {6,12,6}
Number of vertices, edges, etc : 12, 72, 72, 6
Order of s0s1s2s3 : 6
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 : {3,12,6}*864a
3-fold quotients : {6,4,6}*576b
4-fold quotients : {6,6,6}*432a
6-fold quotients : {3,4,6}*288
8-fold quotients : {3,6,6}*216a, {6,6,3}*216a
9-fold quotients : {6,4,2}*192
12-fold quotients : {6,2,6}*144
16-fold quotients : {3,6,3}*108
18-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
24-fold quotients : {3,2,6}*72, {6,2,3}*72
36-fold quotients : {3,4,2}*48, {2,2,6}*48, {6,2,2}*48
48-fold quotients : {3,2,3}*36
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 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 73)
( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 77)
( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 93)
( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 97)
( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)
( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)(116,119)
(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)
(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)
(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)(158,194)
(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)(166,198)
(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)(174,214)
(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(219,220)(221,225)
(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)(236,239)
(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)(255,292)
(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)(263,296)
(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)(271,312)
(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)(279,316)
(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)(287,320)
(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)(341,345)
(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)(356,359)
(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)(368,407)
(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)(376,411)
(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)(384,415)
(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)(392,431)
(393,425)(394,426)(395,428)(396,427);;
s1 := ( 1,253)( 2,256)( 3,255)( 4,254)( 5,261)( 6,264)( 7,263)( 8,262)
( 9,257)( 10,260)( 11,259)( 12,258)( 13,269)( 14,272)( 15,271)( 16,270)
( 17,265)( 18,268)( 19,267)( 20,266)( 21,273)( 22,276)( 23,275)( 24,274)
( 25,285)( 26,288)( 27,287)( 28,286)( 29,281)( 30,284)( 31,283)( 32,282)
( 33,277)( 34,280)( 35,279)( 36,278)( 37,217)( 38,220)( 39,219)( 40,218)
( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)( 48,222)
( 49,233)( 50,236)( 51,235)( 52,234)( 53,229)( 54,232)( 55,231)( 56,230)
( 57,237)( 58,240)( 59,239)( 60,238)( 61,249)( 62,252)( 63,251)( 64,250)
( 65,245)( 66,248)( 67,247)( 68,246)( 69,241)( 70,244)( 71,243)( 72,242)
( 73,289)( 74,292)( 75,291)( 76,290)( 77,297)( 78,300)( 79,299)( 80,298)
( 81,293)( 82,296)( 83,295)( 84,294)( 85,305)( 86,308)( 87,307)( 88,306)
( 89,301)( 90,304)( 91,303)( 92,302)( 93,309)( 94,312)( 95,311)( 96,310)
( 97,321)( 98,324)( 99,323)(100,322)(101,317)(102,320)(103,319)(104,318)
(105,313)(106,316)(107,315)(108,314)(109,361)(110,364)(111,363)(112,362)
(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)(120,366)
(121,377)(122,380)(123,379)(124,378)(125,373)(126,376)(127,375)(128,374)
(129,381)(130,384)(131,383)(132,382)(133,393)(134,396)(135,395)(136,394)
(137,389)(138,392)(139,391)(140,390)(141,385)(142,388)(143,387)(144,386)
(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)(152,334)
(153,329)(154,332)(155,331)(156,330)(157,341)(158,344)(159,343)(160,342)
(161,337)(162,340)(163,339)(164,338)(165,345)(166,348)(167,347)(168,346)
(169,357)(170,360)(171,359)(172,358)(173,353)(174,356)(175,355)(176,354)
(177,349)(178,352)(179,351)(180,350)(181,397)(182,400)(183,399)(184,398)
(185,405)(186,408)(187,407)(188,406)(189,401)(190,404)(191,403)(192,402)
(193,413)(194,416)(195,415)(196,414)(197,409)(198,412)(199,411)(200,410)
(201,417)(202,420)(203,419)(204,418)(205,429)(206,432)(207,431)(208,430)
(209,425)(210,428)(211,427)(212,426)(213,421)(214,424)(215,423)(216,422);;
s2 := ( 1, 14)( 2, 13)( 3, 16)( 4, 15)( 5, 22)( 6, 21)( 7, 24)( 8, 23)
( 9, 18)( 10, 17)( 11, 20)( 12, 19)( 25, 26)( 27, 28)( 29, 34)( 30, 33)
( 31, 36)( 32, 35)( 37, 50)( 38, 49)( 39, 52)( 40, 51)( 41, 58)( 42, 57)
( 43, 60)( 44, 59)( 45, 54)( 46, 53)( 47, 56)( 48, 55)( 61, 62)( 63, 64)
( 65, 70)( 66, 69)( 67, 72)( 68, 71)( 73, 86)( 74, 85)( 75, 88)( 76, 87)
( 77, 94)( 78, 93)( 79, 96)( 80, 95)( 81, 90)( 82, 89)( 83, 92)( 84, 91)
( 97, 98)( 99,100)(101,106)(102,105)(103,108)(104,107)(109,122)(110,121)
(111,124)(112,123)(113,130)(114,129)(115,132)(116,131)(117,126)(118,125)
(119,128)(120,127)(133,134)(135,136)(137,142)(138,141)(139,144)(140,143)
(145,158)(146,157)(147,160)(148,159)(149,166)(150,165)(151,168)(152,167)
(153,162)(154,161)(155,164)(156,163)(169,170)(171,172)(173,178)(174,177)
(175,180)(176,179)(181,194)(182,193)(183,196)(184,195)(185,202)(186,201)
(187,204)(188,203)(189,198)(190,197)(191,200)(192,199)(205,206)(207,208)
(209,214)(210,213)(211,216)(212,215)(217,230)(218,229)(219,232)(220,231)
(221,238)(222,237)(223,240)(224,239)(225,234)(226,233)(227,236)(228,235)
(241,242)(243,244)(245,250)(246,249)(247,252)(248,251)(253,266)(254,265)
(255,268)(256,267)(257,274)(258,273)(259,276)(260,275)(261,270)(262,269)
(263,272)(264,271)(277,278)(279,280)(281,286)(282,285)(283,288)(284,287)
(289,302)(290,301)(291,304)(292,303)(293,310)(294,309)(295,312)(296,311)
(297,306)(298,305)(299,308)(300,307)(313,314)(315,316)(317,322)(318,321)
(319,324)(320,323)(325,338)(326,337)(327,340)(328,339)(329,346)(330,345)
(331,348)(332,347)(333,342)(334,341)(335,344)(336,343)(349,350)(351,352)
(353,358)(354,357)(355,360)(356,359)(361,374)(362,373)(363,376)(364,375)
(365,382)(366,381)(367,384)(368,383)(369,378)(370,377)(371,380)(372,379)
(385,386)(387,388)(389,394)(390,393)(391,396)(392,395)(397,410)(398,409)
(399,412)(400,411)(401,418)(402,417)(403,420)(404,419)(405,414)(406,413)
(407,416)(408,415)(421,422)(423,424)(425,430)(426,429)(427,432)(428,431);;
s3 := ( 1,109)( 2,110)( 3,111)( 4,112)( 5,117)( 6,118)( 7,119)( 8,120)
( 9,113)( 10,114)( 11,115)( 12,116)( 13,133)( 14,134)( 15,135)( 16,136)
( 17,141)( 18,142)( 19,143)( 20,144)( 21,137)( 22,138)( 23,139)( 24,140)
( 25,121)( 26,122)( 27,123)( 28,124)( 29,129)( 30,130)( 31,131)( 32,132)
( 33,125)( 34,126)( 35,127)( 36,128)( 37,145)( 38,146)( 39,147)( 40,148)
( 41,153)( 42,154)( 43,155)( 44,156)( 45,149)( 46,150)( 47,151)( 48,152)
( 49,169)( 50,170)( 51,171)( 52,172)( 53,177)( 54,178)( 55,179)( 56,180)
( 57,173)( 58,174)( 59,175)( 60,176)( 61,157)( 62,158)( 63,159)( 64,160)
( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)( 72,164)
( 73,181)( 74,182)( 75,183)( 76,184)( 77,189)( 78,190)( 79,191)( 80,192)
( 81,185)( 82,186)( 83,187)( 84,188)( 85,205)( 86,206)( 87,207)( 88,208)
( 89,213)( 90,214)( 91,215)( 92,216)( 93,209)( 94,210)( 95,211)( 96,212)
( 97,193)( 98,194)( 99,195)(100,196)(101,201)(102,202)(103,203)(104,204)
(105,197)(106,198)(107,199)(108,200)(217,325)(218,326)(219,327)(220,328)
(221,333)(222,334)(223,335)(224,336)(225,329)(226,330)(227,331)(228,332)
(229,349)(230,350)(231,351)(232,352)(233,357)(234,358)(235,359)(236,360)
(237,353)(238,354)(239,355)(240,356)(241,337)(242,338)(243,339)(244,340)
(245,345)(246,346)(247,347)(248,348)(249,341)(250,342)(251,343)(252,344)
(253,361)(254,362)(255,363)(256,364)(257,369)(258,370)(259,371)(260,372)
(261,365)(262,366)(263,367)(264,368)(265,385)(266,386)(267,387)(268,388)
(269,393)(270,394)(271,395)(272,396)(273,389)(274,390)(275,391)(276,392)
(277,373)(278,374)(279,375)(280,376)(281,381)(282,382)(283,383)(284,384)
(285,377)(286,378)(287,379)(288,380)(289,397)(290,398)(291,399)(292,400)
(293,405)(294,406)(295,407)(296,408)(297,401)(298,402)(299,403)(300,404)
(301,421)(302,422)(303,423)(304,424)(305,429)(306,430)(307,431)(308,432)
(309,425)(310,426)(311,427)(312,428)(313,409)(314,410)(315,411)(316,412)
(317,417)(318,418)(319,419)(320,420)(321,413)(322,414)(323,415)(324,416);;
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, 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*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 21)
( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)
( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)
( 45, 77)( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)
( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)
( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)
( 69,101)( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)
(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)
(138,142)(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)
(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)
(158,194)(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)
(166,198)(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)
(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(219,220)
(221,225)(222,226)(223,228)(224,227)(231,232)(233,237)(234,238)(235,240)
(236,239)(243,244)(245,249)(246,250)(247,252)(248,251)(253,289)(254,290)
(255,292)(256,291)(257,297)(258,298)(259,300)(260,299)(261,293)(262,294)
(263,296)(264,295)(265,301)(266,302)(267,304)(268,303)(269,309)(270,310)
(271,312)(272,311)(273,305)(274,306)(275,308)(276,307)(277,313)(278,314)
(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)
(287,320)(288,319)(327,328)(329,333)(330,334)(331,336)(332,335)(339,340)
(341,345)(342,346)(343,348)(344,347)(351,352)(353,357)(354,358)(355,360)
(356,359)(361,397)(362,398)(363,400)(364,399)(365,405)(366,406)(367,408)
(368,407)(369,401)(370,402)(371,404)(372,403)(373,409)(374,410)(375,412)
(376,411)(377,417)(378,418)(379,420)(380,419)(381,413)(382,414)(383,416)
(384,415)(385,421)(386,422)(387,424)(388,423)(389,429)(390,430)(391,432)
(392,431)(393,425)(394,426)(395,428)(396,427);
s1 := Sym(432)!( 1,253)( 2,256)( 3,255)( 4,254)( 5,261)( 6,264)( 7,263)
( 8,262)( 9,257)( 10,260)( 11,259)( 12,258)( 13,269)( 14,272)( 15,271)
( 16,270)( 17,265)( 18,268)( 19,267)( 20,266)( 21,273)( 22,276)( 23,275)
( 24,274)( 25,285)( 26,288)( 27,287)( 28,286)( 29,281)( 30,284)( 31,283)
( 32,282)( 33,277)( 34,280)( 35,279)( 36,278)( 37,217)( 38,220)( 39,219)
( 40,218)( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)
( 48,222)( 49,233)( 50,236)( 51,235)( 52,234)( 53,229)( 54,232)( 55,231)
( 56,230)( 57,237)( 58,240)( 59,239)( 60,238)( 61,249)( 62,252)( 63,251)
( 64,250)( 65,245)( 66,248)( 67,247)( 68,246)( 69,241)( 70,244)( 71,243)
( 72,242)( 73,289)( 74,292)( 75,291)( 76,290)( 77,297)( 78,300)( 79,299)
( 80,298)( 81,293)( 82,296)( 83,295)( 84,294)( 85,305)( 86,308)( 87,307)
( 88,306)( 89,301)( 90,304)( 91,303)( 92,302)( 93,309)( 94,312)( 95,311)
( 96,310)( 97,321)( 98,324)( 99,323)(100,322)(101,317)(102,320)(103,319)
(104,318)(105,313)(106,316)(107,315)(108,314)(109,361)(110,364)(111,363)
(112,362)(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)
(120,366)(121,377)(122,380)(123,379)(124,378)(125,373)(126,376)(127,375)
(128,374)(129,381)(130,384)(131,383)(132,382)(133,393)(134,396)(135,395)
(136,394)(137,389)(138,392)(139,391)(140,390)(141,385)(142,388)(143,387)
(144,386)(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)
(152,334)(153,329)(154,332)(155,331)(156,330)(157,341)(158,344)(159,343)
(160,342)(161,337)(162,340)(163,339)(164,338)(165,345)(166,348)(167,347)
(168,346)(169,357)(170,360)(171,359)(172,358)(173,353)(174,356)(175,355)
(176,354)(177,349)(178,352)(179,351)(180,350)(181,397)(182,400)(183,399)
(184,398)(185,405)(186,408)(187,407)(188,406)(189,401)(190,404)(191,403)
(192,402)(193,413)(194,416)(195,415)(196,414)(197,409)(198,412)(199,411)
(200,410)(201,417)(202,420)(203,419)(204,418)(205,429)(206,432)(207,431)
(208,430)(209,425)(210,428)(211,427)(212,426)(213,421)(214,424)(215,423)
(216,422);
s2 := Sym(432)!( 1, 14)( 2, 13)( 3, 16)( 4, 15)( 5, 22)( 6, 21)( 7, 24)
( 8, 23)( 9, 18)( 10, 17)( 11, 20)( 12, 19)( 25, 26)( 27, 28)( 29, 34)
( 30, 33)( 31, 36)( 32, 35)( 37, 50)( 38, 49)( 39, 52)( 40, 51)( 41, 58)
( 42, 57)( 43, 60)( 44, 59)( 45, 54)( 46, 53)( 47, 56)( 48, 55)( 61, 62)
( 63, 64)( 65, 70)( 66, 69)( 67, 72)( 68, 71)( 73, 86)( 74, 85)( 75, 88)
( 76, 87)( 77, 94)( 78, 93)( 79, 96)( 80, 95)( 81, 90)( 82, 89)( 83, 92)
( 84, 91)( 97, 98)( 99,100)(101,106)(102,105)(103,108)(104,107)(109,122)
(110,121)(111,124)(112,123)(113,130)(114,129)(115,132)(116,131)(117,126)
(118,125)(119,128)(120,127)(133,134)(135,136)(137,142)(138,141)(139,144)
(140,143)(145,158)(146,157)(147,160)(148,159)(149,166)(150,165)(151,168)
(152,167)(153,162)(154,161)(155,164)(156,163)(169,170)(171,172)(173,178)
(174,177)(175,180)(176,179)(181,194)(182,193)(183,196)(184,195)(185,202)
(186,201)(187,204)(188,203)(189,198)(190,197)(191,200)(192,199)(205,206)
(207,208)(209,214)(210,213)(211,216)(212,215)(217,230)(218,229)(219,232)
(220,231)(221,238)(222,237)(223,240)(224,239)(225,234)(226,233)(227,236)
(228,235)(241,242)(243,244)(245,250)(246,249)(247,252)(248,251)(253,266)
(254,265)(255,268)(256,267)(257,274)(258,273)(259,276)(260,275)(261,270)
(262,269)(263,272)(264,271)(277,278)(279,280)(281,286)(282,285)(283,288)
(284,287)(289,302)(290,301)(291,304)(292,303)(293,310)(294,309)(295,312)
(296,311)(297,306)(298,305)(299,308)(300,307)(313,314)(315,316)(317,322)
(318,321)(319,324)(320,323)(325,338)(326,337)(327,340)(328,339)(329,346)
(330,345)(331,348)(332,347)(333,342)(334,341)(335,344)(336,343)(349,350)
(351,352)(353,358)(354,357)(355,360)(356,359)(361,374)(362,373)(363,376)
(364,375)(365,382)(366,381)(367,384)(368,383)(369,378)(370,377)(371,380)
(372,379)(385,386)(387,388)(389,394)(390,393)(391,396)(392,395)(397,410)
(398,409)(399,412)(400,411)(401,418)(402,417)(403,420)(404,419)(405,414)
(406,413)(407,416)(408,415)(421,422)(423,424)(425,430)(426,429)(427,432)
(428,431);
s3 := Sym(432)!( 1,109)( 2,110)( 3,111)( 4,112)( 5,117)( 6,118)( 7,119)
( 8,120)( 9,113)( 10,114)( 11,115)( 12,116)( 13,133)( 14,134)( 15,135)
( 16,136)( 17,141)( 18,142)( 19,143)( 20,144)( 21,137)( 22,138)( 23,139)
( 24,140)( 25,121)( 26,122)( 27,123)( 28,124)( 29,129)( 30,130)( 31,131)
( 32,132)( 33,125)( 34,126)( 35,127)( 36,128)( 37,145)( 38,146)( 39,147)
( 40,148)( 41,153)( 42,154)( 43,155)( 44,156)( 45,149)( 46,150)( 47,151)
( 48,152)( 49,169)( 50,170)( 51,171)( 52,172)( 53,177)( 54,178)( 55,179)
( 56,180)( 57,173)( 58,174)( 59,175)( 60,176)( 61,157)( 62,158)( 63,159)
( 64,160)( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)
( 72,164)( 73,181)( 74,182)( 75,183)( 76,184)( 77,189)( 78,190)( 79,191)
( 80,192)( 81,185)( 82,186)( 83,187)( 84,188)( 85,205)( 86,206)( 87,207)
( 88,208)( 89,213)( 90,214)( 91,215)( 92,216)( 93,209)( 94,210)( 95,211)
( 96,212)( 97,193)( 98,194)( 99,195)(100,196)(101,201)(102,202)(103,203)
(104,204)(105,197)(106,198)(107,199)(108,200)(217,325)(218,326)(219,327)
(220,328)(221,333)(222,334)(223,335)(224,336)(225,329)(226,330)(227,331)
(228,332)(229,349)(230,350)(231,351)(232,352)(233,357)(234,358)(235,359)
(236,360)(237,353)(238,354)(239,355)(240,356)(241,337)(242,338)(243,339)
(244,340)(245,345)(246,346)(247,347)(248,348)(249,341)(250,342)(251,343)
(252,344)(253,361)(254,362)(255,363)(256,364)(257,369)(258,370)(259,371)
(260,372)(261,365)(262,366)(263,367)(264,368)(265,385)(266,386)(267,387)
(268,388)(269,393)(270,394)(271,395)(272,396)(273,389)(274,390)(275,391)
(276,392)(277,373)(278,374)(279,375)(280,376)(281,381)(282,382)(283,383)
(284,384)(285,377)(286,378)(287,379)(288,380)(289,397)(290,398)(291,399)
(292,400)(293,405)(294,406)(295,407)(296,408)(297,401)(298,402)(299,403)
(300,404)(301,421)(302,422)(303,423)(304,424)(305,429)(306,430)(307,431)
(308,432)(309,425)(310,426)(311,427)(312,428)(313,409)(314,410)(315,411)
(316,412)(317,417)(318,418)(319,419)(320,420)(321,413)(322,414)(323,415)
(324,416);
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,
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*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >;
References : None.
to this polytope