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# Polytope of Type {12,18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,18,4}*1728e
if this polytope has a name.
Group : SmallGroup(1728,46118)
Rank : 4
Schlafli Type : {12,18,4}
Number of vertices, edges, etc : 12, 108, 36, 4
Order of s0s1s2s3 : 9
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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) :
3-fold quotients : {4,18,4}*576f, {12,6,4}*576f
6-fold quotients : {4,9,4}*288
9-fold quotients : {4,6,4}*192f
18-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49,105)( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)
( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61,101)( 62,102)( 63,103)( 64,104)
( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,127)( 72,128)
( 73,113)( 74,114)( 75,115)( 76,116)( 77,117)( 78,118)( 79,119)( 80,120)
( 81,137)( 82,138)( 83,139)( 84,140)( 85,141)( 86,142)( 87,143)( 88,144)
( 89,129)( 90,130)( 91,131)( 92,132)( 93,133)( 94,134)( 95,135)( 96,136)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,249)(194,250)(195,251)(196,252)(197,253)(198,254)(199,255)(200,256)
(201,241)(202,242)(203,243)(204,244)(205,245)(206,246)(207,247)(208,248)
(209,265)(210,266)(211,267)(212,268)(213,269)(214,270)(215,271)(216,272)
(217,257)(218,258)(219,259)(220,260)(221,261)(222,262)(223,263)(224,264)
(225,281)(226,282)(227,283)(228,284)(229,285)(230,286)(231,287)(232,288)
(233,273)(234,274)(235,275)(236,276)(237,277)(238,278)(239,279)(240,280)
(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,393)(338,394)(339,395)(340,396)(341,397)(342,398)(343,399)(344,400)
(345,385)(346,386)(347,387)(348,388)(349,389)(350,390)(351,391)(352,392)
(353,409)(354,410)(355,411)(356,412)(357,413)(358,414)(359,415)(360,416)
(361,401)(362,402)(363,403)(364,404)(365,405)(366,406)(367,407)(368,408)
(369,425)(370,426)(371,427)(372,428)(373,429)(374,430)(375,431)(376,432)
(377,417)(378,418)(379,419)(380,420)(381,421)(382,422)(383,423)(384,424);;
s1 := (  1, 49)(  2, 50)(  3, 52)(  4, 51)(  5, 53)(  6, 54)(  7, 56)(  8, 55)
(  9, 61)( 10, 62)( 11, 64)( 12, 63)( 13, 57)( 14, 58)( 15, 60)( 16, 59)
( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 85)( 22, 86)( 23, 88)( 24, 87)
( 25, 93)( 26, 94)( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)
( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 69)( 38, 70)( 39, 72)( 40, 71)
( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)
( 99,100)(103,104)(105,109)(106,110)(107,112)(108,111)(113,129)(114,130)
(115,132)(116,131)(117,133)(118,134)(119,136)(120,135)(121,141)(122,142)
(123,144)(124,143)(125,137)(126,138)(127,140)(128,139)(145,369)(146,370)
(147,372)(148,371)(149,373)(150,374)(151,376)(152,375)(153,381)(154,382)
(155,384)(156,383)(157,377)(158,378)(159,380)(160,379)(161,353)(162,354)
(163,356)(164,355)(165,357)(166,358)(167,360)(168,359)(169,365)(170,366)
(171,368)(172,367)(173,361)(174,362)(175,364)(176,363)(177,337)(178,338)
(179,340)(180,339)(181,341)(182,342)(183,344)(184,343)(185,349)(186,350)
(187,352)(188,351)(189,345)(190,346)(191,348)(192,347)(193,321)(194,322)
(195,324)(196,323)(197,325)(198,326)(199,328)(200,327)(201,333)(202,334)
(203,336)(204,335)(205,329)(206,330)(207,332)(208,331)(209,305)(210,306)
(211,308)(212,307)(213,309)(214,310)(215,312)(216,311)(217,317)(218,318)
(219,320)(220,319)(221,313)(222,314)(223,316)(224,315)(225,289)(226,290)
(227,292)(228,291)(229,293)(230,294)(231,296)(232,295)(233,301)(234,302)
(235,304)(236,303)(237,297)(238,298)(239,300)(240,299)(241,417)(242,418)
(243,420)(244,419)(245,421)(246,422)(247,424)(248,423)(249,429)(250,430)
(251,432)(252,431)(253,425)(254,426)(255,428)(256,427)(257,401)(258,402)
(259,404)(260,403)(261,405)(262,406)(263,408)(264,407)(265,413)(266,414)
(267,416)(268,415)(269,409)(270,410)(271,412)(272,411)(273,385)(274,386)
(275,388)(276,387)(277,389)(278,390)(279,392)(280,391)(281,397)(282,398)
(283,400)(284,399)(285,393)(286,394)(287,396)(288,395);;
s2 := (  1,145)(  2,148)(  3,147)(  4,146)(  5,157)(  6,160)(  7,159)(  8,158)
(  9,153)( 10,156)( 11,155)( 12,154)( 13,149)( 14,152)( 15,151)( 16,150)
( 17,177)( 18,180)( 19,179)( 20,178)( 21,189)( 22,192)( 23,191)( 24,190)
( 25,185)( 26,188)( 27,187)( 28,186)( 29,181)( 30,184)( 31,183)( 32,182)
( 33,161)( 34,164)( 35,163)( 36,162)( 37,173)( 38,176)( 39,175)( 40,174)
( 41,169)( 42,172)( 43,171)( 44,170)( 45,165)( 46,168)( 47,167)( 48,166)
( 49,193)( 50,196)( 51,195)( 52,194)( 53,205)( 54,208)( 55,207)( 56,206)
( 57,201)( 58,204)( 59,203)( 60,202)( 61,197)( 62,200)( 63,199)( 64,198)
( 65,225)( 66,228)( 67,227)( 68,226)( 69,237)( 70,240)( 71,239)( 72,238)
( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)( 80,230)
( 81,209)( 82,212)( 83,211)( 84,210)( 85,221)( 86,224)( 87,223)( 88,222)
( 89,217)( 90,220)( 91,219)( 92,218)( 93,213)( 94,216)( 95,215)( 96,214)
( 97,241)( 98,244)( 99,243)(100,242)(101,253)(102,256)(103,255)(104,254)
(105,249)(106,252)(107,251)(108,250)(109,245)(110,248)(111,247)(112,246)
(113,273)(114,276)(115,275)(116,274)(117,285)(118,288)(119,287)(120,286)
(121,281)(122,284)(123,283)(124,282)(125,277)(126,280)(127,279)(128,278)
(129,257)(130,260)(131,259)(132,258)(133,269)(134,272)(135,271)(136,270)
(137,265)(138,268)(139,267)(140,266)(141,261)(142,264)(143,263)(144,262)
(289,321)(290,324)(291,323)(292,322)(293,333)(294,336)(295,335)(296,334)
(297,329)(298,332)(299,331)(300,330)(301,325)(302,328)(303,327)(304,326)
(306,308)(309,317)(310,320)(311,319)(312,318)(314,316)(337,369)(338,372)
(339,371)(340,370)(341,381)(342,384)(343,383)(344,382)(345,377)(346,380)
(347,379)(348,378)(349,373)(350,376)(351,375)(352,374)(354,356)(357,365)
(358,368)(359,367)(360,366)(362,364)(385,417)(386,420)(387,419)(388,418)
(389,429)(390,432)(391,431)(392,430)(393,425)(394,428)(395,427)(396,426)
(397,421)(398,424)(399,423)(400,422)(402,404)(405,413)(406,416)(407,415)
(408,414)(410,412);;
s3 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432);;
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*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope