Polytope of Type {4,36}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,36}*1152c
if this polytope has a name.
Group : SmallGroup(1152,153957)
Rank : 3
Schlafli Type : {4,36}
Number of vertices, edges, etc : 16, 288, 144
Order of s0s1s2 : 36
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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 : {4,18}*576a
3-fold quotients : {4,12}*384c
4-fold quotients : {4,36}*288c
6-fold quotients : {4,6}*192a
8-fold quotients : {4,18}*144b
12-fold quotients : {4,12}*96c
16-fold quotients : {4,9}*72
24-fold quotients : {4,6}*48c
48-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)( 8,160)
( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)( 16,152)
( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)( 24,176)
( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)( 32,168)
( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)( 40,192)
( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)
( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)( 56,208)
( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)( 64,200)
( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)( 72,224)
( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)( 80,216)
( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)
( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)( 96,232)
( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)(104,256)
(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)(112,248)
(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)(120,272)
(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)(128,264)
(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)
(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)(144,280)
(289,441)(290,442)(291,443)(292,444)(293,445)(294,446)(295,447)(296,448)
(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)(304,440)
(305,457)(306,458)(307,459)(308,460)(309,461)(310,462)(311,463)(312,464)
(313,449)(314,450)(315,451)(316,452)(317,453)(318,454)(319,455)(320,456)
(321,473)(322,474)(323,475)(324,476)(325,477)(326,478)(327,479)(328,480)
(329,465)(330,466)(331,467)(332,468)(333,469)(334,470)(335,471)(336,472)
(337,489)(338,490)(339,491)(340,492)(341,493)(342,494)(343,495)(344,496)
(345,481)(346,482)(347,483)(348,484)(349,485)(350,486)(351,487)(352,488)
(353,505)(354,506)(355,507)(356,508)(357,509)(358,510)(359,511)(360,512)
(361,497)(362,498)(363,499)(364,500)(365,501)(366,502)(367,503)(368,504)
(369,521)(370,522)(371,523)(372,524)(373,525)(374,526)(375,527)(376,528)
(377,513)(378,514)(379,515)(380,516)(381,517)(382,518)(383,519)(384,520)
(385,537)(386,538)(387,539)(388,540)(389,541)(390,542)(391,543)(392,544)
(393,529)(394,530)(395,531)(396,532)(397,533)(398,534)(399,535)(400,536)
(401,553)(402,554)(403,555)(404,556)(405,557)(406,558)(407,559)(408,560)
(409,545)(410,546)(411,547)(412,548)(413,549)(414,550)(415,551)(416,552)
(417,569)(418,570)(419,571)(420,572)(421,573)(422,574)(423,575)(424,576)
(425,561)(426,562)(427,563)(428,564)(429,565)(430,566)(431,567)(432,568);;
s1 := ( 1,289)( 2,290)( 3,292)( 4,291)( 5,294)( 6,293)( 7,295)( 8,296)
( 9,304)( 10,303)( 11,301)( 12,302)( 13,299)( 14,300)( 15,298)( 16,297)
( 17,321)( 18,322)( 19,324)( 20,323)( 21,326)( 22,325)( 23,327)( 24,328)
( 25,336)( 26,335)( 27,333)( 28,334)( 29,331)( 30,332)( 31,330)( 32,329)
( 33,305)( 34,306)( 35,308)( 36,307)( 37,310)( 38,309)( 39,311)( 40,312)
( 41,320)( 42,319)( 43,317)( 44,318)( 45,315)( 46,316)( 47,314)( 48,313)
( 49,417)( 50,418)( 51,420)( 52,419)( 53,422)( 54,421)( 55,423)( 56,424)
( 57,432)( 58,431)( 59,429)( 60,430)( 61,427)( 62,428)( 63,426)( 64,425)
( 65,401)( 66,402)( 67,404)( 68,403)( 69,406)( 70,405)( 71,407)( 72,408)
( 73,416)( 74,415)( 75,413)( 76,414)( 77,411)( 78,412)( 79,410)( 80,409)
( 81,385)( 82,386)( 83,388)( 84,387)( 85,390)( 86,389)( 87,391)( 88,392)
( 89,400)( 90,399)( 91,397)( 92,398)( 93,395)( 94,396)( 95,394)( 96,393)
( 97,369)( 98,370)( 99,372)(100,371)(101,374)(102,373)(103,375)(104,376)
(105,384)(106,383)(107,381)(108,382)(109,379)(110,380)(111,378)(112,377)
(113,353)(114,354)(115,356)(116,355)(117,358)(118,357)(119,359)(120,360)
(121,368)(122,367)(123,365)(124,366)(125,363)(126,364)(127,362)(128,361)
(129,337)(130,338)(131,340)(132,339)(133,342)(134,341)(135,343)(136,344)
(137,352)(138,351)(139,349)(140,350)(141,347)(142,348)(143,346)(144,345)
(145,433)(146,434)(147,436)(148,435)(149,438)(150,437)(151,439)(152,440)
(153,448)(154,447)(155,445)(156,446)(157,443)(158,444)(159,442)(160,441)
(161,465)(162,466)(163,468)(164,467)(165,470)(166,469)(167,471)(168,472)
(169,480)(170,479)(171,477)(172,478)(173,475)(174,476)(175,474)(176,473)
(177,449)(178,450)(179,452)(180,451)(181,454)(182,453)(183,455)(184,456)
(185,464)(186,463)(187,461)(188,462)(189,459)(190,460)(191,458)(192,457)
(193,561)(194,562)(195,564)(196,563)(197,566)(198,565)(199,567)(200,568)
(201,576)(202,575)(203,573)(204,574)(205,571)(206,572)(207,570)(208,569)
(209,545)(210,546)(211,548)(212,547)(213,550)(214,549)(215,551)(216,552)
(217,560)(218,559)(219,557)(220,558)(221,555)(222,556)(223,554)(224,553)
(225,529)(226,530)(227,532)(228,531)(229,534)(230,533)(231,535)(232,536)
(233,544)(234,543)(235,541)(236,542)(237,539)(238,540)(239,538)(240,537)
(241,513)(242,514)(243,516)(244,515)(245,518)(246,517)(247,519)(248,520)
(249,528)(250,527)(251,525)(252,526)(253,523)(254,524)(255,522)(256,521)
(257,497)(258,498)(259,500)(260,499)(261,502)(262,501)(263,503)(264,504)
(265,512)(266,511)(267,509)(268,510)(269,507)(270,508)(271,506)(272,505)
(273,481)(274,482)(275,484)(276,483)(277,486)(278,485)(279,487)(280,488)
(281,496)(282,495)(283,493)(284,494)(285,491)(286,492)(287,490)(288,489);;
s2 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 61)( 6, 64)( 7, 63)( 8, 62)
( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)( 16, 54)
( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)
( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)
( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 77)( 38, 80)( 39, 79)( 40, 78)
( 41, 73)( 42, 76)( 43, 75)( 44, 74)( 45, 69)( 46, 72)( 47, 71)( 48, 70)
( 97,129)( 98,132)( 99,131)(100,130)(101,141)(102,144)(103,143)(104,142)
(105,137)(106,140)(107,139)(108,138)(109,133)(110,136)(111,135)(112,134)
(114,116)(117,125)(118,128)(119,127)(120,126)(122,124)(145,193)(146,196)
(147,195)(148,194)(149,205)(150,208)(151,207)(152,206)(153,201)(154,204)
(155,203)(156,202)(157,197)(158,200)(159,199)(160,198)(161,225)(162,228)
(163,227)(164,226)(165,237)(166,240)(167,239)(168,238)(169,233)(170,236)
(171,235)(172,234)(173,229)(174,232)(175,231)(176,230)(177,209)(178,212)
(179,211)(180,210)(181,221)(182,224)(183,223)(184,222)(185,217)(186,220)
(187,219)(188,218)(189,213)(190,216)(191,215)(192,214)(241,273)(242,276)
(243,275)(244,274)(245,285)(246,288)(247,287)(248,286)(249,281)(250,284)
(251,283)(252,282)(253,277)(254,280)(255,279)(256,278)(258,260)(261,269)
(262,272)(263,271)(264,270)(266,268)(289,481)(290,484)(291,483)(292,482)
(293,493)(294,496)(295,495)(296,494)(297,489)(298,492)(299,491)(300,490)
(301,485)(302,488)(303,487)(304,486)(305,513)(306,516)(307,515)(308,514)
(309,525)(310,528)(311,527)(312,526)(313,521)(314,524)(315,523)(316,522)
(317,517)(318,520)(319,519)(320,518)(321,497)(322,500)(323,499)(324,498)
(325,509)(326,512)(327,511)(328,510)(329,505)(330,508)(331,507)(332,506)
(333,501)(334,504)(335,503)(336,502)(337,433)(338,436)(339,435)(340,434)
(341,445)(342,448)(343,447)(344,446)(345,441)(346,444)(347,443)(348,442)
(349,437)(350,440)(351,439)(352,438)(353,465)(354,468)(355,467)(356,466)
(357,477)(358,480)(359,479)(360,478)(361,473)(362,476)(363,475)(364,474)
(365,469)(366,472)(367,471)(368,470)(369,449)(370,452)(371,451)(372,450)
(373,461)(374,464)(375,463)(376,462)(377,457)(378,460)(379,459)(380,458)
(381,453)(382,456)(383,455)(384,454)(385,561)(386,564)(387,563)(388,562)
(389,573)(390,576)(391,575)(392,574)(393,569)(394,572)(395,571)(396,570)
(397,565)(398,568)(399,567)(400,566)(401,545)(402,548)(403,547)(404,546)
(405,557)(406,560)(407,559)(408,558)(409,553)(410,556)(411,555)(412,554)
(413,549)(414,552)(415,551)(416,550)(417,529)(418,532)(419,531)(420,530)
(421,541)(422,544)(423,543)(424,542)(425,537)(426,540)(427,539)(428,538)
(429,533)(430,536)(431,535)(432,534);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)
( 8,160)( 9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)
( 16,152)( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)
( 24,176)( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)
( 32,168)( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)
( 40,192)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)
( 48,184)( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)
( 56,208)( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)
( 64,200)( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)
( 72,224)( 73,209)( 74,210)( 75,211)( 76,212)( 77,213)( 78,214)( 79,215)
( 80,216)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)
( 88,240)( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)
( 96,232)( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)
(104,256)(105,241)(106,242)(107,243)(108,244)(109,245)(110,246)(111,247)
(112,248)(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)
(120,272)(121,257)(122,258)(123,259)(124,260)(125,261)(126,262)(127,263)
(128,264)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)
(136,288)(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)
(144,280)(289,441)(290,442)(291,443)(292,444)(293,445)(294,446)(295,447)
(296,448)(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)
(304,440)(305,457)(306,458)(307,459)(308,460)(309,461)(310,462)(311,463)
(312,464)(313,449)(314,450)(315,451)(316,452)(317,453)(318,454)(319,455)
(320,456)(321,473)(322,474)(323,475)(324,476)(325,477)(326,478)(327,479)
(328,480)(329,465)(330,466)(331,467)(332,468)(333,469)(334,470)(335,471)
(336,472)(337,489)(338,490)(339,491)(340,492)(341,493)(342,494)(343,495)
(344,496)(345,481)(346,482)(347,483)(348,484)(349,485)(350,486)(351,487)
(352,488)(353,505)(354,506)(355,507)(356,508)(357,509)(358,510)(359,511)
(360,512)(361,497)(362,498)(363,499)(364,500)(365,501)(366,502)(367,503)
(368,504)(369,521)(370,522)(371,523)(372,524)(373,525)(374,526)(375,527)
(376,528)(377,513)(378,514)(379,515)(380,516)(381,517)(382,518)(383,519)
(384,520)(385,537)(386,538)(387,539)(388,540)(389,541)(390,542)(391,543)
(392,544)(393,529)(394,530)(395,531)(396,532)(397,533)(398,534)(399,535)
(400,536)(401,553)(402,554)(403,555)(404,556)(405,557)(406,558)(407,559)
(408,560)(409,545)(410,546)(411,547)(412,548)(413,549)(414,550)(415,551)
(416,552)(417,569)(418,570)(419,571)(420,572)(421,573)(422,574)(423,575)
(424,576)(425,561)(426,562)(427,563)(428,564)(429,565)(430,566)(431,567)
(432,568);
s1 := Sym(576)!( 1,289)( 2,290)( 3,292)( 4,291)( 5,294)( 6,293)( 7,295)
( 8,296)( 9,304)( 10,303)( 11,301)( 12,302)( 13,299)( 14,300)( 15,298)
( 16,297)( 17,321)( 18,322)( 19,324)( 20,323)( 21,326)( 22,325)( 23,327)
( 24,328)( 25,336)( 26,335)( 27,333)( 28,334)( 29,331)( 30,332)( 31,330)
( 32,329)( 33,305)( 34,306)( 35,308)( 36,307)( 37,310)( 38,309)( 39,311)
( 40,312)( 41,320)( 42,319)( 43,317)( 44,318)( 45,315)( 46,316)( 47,314)
( 48,313)( 49,417)( 50,418)( 51,420)( 52,419)( 53,422)( 54,421)( 55,423)
( 56,424)( 57,432)( 58,431)( 59,429)( 60,430)( 61,427)( 62,428)( 63,426)
( 64,425)( 65,401)( 66,402)( 67,404)( 68,403)( 69,406)( 70,405)( 71,407)
( 72,408)( 73,416)( 74,415)( 75,413)( 76,414)( 77,411)( 78,412)( 79,410)
( 80,409)( 81,385)( 82,386)( 83,388)( 84,387)( 85,390)( 86,389)( 87,391)
( 88,392)( 89,400)( 90,399)( 91,397)( 92,398)( 93,395)( 94,396)( 95,394)
( 96,393)( 97,369)( 98,370)( 99,372)(100,371)(101,374)(102,373)(103,375)
(104,376)(105,384)(106,383)(107,381)(108,382)(109,379)(110,380)(111,378)
(112,377)(113,353)(114,354)(115,356)(116,355)(117,358)(118,357)(119,359)
(120,360)(121,368)(122,367)(123,365)(124,366)(125,363)(126,364)(127,362)
(128,361)(129,337)(130,338)(131,340)(132,339)(133,342)(134,341)(135,343)
(136,344)(137,352)(138,351)(139,349)(140,350)(141,347)(142,348)(143,346)
(144,345)(145,433)(146,434)(147,436)(148,435)(149,438)(150,437)(151,439)
(152,440)(153,448)(154,447)(155,445)(156,446)(157,443)(158,444)(159,442)
(160,441)(161,465)(162,466)(163,468)(164,467)(165,470)(166,469)(167,471)
(168,472)(169,480)(170,479)(171,477)(172,478)(173,475)(174,476)(175,474)
(176,473)(177,449)(178,450)(179,452)(180,451)(181,454)(182,453)(183,455)
(184,456)(185,464)(186,463)(187,461)(188,462)(189,459)(190,460)(191,458)
(192,457)(193,561)(194,562)(195,564)(196,563)(197,566)(198,565)(199,567)
(200,568)(201,576)(202,575)(203,573)(204,574)(205,571)(206,572)(207,570)
(208,569)(209,545)(210,546)(211,548)(212,547)(213,550)(214,549)(215,551)
(216,552)(217,560)(218,559)(219,557)(220,558)(221,555)(222,556)(223,554)
(224,553)(225,529)(226,530)(227,532)(228,531)(229,534)(230,533)(231,535)
(232,536)(233,544)(234,543)(235,541)(236,542)(237,539)(238,540)(239,538)
(240,537)(241,513)(242,514)(243,516)(244,515)(245,518)(246,517)(247,519)
(248,520)(249,528)(250,527)(251,525)(252,526)(253,523)(254,524)(255,522)
(256,521)(257,497)(258,498)(259,500)(260,499)(261,502)(262,501)(263,503)
(264,504)(265,512)(266,511)(267,509)(268,510)(269,507)(270,508)(271,506)
(272,505)(273,481)(274,482)(275,484)(276,483)(277,486)(278,485)(279,487)
(280,488)(281,496)(282,495)(283,493)(284,494)(285,491)(286,492)(287,490)
(288,489);
s2 := Sym(576)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 61)( 6, 64)( 7, 63)
( 8, 62)( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)
( 16, 54)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)
( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)
( 32, 86)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 77)( 38, 80)( 39, 79)
( 40, 78)( 41, 73)( 42, 76)( 43, 75)( 44, 74)( 45, 69)( 46, 72)( 47, 71)
( 48, 70)( 97,129)( 98,132)( 99,131)(100,130)(101,141)(102,144)(103,143)
(104,142)(105,137)(106,140)(107,139)(108,138)(109,133)(110,136)(111,135)
(112,134)(114,116)(117,125)(118,128)(119,127)(120,126)(122,124)(145,193)
(146,196)(147,195)(148,194)(149,205)(150,208)(151,207)(152,206)(153,201)
(154,204)(155,203)(156,202)(157,197)(158,200)(159,199)(160,198)(161,225)
(162,228)(163,227)(164,226)(165,237)(166,240)(167,239)(168,238)(169,233)
(170,236)(171,235)(172,234)(173,229)(174,232)(175,231)(176,230)(177,209)
(178,212)(179,211)(180,210)(181,221)(182,224)(183,223)(184,222)(185,217)
(186,220)(187,219)(188,218)(189,213)(190,216)(191,215)(192,214)(241,273)
(242,276)(243,275)(244,274)(245,285)(246,288)(247,287)(248,286)(249,281)
(250,284)(251,283)(252,282)(253,277)(254,280)(255,279)(256,278)(258,260)
(261,269)(262,272)(263,271)(264,270)(266,268)(289,481)(290,484)(291,483)
(292,482)(293,493)(294,496)(295,495)(296,494)(297,489)(298,492)(299,491)
(300,490)(301,485)(302,488)(303,487)(304,486)(305,513)(306,516)(307,515)
(308,514)(309,525)(310,528)(311,527)(312,526)(313,521)(314,524)(315,523)
(316,522)(317,517)(318,520)(319,519)(320,518)(321,497)(322,500)(323,499)
(324,498)(325,509)(326,512)(327,511)(328,510)(329,505)(330,508)(331,507)
(332,506)(333,501)(334,504)(335,503)(336,502)(337,433)(338,436)(339,435)
(340,434)(341,445)(342,448)(343,447)(344,446)(345,441)(346,444)(347,443)
(348,442)(349,437)(350,440)(351,439)(352,438)(353,465)(354,468)(355,467)
(356,466)(357,477)(358,480)(359,479)(360,478)(361,473)(362,476)(363,475)
(364,474)(365,469)(366,472)(367,471)(368,470)(369,449)(370,452)(371,451)
(372,450)(373,461)(374,464)(375,463)(376,462)(377,457)(378,460)(379,459)
(380,458)(381,453)(382,456)(383,455)(384,454)(385,561)(386,564)(387,563)
(388,562)(389,573)(390,576)(391,575)(392,574)(393,569)(394,572)(395,571)
(396,570)(397,565)(398,568)(399,567)(400,566)(401,545)(402,548)(403,547)
(404,546)(405,557)(406,560)(407,559)(408,558)(409,553)(410,556)(411,555)
(412,554)(413,549)(414,552)(415,551)(416,550)(417,529)(418,532)(419,531)
(420,530)(421,541)(422,544)(423,543)(424,542)(425,537)(426,540)(427,539)
(428,538)(429,533)(430,536)(431,535)(432,534);
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope