Polytope of Type {16,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,32302)
Rank : 3
Schlafli Type : {16,12}
Number of vertices, edges, etc : 48, 288, 36
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,12}*576a
   4-fold quotients : {8,6}*288, {4,12}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {16,4}*128b
   16-fold quotients : {4,6}*72
   18-fold quotients : {8,4}*64a
   36-fold quotients : {4,4}*32, {8,2}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,289)(  2,291)(  3,290)(  4,293)(  5,292)(  6,294)(  7,297)(  8,296)
(  9,295)( 10,298)( 11,300)( 12,299)( 13,302)( 14,301)( 15,303)( 16,306)
( 17,305)( 18,304)( 19,316)( 20,318)( 21,317)( 22,320)( 23,319)( 24,321)
( 25,324)( 26,323)( 27,322)( 28,307)( 29,309)( 30,308)( 31,311)( 32,310)
( 33,312)( 34,315)( 35,314)( 36,313)( 37,334)( 38,336)( 39,335)( 40,338)
( 41,337)( 42,339)( 43,342)( 44,341)( 45,340)( 46,325)( 47,327)( 48,326)
( 49,329)( 50,328)( 51,330)( 52,333)( 53,332)( 54,331)( 55,343)( 56,345)
( 57,344)( 58,347)( 59,346)( 60,348)( 61,351)( 62,350)( 63,349)( 64,352)
( 65,354)( 66,353)( 67,356)( 68,355)( 69,357)( 70,360)( 71,359)( 72,358)
( 73,379)( 74,381)( 75,380)( 76,383)( 77,382)( 78,384)( 79,387)( 80,386)
( 81,385)( 82,388)( 83,390)( 84,389)( 85,392)( 86,391)( 87,393)( 88,396)
( 89,395)( 90,394)( 91,361)( 92,363)( 93,362)( 94,365)( 95,364)( 96,366)
( 97,369)( 98,368)( 99,367)(100,370)(101,372)(102,371)(103,374)(104,373)
(105,375)(106,378)(107,377)(108,376)(109,424)(110,426)(111,425)(112,428)
(113,427)(114,429)(115,432)(116,431)(117,430)(118,415)(119,417)(120,416)
(121,419)(122,418)(123,420)(124,423)(125,422)(126,421)(127,406)(128,408)
(129,407)(130,410)(131,409)(132,411)(133,414)(134,413)(135,412)(136,397)
(137,399)(138,398)(139,401)(140,400)(141,402)(142,405)(143,404)(144,403)
(145,433)(146,435)(147,434)(148,437)(149,436)(150,438)(151,441)(152,440)
(153,439)(154,442)(155,444)(156,443)(157,446)(158,445)(159,447)(160,450)
(161,449)(162,448)(163,460)(164,462)(165,461)(166,464)(167,463)(168,465)
(169,468)(170,467)(171,466)(172,451)(173,453)(174,452)(175,455)(176,454)
(177,456)(178,459)(179,458)(180,457)(181,478)(182,480)(183,479)(184,482)
(185,481)(186,483)(187,486)(188,485)(189,484)(190,469)(191,471)(192,470)
(193,473)(194,472)(195,474)(196,477)(197,476)(198,475)(199,487)(200,489)
(201,488)(202,491)(203,490)(204,492)(205,495)(206,494)(207,493)(208,496)
(209,498)(210,497)(211,500)(212,499)(213,501)(214,504)(215,503)(216,502)
(217,523)(218,525)(219,524)(220,527)(221,526)(222,528)(223,531)(224,530)
(225,529)(226,532)(227,534)(228,533)(229,536)(230,535)(231,537)(232,540)
(233,539)(234,538)(235,505)(236,507)(237,506)(238,509)(239,508)(240,510)
(241,513)(242,512)(243,511)(244,514)(245,516)(246,515)(247,518)(248,517)
(249,519)(250,522)(251,521)(252,520)(253,568)(254,570)(255,569)(256,572)
(257,571)(258,573)(259,576)(260,575)(261,574)(262,559)(263,561)(264,560)
(265,563)(266,562)(267,564)(268,567)(269,566)(270,565)(271,550)(272,552)
(273,551)(274,554)(275,553)(276,555)(277,558)(278,557)(279,556)(280,541)
(281,543)(282,542)(283,545)(284,544)(285,546)(286,549)(287,548)(288,547);;
s1 := (  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)( 20, 33)
( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)( 38, 42)
( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)( 57, 71)
( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 91)( 74, 96)
( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)( 80, 93)( 81, 95)( 82,100)
( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)( 88,106)( 89,102)( 90,104)
(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)(115,133)(116,129)
(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)(123,137)(124,142)
(125,138)(126,140)(145,181)(146,186)(147,188)(148,184)(149,189)(150,182)
(151,187)(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)(158,198)
(159,191)(160,196)(161,192)(162,194)(163,208)(164,213)(165,215)(166,211)
(167,216)(168,209)(169,214)(170,210)(171,212)(172,199)(173,204)(174,206)
(175,202)(176,207)(177,200)(178,205)(179,201)(180,203)(217,271)(218,276)
(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)(225,275)(226,280)
(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)(233,282)(234,284)
(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)(241,259)(242,255)
(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)(249,263)(250,268)
(251,264)(252,266)(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)
(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)
(303,371)(304,376)(305,372)(306,374)(307,388)(308,393)(309,395)(310,391)
(311,396)(312,389)(313,394)(314,390)(315,392)(316,379)(317,384)(318,386)
(319,382)(320,387)(321,380)(322,385)(323,381)(324,383)(325,397)(326,402)
(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)
(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)
(343,424)(344,429)(345,431)(346,427)(347,432)(348,425)(349,430)(350,426)
(351,428)(352,415)(353,420)(354,422)(355,418)(356,423)(357,416)(358,421)
(359,417)(360,419)(433,550)(434,555)(435,557)(436,553)(437,558)(438,551)
(439,556)(440,552)(441,554)(442,541)(443,546)(444,548)(445,544)(446,549)
(447,542)(448,547)(449,543)(450,545)(451,559)(452,564)(453,566)(454,562)
(455,567)(456,560)(457,565)(458,561)(459,563)(460,568)(461,573)(462,575)
(463,571)(464,576)(465,569)(466,574)(467,570)(468,572)(469,514)(470,519)
(471,521)(472,517)(473,522)(474,515)(475,520)(476,516)(477,518)(478,505)
(479,510)(480,512)(481,508)(482,513)(483,506)(484,511)(485,507)(486,509)
(487,523)(488,528)(489,530)(490,526)(491,531)(492,524)(493,529)(494,525)
(495,527)(496,532)(497,537)(498,539)(499,535)(500,540)(501,533)(502,538)
(503,534)(504,536);;
s2 := (  1,152)(  2,151)(  3,153)(  4,149)(  5,148)(  6,150)(  7,146)(  8,145)
(  9,147)( 10,161)( 11,160)( 12,162)( 13,158)( 14,157)( 15,159)( 16,155)
( 17,154)( 18,156)( 19,170)( 20,169)( 21,171)( 22,167)( 23,166)( 24,168)
( 25,164)( 26,163)( 27,165)( 28,179)( 29,178)( 30,180)( 31,176)( 32,175)
( 33,177)( 34,173)( 35,172)( 36,174)( 37,188)( 38,187)( 39,189)( 40,185)
( 41,184)( 42,186)( 43,182)( 44,181)( 45,183)( 46,197)( 47,196)( 48,198)
( 49,194)( 50,193)( 51,195)( 52,191)( 53,190)( 54,192)( 55,206)( 56,205)
( 57,207)( 58,203)( 59,202)( 60,204)( 61,200)( 62,199)( 63,201)( 64,215)
( 65,214)( 66,216)( 67,212)( 68,211)( 69,213)( 70,209)( 71,208)( 72,210)
( 73,233)( 74,232)( 75,234)( 76,230)( 77,229)( 78,231)( 79,227)( 80,226)
( 81,228)( 82,224)( 83,223)( 84,225)( 85,221)( 86,220)( 87,222)( 88,218)
( 89,217)( 90,219)( 91,251)( 92,250)( 93,252)( 94,248)( 95,247)( 96,249)
( 97,245)( 98,244)( 99,246)(100,242)(101,241)(102,243)(103,239)(104,238)
(105,240)(106,236)(107,235)(108,237)(109,269)(110,268)(111,270)(112,266)
(113,265)(114,267)(115,263)(116,262)(117,264)(118,260)(119,259)(120,261)
(121,257)(122,256)(123,258)(124,254)(125,253)(126,255)(127,287)(128,286)
(129,288)(130,284)(131,283)(132,285)(133,281)(134,280)(135,282)(136,278)
(137,277)(138,279)(139,275)(140,274)(141,276)(142,272)(143,271)(144,273)
(289,440)(290,439)(291,441)(292,437)(293,436)(294,438)(295,434)(296,433)
(297,435)(298,449)(299,448)(300,450)(301,446)(302,445)(303,447)(304,443)
(305,442)(306,444)(307,458)(308,457)(309,459)(310,455)(311,454)(312,456)
(313,452)(314,451)(315,453)(316,467)(317,466)(318,468)(319,464)(320,463)
(321,465)(322,461)(323,460)(324,462)(325,476)(326,475)(327,477)(328,473)
(329,472)(330,474)(331,470)(332,469)(333,471)(334,485)(335,484)(336,486)
(337,482)(338,481)(339,483)(340,479)(341,478)(342,480)(343,494)(344,493)
(345,495)(346,491)(347,490)(348,492)(349,488)(350,487)(351,489)(352,503)
(353,502)(354,504)(355,500)(356,499)(357,501)(358,497)(359,496)(360,498)
(361,521)(362,520)(363,522)(364,518)(365,517)(366,519)(367,515)(368,514)
(369,516)(370,512)(371,511)(372,513)(373,509)(374,508)(375,510)(376,506)
(377,505)(378,507)(379,539)(380,538)(381,540)(382,536)(383,535)(384,537)
(385,533)(386,532)(387,534)(388,530)(389,529)(390,531)(391,527)(392,526)
(393,528)(394,524)(395,523)(396,525)(397,557)(398,556)(399,558)(400,554)
(401,553)(402,555)(403,551)(404,550)(405,552)(406,548)(407,547)(408,549)
(409,545)(410,544)(411,546)(412,542)(413,541)(414,543)(415,575)(416,574)
(417,576)(418,572)(419,571)(420,573)(421,569)(422,568)(423,570)(424,566)
(425,565)(426,567)(427,563)(428,562)(429,564)(430,560)(431,559)(432,561);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(576)!(  1,289)(  2,291)(  3,290)(  4,293)(  5,292)(  6,294)(  7,297)
(  8,296)(  9,295)( 10,298)( 11,300)( 12,299)( 13,302)( 14,301)( 15,303)
( 16,306)( 17,305)( 18,304)( 19,316)( 20,318)( 21,317)( 22,320)( 23,319)
( 24,321)( 25,324)( 26,323)( 27,322)( 28,307)( 29,309)( 30,308)( 31,311)
( 32,310)( 33,312)( 34,315)( 35,314)( 36,313)( 37,334)( 38,336)( 39,335)
( 40,338)( 41,337)( 42,339)( 43,342)( 44,341)( 45,340)( 46,325)( 47,327)
( 48,326)( 49,329)( 50,328)( 51,330)( 52,333)( 53,332)( 54,331)( 55,343)
( 56,345)( 57,344)( 58,347)( 59,346)( 60,348)( 61,351)( 62,350)( 63,349)
( 64,352)( 65,354)( 66,353)( 67,356)( 68,355)( 69,357)( 70,360)( 71,359)
( 72,358)( 73,379)( 74,381)( 75,380)( 76,383)( 77,382)( 78,384)( 79,387)
( 80,386)( 81,385)( 82,388)( 83,390)( 84,389)( 85,392)( 86,391)( 87,393)
( 88,396)( 89,395)( 90,394)( 91,361)( 92,363)( 93,362)( 94,365)( 95,364)
( 96,366)( 97,369)( 98,368)( 99,367)(100,370)(101,372)(102,371)(103,374)
(104,373)(105,375)(106,378)(107,377)(108,376)(109,424)(110,426)(111,425)
(112,428)(113,427)(114,429)(115,432)(116,431)(117,430)(118,415)(119,417)
(120,416)(121,419)(122,418)(123,420)(124,423)(125,422)(126,421)(127,406)
(128,408)(129,407)(130,410)(131,409)(132,411)(133,414)(134,413)(135,412)
(136,397)(137,399)(138,398)(139,401)(140,400)(141,402)(142,405)(143,404)
(144,403)(145,433)(146,435)(147,434)(148,437)(149,436)(150,438)(151,441)
(152,440)(153,439)(154,442)(155,444)(156,443)(157,446)(158,445)(159,447)
(160,450)(161,449)(162,448)(163,460)(164,462)(165,461)(166,464)(167,463)
(168,465)(169,468)(170,467)(171,466)(172,451)(173,453)(174,452)(175,455)
(176,454)(177,456)(178,459)(179,458)(180,457)(181,478)(182,480)(183,479)
(184,482)(185,481)(186,483)(187,486)(188,485)(189,484)(190,469)(191,471)
(192,470)(193,473)(194,472)(195,474)(196,477)(197,476)(198,475)(199,487)
(200,489)(201,488)(202,491)(203,490)(204,492)(205,495)(206,494)(207,493)
(208,496)(209,498)(210,497)(211,500)(212,499)(213,501)(214,504)(215,503)
(216,502)(217,523)(218,525)(219,524)(220,527)(221,526)(222,528)(223,531)
(224,530)(225,529)(226,532)(227,534)(228,533)(229,536)(230,535)(231,537)
(232,540)(233,539)(234,538)(235,505)(236,507)(237,506)(238,509)(239,508)
(240,510)(241,513)(242,512)(243,511)(244,514)(245,516)(246,515)(247,518)
(248,517)(249,519)(250,522)(251,521)(252,520)(253,568)(254,570)(255,569)
(256,572)(257,571)(258,573)(259,576)(260,575)(261,574)(262,559)(263,561)
(264,560)(265,563)(266,562)(267,564)(268,567)(269,566)(270,565)(271,550)
(272,552)(273,551)(274,554)(275,553)(276,555)(277,558)(278,557)(279,556)
(280,541)(281,543)(282,542)(283,545)(284,544)(285,546)(286,549)(287,548)
(288,547);
s1 := Sym(576)!(  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)
( 20, 33)( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)
( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)
( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 91)
( 74, 96)( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)( 80, 93)( 81, 95)
( 82,100)( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)( 88,106)( 89,102)
( 90,104)(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)(115,133)
(116,129)(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)(123,137)
(124,142)(125,138)(126,140)(145,181)(146,186)(147,188)(148,184)(149,189)
(150,182)(151,187)(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)
(158,198)(159,191)(160,196)(161,192)(162,194)(163,208)(164,213)(165,215)
(166,211)(167,216)(168,209)(169,214)(170,210)(171,212)(172,199)(173,204)
(174,206)(175,202)(176,207)(177,200)(178,205)(179,201)(180,203)(217,271)
(218,276)(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)(225,275)
(226,280)(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)(233,282)
(234,284)(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)(241,259)
(242,255)(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)(249,263)
(250,268)(251,264)(252,266)(289,361)(290,366)(291,368)(292,364)(293,369)
(294,362)(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)
(302,378)(303,371)(304,376)(305,372)(306,374)(307,388)(308,393)(309,395)
(310,391)(311,396)(312,389)(313,394)(314,390)(315,392)(316,379)(317,384)
(318,386)(319,382)(320,387)(321,380)(322,385)(323,381)(324,383)(325,397)
(326,402)(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)
(334,406)(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)
(342,410)(343,424)(344,429)(345,431)(346,427)(347,432)(348,425)(349,430)
(350,426)(351,428)(352,415)(353,420)(354,422)(355,418)(356,423)(357,416)
(358,421)(359,417)(360,419)(433,550)(434,555)(435,557)(436,553)(437,558)
(438,551)(439,556)(440,552)(441,554)(442,541)(443,546)(444,548)(445,544)
(446,549)(447,542)(448,547)(449,543)(450,545)(451,559)(452,564)(453,566)
(454,562)(455,567)(456,560)(457,565)(458,561)(459,563)(460,568)(461,573)
(462,575)(463,571)(464,576)(465,569)(466,574)(467,570)(468,572)(469,514)
(470,519)(471,521)(472,517)(473,522)(474,515)(475,520)(476,516)(477,518)
(478,505)(479,510)(480,512)(481,508)(482,513)(483,506)(484,511)(485,507)
(486,509)(487,523)(488,528)(489,530)(490,526)(491,531)(492,524)(493,529)
(494,525)(495,527)(496,532)(497,537)(498,539)(499,535)(500,540)(501,533)
(502,538)(503,534)(504,536);
s2 := Sym(576)!(  1,152)(  2,151)(  3,153)(  4,149)(  5,148)(  6,150)(  7,146)
(  8,145)(  9,147)( 10,161)( 11,160)( 12,162)( 13,158)( 14,157)( 15,159)
( 16,155)( 17,154)( 18,156)( 19,170)( 20,169)( 21,171)( 22,167)( 23,166)
( 24,168)( 25,164)( 26,163)( 27,165)( 28,179)( 29,178)( 30,180)( 31,176)
( 32,175)( 33,177)( 34,173)( 35,172)( 36,174)( 37,188)( 38,187)( 39,189)
( 40,185)( 41,184)( 42,186)( 43,182)( 44,181)( 45,183)( 46,197)( 47,196)
( 48,198)( 49,194)( 50,193)( 51,195)( 52,191)( 53,190)( 54,192)( 55,206)
( 56,205)( 57,207)( 58,203)( 59,202)( 60,204)( 61,200)( 62,199)( 63,201)
( 64,215)( 65,214)( 66,216)( 67,212)( 68,211)( 69,213)( 70,209)( 71,208)
( 72,210)( 73,233)( 74,232)( 75,234)( 76,230)( 77,229)( 78,231)( 79,227)
( 80,226)( 81,228)( 82,224)( 83,223)( 84,225)( 85,221)( 86,220)( 87,222)
( 88,218)( 89,217)( 90,219)( 91,251)( 92,250)( 93,252)( 94,248)( 95,247)
( 96,249)( 97,245)( 98,244)( 99,246)(100,242)(101,241)(102,243)(103,239)
(104,238)(105,240)(106,236)(107,235)(108,237)(109,269)(110,268)(111,270)
(112,266)(113,265)(114,267)(115,263)(116,262)(117,264)(118,260)(119,259)
(120,261)(121,257)(122,256)(123,258)(124,254)(125,253)(126,255)(127,287)
(128,286)(129,288)(130,284)(131,283)(132,285)(133,281)(134,280)(135,282)
(136,278)(137,277)(138,279)(139,275)(140,274)(141,276)(142,272)(143,271)
(144,273)(289,440)(290,439)(291,441)(292,437)(293,436)(294,438)(295,434)
(296,433)(297,435)(298,449)(299,448)(300,450)(301,446)(302,445)(303,447)
(304,443)(305,442)(306,444)(307,458)(308,457)(309,459)(310,455)(311,454)
(312,456)(313,452)(314,451)(315,453)(316,467)(317,466)(318,468)(319,464)
(320,463)(321,465)(322,461)(323,460)(324,462)(325,476)(326,475)(327,477)
(328,473)(329,472)(330,474)(331,470)(332,469)(333,471)(334,485)(335,484)
(336,486)(337,482)(338,481)(339,483)(340,479)(341,478)(342,480)(343,494)
(344,493)(345,495)(346,491)(347,490)(348,492)(349,488)(350,487)(351,489)
(352,503)(353,502)(354,504)(355,500)(356,499)(357,501)(358,497)(359,496)
(360,498)(361,521)(362,520)(363,522)(364,518)(365,517)(366,519)(367,515)
(368,514)(369,516)(370,512)(371,511)(372,513)(373,509)(374,508)(375,510)
(376,506)(377,505)(378,507)(379,539)(380,538)(381,540)(382,536)(383,535)
(384,537)(385,533)(386,532)(387,534)(388,530)(389,529)(390,531)(391,527)
(392,526)(393,528)(394,524)(395,523)(396,525)(397,557)(398,556)(399,558)
(400,554)(401,553)(402,555)(403,551)(404,550)(405,552)(406,548)(407,547)
(408,549)(409,545)(410,544)(411,546)(412,542)(413,541)(414,543)(415,575)
(416,574)(417,576)(418,572)(419,571)(420,573)(421,569)(422,568)(423,570)
(424,566)(425,565)(426,567)(427,563)(428,562)(429,564)(430,560)(431,559)
(432,561);
poly := sub<Sym(576)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope