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Polytope of Type {4,6,12}

Atlas Canonical Name : {4,6,12}*1728b
if this polytope has a name.
Group : SmallGroup(1728,16950)
Rank : 4
Schlafli Type : {4,6,12}
Number of vertices, edges, etc : 4, 36, 108, 36
Order of s0s1s2s3 : 12
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 : {2,6,12}*864a, {4,6,6}*864c
3-fold quotients : {4,6,12}*576b
4-fold quotients : {4,6,3}*432a, {2,6,6}*432a
6-fold quotients : {2,6,12}*288b, {4,6,6}*288c
8-fold quotients : {2,6,3}*216
9-fold quotients : {4,2,12}*192
12-fold quotients : {4,6,3}*144, {2,6,6}*144b
18-fold quotients : {2,2,12}*96, {4,2,6}*96
24-fold quotients : {2,6,3}*72
27-fold quotients : {4,2,4}*64
36-fold quotients : {4,2,3}*48, {2,2,6}*48
54-fold quotients : {2,2,4}*32, {4,2,2}*32
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 := (  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)(  8,224)
(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)( 16,232)
( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)( 40,256)
( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)( 56,272)
( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)( 96,312)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)
(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)(120,336)
(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)(128,344)
(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,352)
(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)
(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)(152,368)
(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)
(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)(168,384)
(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)(176,392)
(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)(184,400)
(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)(192,408)
(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)(200,416)
(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)(208,424)
(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)(216,432);;
s1 := (  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)
(217,244)(218,246)(219,245)(220,247)(221,249)(222,248)(223,250)(224,252)
(225,251)(226,262)(227,264)(228,263)(229,265)(230,267)(231,266)(232,268)
(233,270)(234,269)(235,253)(236,255)(237,254)(238,256)(239,258)(240,257)
(241,259)(242,261)(243,260)(271,298)(272,300)(273,299)(274,301)(275,303)
(276,302)(277,304)(278,306)(279,305)(280,316)(281,318)(282,317)(283,319)
(284,321)(285,320)(286,322)(287,324)(288,323)(289,307)(290,309)(291,308)
(292,310)(293,312)(294,311)(295,313)(296,315)(297,314)(325,352)(326,354)
(327,353)(328,355)(329,357)(330,356)(331,358)(332,360)(333,359)(334,370)
(335,372)(336,371)(337,373)(338,375)(339,374)(340,376)(341,378)(342,377)
(343,361)(344,363)(345,362)(346,364)(347,366)(348,365)(349,367)(350,369)
(351,368)(379,406)(380,408)(381,407)(382,409)(383,411)(384,410)(385,412)
(386,414)(387,413)(388,424)(389,426)(390,425)(391,427)(392,429)(393,428)
(394,430)(395,432)(396,431)(397,415)(398,417)(399,416)(400,418)(401,420)
(402,419)(403,421)(404,423)(405,422);;
s2 := (  1, 10)(  2, 11)(  3, 12)(  4, 18)(  5, 16)(  6, 17)(  7, 14)(  8, 15)
(  9, 13)( 22, 27)( 23, 25)( 24, 26)( 28, 37)( 29, 38)( 30, 39)( 31, 45)
( 32, 43)( 33, 44)( 34, 41)( 35, 42)( 36, 40)( 49, 54)( 50, 52)( 51, 53)
( 55, 64)( 56, 65)( 57, 66)( 58, 72)( 59, 70)( 60, 71)( 61, 68)( 62, 69)
( 63, 67)( 76, 81)( 77, 79)( 78, 80)( 82, 91)( 83, 92)( 84, 93)( 85, 99)
( 86, 97)( 87, 98)( 88, 95)( 89, 96)( 90, 94)(103,108)(104,106)(105,107)
(109,172)(110,173)(111,174)(112,180)(113,178)(114,179)(115,176)(116,177)
(117,175)(118,163)(119,164)(120,165)(121,171)(122,169)(123,170)(124,167)
(125,168)(126,166)(127,181)(128,182)(129,183)(130,189)(131,187)(132,188)
(133,185)(134,186)(135,184)(136,199)(137,200)(138,201)(139,207)(140,205)
(141,206)(142,203)(143,204)(144,202)(145,190)(146,191)(147,192)(148,198)
(149,196)(150,197)(151,194)(152,195)(153,193)(154,208)(155,209)(156,210)
(157,216)(158,214)(159,215)(160,212)(161,213)(162,211)(217,226)(218,227)
(219,228)(220,234)(221,232)(222,233)(223,230)(224,231)(225,229)(238,243)
(239,241)(240,242)(244,253)(245,254)(246,255)(247,261)(248,259)(249,260)
(250,257)(251,258)(252,256)(265,270)(266,268)(267,269)(271,280)(272,281)
(273,282)(274,288)(275,286)(276,287)(277,284)(278,285)(279,283)(292,297)
(293,295)(294,296)(298,307)(299,308)(300,309)(301,315)(302,313)(303,314)
(304,311)(305,312)(306,310)(319,324)(320,322)(321,323)(325,388)(326,389)
(327,390)(328,396)(329,394)(330,395)(331,392)(332,393)(333,391)(334,379)
(335,380)(336,381)(337,387)(338,385)(339,386)(340,383)(341,384)(342,382)
(343,397)(344,398)(345,399)(346,405)(347,403)(348,404)(349,401)(350,402)
(351,400)(352,415)(353,416)(354,417)(355,423)(356,421)(357,422)(358,419)
(359,420)(360,418)(361,406)(362,407)(363,408)(364,414)(365,412)(366,413)
(367,410)(368,411)(369,409)(370,424)(371,425)(372,426)(373,432)(374,430)
(375,431)(376,428)(377,429)(378,427);;
s3 := (  1,112)(  2,113)(  3,114)(  4,109)(  5,110)(  6,111)(  7,115)(  8,116)
(  9,117)( 10,130)( 11,131)( 12,132)( 13,127)( 14,128)( 15,129)( 16,133)
( 17,134)( 18,135)( 19,121)( 20,122)( 21,123)( 22,118)( 23,119)( 24,120)
( 25,124)( 26,125)( 27,126)( 28,139)( 29,140)( 30,141)( 31,136)( 32,137)
( 33,138)( 34,142)( 35,143)( 36,144)( 37,157)( 38,158)( 39,159)( 40,154)
( 41,155)( 42,156)( 43,160)( 44,161)( 45,162)( 46,148)( 47,149)( 48,150)
( 49,145)( 50,146)( 51,147)( 52,151)( 53,152)( 54,153)( 55,166)( 56,167)
( 57,168)( 58,163)( 59,164)( 60,165)( 61,169)( 62,170)( 63,171)( 64,184)
( 65,185)( 66,186)( 67,181)( 68,182)( 69,183)( 70,187)( 71,188)( 72,189)
( 73,175)( 74,176)( 75,177)( 76,172)( 77,173)( 78,174)( 79,178)( 80,179)
( 81,180)( 82,193)( 83,194)( 84,195)( 85,190)( 86,191)( 87,192)( 88,196)
( 89,197)( 90,198)( 91,211)( 92,212)( 93,213)( 94,208)( 95,209)( 96,210)
( 97,214)( 98,215)( 99,216)(100,202)(101,203)(102,204)(103,199)(104,200)
(105,201)(106,205)(107,206)(108,207)(217,328)(218,329)(219,330)(220,325)
(221,326)(222,327)(223,331)(224,332)(225,333)(226,346)(227,347)(228,348)
(229,343)(230,344)(231,345)(232,349)(233,350)(234,351)(235,337)(236,338)
(237,339)(238,334)(239,335)(240,336)(241,340)(242,341)(243,342)(244,355)
(245,356)(246,357)(247,352)(248,353)(249,354)(250,358)(251,359)(252,360)
(253,373)(254,374)(255,375)(256,370)(257,371)(258,372)(259,376)(260,377)
(261,378)(262,364)(263,365)(264,366)(265,361)(266,362)(267,363)(268,367)
(269,368)(270,369)(271,382)(272,383)(273,384)(274,379)(275,380)(276,381)
(277,385)(278,386)(279,387)(280,400)(281,401)(282,402)(283,397)(284,398)
(285,399)(286,403)(287,404)(288,405)(289,391)(290,392)(291,393)(292,388)
(293,389)(294,390)(295,394)(296,395)(297,396)(298,409)(299,410)(300,411)
(301,406)(302,407)(303,408)(304,412)(305,413)(306,414)(307,427)(308,428)
(309,429)(310,424)(311,425)(312,426)(313,430)(314,431)(315,432)(316,418)
(317,419)(318,420)(319,415)(320,416)(321,417)(322,421)(323,422)(324,423);;
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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*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 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(432)!(  1,217)(  2,218)(  3,219)(  4,220)(  5,221)(  6,222)(  7,223)
(  8,224)(  9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)
( 16,232)( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)
( 40,256)( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)
( 56,272)( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)
( 96,312)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)
(112,328)(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)
(120,336)(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)
(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)
(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)
(144,360)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)
(152,368)(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)
(160,376)(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)
(168,384)(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)
(176,392)(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)
(184,400)(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)
(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)
(200,416)(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)
(208,424)(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)
(216,432);
s1 := 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)(217,244)(218,246)(219,245)(220,247)(221,249)(222,248)(223,250)
(224,252)(225,251)(226,262)(227,264)(228,263)(229,265)(230,267)(231,266)
(232,268)(233,270)(234,269)(235,253)(236,255)(237,254)(238,256)(239,258)
(240,257)(241,259)(242,261)(243,260)(271,298)(272,300)(273,299)(274,301)
(275,303)(276,302)(277,304)(278,306)(279,305)(280,316)(281,318)(282,317)
(283,319)(284,321)(285,320)(286,322)(287,324)(288,323)(289,307)(290,309)
(291,308)(292,310)(293,312)(294,311)(295,313)(296,315)(297,314)(325,352)
(326,354)(327,353)(328,355)(329,357)(330,356)(331,358)(332,360)(333,359)
(334,370)(335,372)(336,371)(337,373)(338,375)(339,374)(340,376)(341,378)
(342,377)(343,361)(344,363)(345,362)(346,364)(347,366)(348,365)(349,367)
(350,369)(351,368)(379,406)(380,408)(381,407)(382,409)(383,411)(384,410)
(385,412)(386,414)(387,413)(388,424)(389,426)(390,425)(391,427)(392,429)
(393,428)(394,430)(395,432)(396,431)(397,415)(398,417)(399,416)(400,418)
(401,420)(402,419)(403,421)(404,423)(405,422);
s2 := Sym(432)!(  1, 10)(  2, 11)(  3, 12)(  4, 18)(  5, 16)(  6, 17)(  7, 14)
(  8, 15)(  9, 13)( 22, 27)( 23, 25)( 24, 26)( 28, 37)( 29, 38)( 30, 39)
( 31, 45)( 32, 43)( 33, 44)( 34, 41)( 35, 42)( 36, 40)( 49, 54)( 50, 52)
( 51, 53)( 55, 64)( 56, 65)( 57, 66)( 58, 72)( 59, 70)( 60, 71)( 61, 68)
( 62, 69)( 63, 67)( 76, 81)( 77, 79)( 78, 80)( 82, 91)( 83, 92)( 84, 93)
( 85, 99)( 86, 97)( 87, 98)( 88, 95)( 89, 96)( 90, 94)(103,108)(104,106)
(105,107)(109,172)(110,173)(111,174)(112,180)(113,178)(114,179)(115,176)
(116,177)(117,175)(118,163)(119,164)(120,165)(121,171)(122,169)(123,170)
(124,167)(125,168)(126,166)(127,181)(128,182)(129,183)(130,189)(131,187)
(132,188)(133,185)(134,186)(135,184)(136,199)(137,200)(138,201)(139,207)
(140,205)(141,206)(142,203)(143,204)(144,202)(145,190)(146,191)(147,192)
(148,198)(149,196)(150,197)(151,194)(152,195)(153,193)(154,208)(155,209)
(156,210)(157,216)(158,214)(159,215)(160,212)(161,213)(162,211)(217,226)
(218,227)(219,228)(220,234)(221,232)(222,233)(223,230)(224,231)(225,229)
(238,243)(239,241)(240,242)(244,253)(245,254)(246,255)(247,261)(248,259)
(249,260)(250,257)(251,258)(252,256)(265,270)(266,268)(267,269)(271,280)
(272,281)(273,282)(274,288)(275,286)(276,287)(277,284)(278,285)(279,283)
(292,297)(293,295)(294,296)(298,307)(299,308)(300,309)(301,315)(302,313)
(303,314)(304,311)(305,312)(306,310)(319,324)(320,322)(321,323)(325,388)
(326,389)(327,390)(328,396)(329,394)(330,395)(331,392)(332,393)(333,391)
(334,379)(335,380)(336,381)(337,387)(338,385)(339,386)(340,383)(341,384)
(342,382)(343,397)(344,398)(345,399)(346,405)(347,403)(348,404)(349,401)
(350,402)(351,400)(352,415)(353,416)(354,417)(355,423)(356,421)(357,422)
(358,419)(359,420)(360,418)(361,406)(362,407)(363,408)(364,414)(365,412)
(366,413)(367,410)(368,411)(369,409)(370,424)(371,425)(372,426)(373,432)
(374,430)(375,431)(376,428)(377,429)(378,427);
s3 := Sym(432)!(  1,112)(  2,113)(  3,114)(  4,109)(  5,110)(  6,111)(  7,115)
(  8,116)(  9,117)( 10,130)( 11,131)( 12,132)( 13,127)( 14,128)( 15,129)
( 16,133)( 17,134)( 18,135)( 19,121)( 20,122)( 21,123)( 22,118)( 23,119)
( 24,120)( 25,124)( 26,125)( 27,126)( 28,139)( 29,140)( 30,141)( 31,136)
( 32,137)( 33,138)( 34,142)( 35,143)( 36,144)( 37,157)( 38,158)( 39,159)
( 40,154)( 41,155)( 42,156)( 43,160)( 44,161)( 45,162)( 46,148)( 47,149)
( 48,150)( 49,145)( 50,146)( 51,147)( 52,151)( 53,152)( 54,153)( 55,166)
( 56,167)( 57,168)( 58,163)( 59,164)( 60,165)( 61,169)( 62,170)( 63,171)
( 64,184)( 65,185)( 66,186)( 67,181)( 68,182)( 69,183)( 70,187)( 71,188)
( 72,189)( 73,175)( 74,176)( 75,177)( 76,172)( 77,173)( 78,174)( 79,178)
( 80,179)( 81,180)( 82,193)( 83,194)( 84,195)( 85,190)( 86,191)( 87,192)
( 88,196)( 89,197)( 90,198)( 91,211)( 92,212)( 93,213)( 94,208)( 95,209)
( 96,210)( 97,214)( 98,215)( 99,216)(100,202)(101,203)(102,204)(103,199)
(104,200)(105,201)(106,205)(107,206)(108,207)(217,328)(218,329)(219,330)
(220,325)(221,326)(222,327)(223,331)(224,332)(225,333)(226,346)(227,347)
(228,348)(229,343)(230,344)(231,345)(232,349)(233,350)(234,351)(235,337)
(236,338)(237,339)(238,334)(239,335)(240,336)(241,340)(242,341)(243,342)
(244,355)(245,356)(246,357)(247,352)(248,353)(249,354)(250,358)(251,359)
(252,360)(253,373)(254,374)(255,375)(256,370)(257,371)(258,372)(259,376)
(260,377)(261,378)(262,364)(263,365)(264,366)(265,361)(266,362)(267,363)
(268,367)(269,368)(270,369)(271,382)(272,383)(273,384)(274,379)(275,380)
(276,381)(277,385)(278,386)(279,387)(280,400)(281,401)(282,402)(283,397)
(284,398)(285,399)(286,403)(287,404)(288,405)(289,391)(290,392)(291,393)
(292,388)(293,389)(294,390)(295,394)(296,395)(297,396)(298,409)(299,410)
(300,411)(301,406)(302,407)(303,408)(304,412)(305,413)(306,414)(307,427)
(308,428)(309,429)(310,424)(311,425)(312,426)(313,430)(314,431)(315,432)
(316,418)(317,419)(318,420)(319,415)(320,416)(321,417)(322,421)(323,422)
(324,423);
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*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 >;

```
References : None.
to this polytope