Polytope of Type {36,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,16}*1152a
Also Known As : {36,16|2}. if this polytope has another name.
Group : SmallGroup(1152,32064)
Rank : 3
Schlafli Type : {36,16}
Number of vertices, edges, etc : 36, 288, 16
Order of s0s1s2 : 144
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {36,8}*576a, {18,16}*576
3-fold quotients : {12,16}*384a
4-fold quotients : {36,4}*288a, {18,8}*288
6-fold quotients : {12,8}*192a, {6,16}*192
8-fold quotients : {36,2}*144, {18,4}*144a
9-fold quotients : {4,16}*128a
12-fold quotients : {12,4}*96a, {6,8}*96
16-fold quotients : {18,2}*72
18-fold quotients : {4,8}*64a, {2,16}*64
24-fold quotients : {12,2}*48, {6,4}*48a
32-fold quotients : {9,2}*36
36-fold quotients : {4,4}*32, {2,8}*32
48-fold quotients : {6,2}*24
72-fold quotients : {2,4}*16, {4,2}*16
96-fold quotients : {3,2}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,145)( 2,147)( 3,146)( 4,153)( 5,152)( 6,151)( 7,150)( 8,149)
( 9,148)( 10,154)( 11,156)( 12,155)( 13,162)( 14,161)( 15,160)( 16,159)
( 17,158)( 18,157)( 19,163)( 20,165)( 21,164)( 22,171)( 23,170)( 24,169)
( 25,168)( 26,167)( 27,166)( 28,172)( 29,174)( 30,173)( 31,180)( 32,179)
( 33,178)( 34,177)( 35,176)( 36,175)( 37,181)( 38,183)( 39,182)( 40,189)
( 41,188)( 42,187)( 43,186)( 44,185)( 45,184)( 46,190)( 47,192)( 48,191)
( 49,198)( 50,197)( 51,196)( 52,195)( 53,194)( 54,193)( 55,199)( 56,201)
( 57,200)( 58,207)( 59,206)( 60,205)( 61,204)( 62,203)( 63,202)( 64,208)
( 65,210)( 66,209)( 67,216)( 68,215)( 69,214)( 70,213)( 71,212)( 72,211)
( 73,217)( 74,219)( 75,218)( 76,225)( 77,224)( 78,223)( 79,222)( 80,221)
( 81,220)( 82,226)( 83,228)( 84,227)( 85,234)( 86,233)( 87,232)( 88,231)
( 89,230)( 90,229)( 91,235)( 92,237)( 93,236)( 94,243)( 95,242)( 96,241)
( 97,240)( 98,239)( 99,238)(100,244)(101,246)(102,245)(103,252)(104,251)
(105,250)(106,249)(107,248)(108,247)(109,253)(110,255)(111,254)(112,261)
(113,260)(114,259)(115,258)(116,257)(117,256)(118,262)(119,264)(120,263)
(121,270)(122,269)(123,268)(124,267)(125,266)(126,265)(127,271)(128,273)
(129,272)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)(136,280)
(137,282)(138,281)(139,288)(140,287)(141,286)(142,285)(143,284)(144,283)
(289,433)(290,435)(291,434)(292,441)(293,440)(294,439)(295,438)(296,437)
(297,436)(298,442)(299,444)(300,443)(301,450)(302,449)(303,448)(304,447)
(305,446)(306,445)(307,451)(308,453)(309,452)(310,459)(311,458)(312,457)
(313,456)(314,455)(315,454)(316,460)(317,462)(318,461)(319,468)(320,467)
(321,466)(322,465)(323,464)(324,463)(325,469)(326,471)(327,470)(328,477)
(329,476)(330,475)(331,474)(332,473)(333,472)(334,478)(335,480)(336,479)
(337,486)(338,485)(339,484)(340,483)(341,482)(342,481)(343,487)(344,489)
(345,488)(346,495)(347,494)(348,493)(349,492)(350,491)(351,490)(352,496)
(353,498)(354,497)(355,504)(356,503)(357,502)(358,501)(359,500)(360,499)
(361,505)(362,507)(363,506)(364,513)(365,512)(366,511)(367,510)(368,509)
(369,508)(370,514)(371,516)(372,515)(373,522)(374,521)(375,520)(376,519)
(377,518)(378,517)(379,523)(380,525)(381,524)(382,531)(383,530)(384,529)
(385,528)(386,527)(387,526)(388,532)(389,534)(390,533)(391,540)(392,539)
(393,538)(394,537)(395,536)(396,535)(397,541)(398,543)(399,542)(400,549)
(401,548)(402,547)(403,546)(404,545)(405,544)(406,550)(407,552)(408,551)
(409,558)(410,557)(411,556)(412,555)(413,554)(414,553)(415,559)(416,561)
(417,560)(418,567)(419,566)(420,565)(421,564)(422,563)(423,562)(424,568)
(425,570)(426,569)(427,576)(428,575)(429,574)(430,573)(431,572)(432,571);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)
( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)( 26, 35)
( 27, 34)( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)( 48, 50)
( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)
( 62, 71)( 63, 70)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)
( 79, 99)( 80, 98)( 81, 97)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)
( 87,101)( 88,108)( 89,107)( 90,106)(109,130)(110,132)(111,131)(112,127)
(113,129)(114,128)(115,135)(116,134)(117,133)(118,139)(119,141)(120,140)
(121,136)(122,138)(123,137)(124,144)(125,143)(126,142)(145,184)(146,186)
(147,185)(148,181)(149,183)(150,182)(151,189)(152,188)(153,187)(154,193)
(155,195)(156,194)(157,190)(158,192)(159,191)(160,198)(161,197)(162,196)
(163,211)(164,213)(165,212)(166,208)(167,210)(168,209)(169,216)(170,215)
(171,214)(172,202)(173,204)(174,203)(175,199)(176,201)(177,200)(178,207)
(179,206)(180,205)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)
(223,279)(224,278)(225,277)(226,283)(227,285)(228,284)(229,280)(230,282)
(231,281)(232,288)(233,287)(234,286)(235,256)(236,258)(237,257)(238,253)
(239,255)(240,254)(241,261)(242,260)(243,259)(244,265)(245,267)(246,266)
(247,262)(248,264)(249,263)(250,270)(251,269)(252,268)(289,364)(290,366)
(291,365)(292,361)(293,363)(294,362)(295,369)(296,368)(297,367)(298,373)
(299,375)(300,374)(301,370)(302,372)(303,371)(304,378)(305,377)(306,376)
(307,391)(308,393)(309,392)(310,388)(311,390)(312,389)(313,396)(314,395)
(315,394)(316,382)(317,384)(318,383)(319,379)(320,381)(321,380)(322,387)
(323,386)(324,385)(325,400)(326,402)(327,401)(328,397)(329,399)(330,398)
(331,405)(332,404)(333,403)(334,409)(335,411)(336,410)(337,406)(338,408)
(339,407)(340,414)(341,413)(342,412)(343,427)(344,429)(345,428)(346,424)
(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)(354,419)
(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(433,544)(434,546)
(435,545)(436,541)(437,543)(438,542)(439,549)(440,548)(441,547)(442,553)
(443,555)(444,554)(445,550)(446,552)(447,551)(448,558)(449,557)(450,556)
(451,571)(452,573)(453,572)(454,568)(455,570)(456,569)(457,576)(458,575)
(459,574)(460,562)(461,564)(462,563)(463,559)(464,561)(465,560)(466,567)
(467,566)(468,565)(469,508)(470,510)(471,509)(472,505)(473,507)(474,506)
(475,513)(476,512)(477,511)(478,517)(479,519)(480,518)(481,514)(482,516)
(483,515)(484,522)(485,521)(486,520)(487,535)(488,537)(489,536)(490,532)
(491,534)(492,533)(493,540)(494,539)(495,538)(496,526)(497,528)(498,527)
(499,523)(500,525)(501,524)(502,531)(503,530)(504,529);;
s2 := ( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)
( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)
( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)( 24,321)
( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)( 32,311)
( 33,312)( 34,313)( 35,314)( 36,315)( 37,325)( 38,326)( 39,327)( 40,328)
( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)( 48,336)
( 49,337)( 50,338)( 51,339)( 52,340)( 53,341)( 54,342)( 55,352)( 56,353)
( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)
( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)
( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)( 80,386)
( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)( 88,394)
( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)( 96,366)
( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)(104,374)
(105,375)(106,376)(107,377)(108,378)(109,415)(110,416)(111,417)(112,418)
(113,419)(114,420)(115,421)(116,422)(117,423)(118,424)(119,425)(120,426)
(121,427)(122,428)(123,429)(124,430)(125,431)(126,432)(127,397)(128,398)
(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)
(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)(144,414)
(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)
(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)
(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)(168,465)
(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)(176,455)
(177,456)(178,457)(179,458)(180,459)(181,469)(182,470)(183,471)(184,472)
(185,473)(186,474)(187,475)(188,476)(189,477)(190,478)(191,479)(192,480)
(193,481)(194,482)(195,483)(196,484)(197,485)(198,486)(199,496)(200,497)
(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)
(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)
(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)(224,530)
(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)(232,538)
(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)(240,510)
(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)(248,518)
(249,519)(250,520)(251,521)(252,522)(253,559)(254,560)(255,561)(256,562)
(257,563)(258,564)(259,565)(260,566)(261,567)(262,568)(263,569)(264,570)
(265,571)(266,572)(267,573)(268,574)(269,575)(270,576)(271,541)(272,542)
(273,543)(274,544)(275,545)(276,546)(277,547)(278,548)(279,549)(280,550)
(281,551)(282,552)(283,553)(284,554)(285,555)(286,556)(287,557)(288,558);;
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*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,145)( 2,147)( 3,146)( 4,153)( 5,152)( 6,151)( 7,150)
( 8,149)( 9,148)( 10,154)( 11,156)( 12,155)( 13,162)( 14,161)( 15,160)
( 16,159)( 17,158)( 18,157)( 19,163)( 20,165)( 21,164)( 22,171)( 23,170)
( 24,169)( 25,168)( 26,167)( 27,166)( 28,172)( 29,174)( 30,173)( 31,180)
( 32,179)( 33,178)( 34,177)( 35,176)( 36,175)( 37,181)( 38,183)( 39,182)
( 40,189)( 41,188)( 42,187)( 43,186)( 44,185)( 45,184)( 46,190)( 47,192)
( 48,191)( 49,198)( 50,197)( 51,196)( 52,195)( 53,194)( 54,193)( 55,199)
( 56,201)( 57,200)( 58,207)( 59,206)( 60,205)( 61,204)( 62,203)( 63,202)
( 64,208)( 65,210)( 66,209)( 67,216)( 68,215)( 69,214)( 70,213)( 71,212)
( 72,211)( 73,217)( 74,219)( 75,218)( 76,225)( 77,224)( 78,223)( 79,222)
( 80,221)( 81,220)( 82,226)( 83,228)( 84,227)( 85,234)( 86,233)( 87,232)
( 88,231)( 89,230)( 90,229)( 91,235)( 92,237)( 93,236)( 94,243)( 95,242)
( 96,241)( 97,240)( 98,239)( 99,238)(100,244)(101,246)(102,245)(103,252)
(104,251)(105,250)(106,249)(107,248)(108,247)(109,253)(110,255)(111,254)
(112,261)(113,260)(114,259)(115,258)(116,257)(117,256)(118,262)(119,264)
(120,263)(121,270)(122,269)(123,268)(124,267)(125,266)(126,265)(127,271)
(128,273)(129,272)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)
(136,280)(137,282)(138,281)(139,288)(140,287)(141,286)(142,285)(143,284)
(144,283)(289,433)(290,435)(291,434)(292,441)(293,440)(294,439)(295,438)
(296,437)(297,436)(298,442)(299,444)(300,443)(301,450)(302,449)(303,448)
(304,447)(305,446)(306,445)(307,451)(308,453)(309,452)(310,459)(311,458)
(312,457)(313,456)(314,455)(315,454)(316,460)(317,462)(318,461)(319,468)
(320,467)(321,466)(322,465)(323,464)(324,463)(325,469)(326,471)(327,470)
(328,477)(329,476)(330,475)(331,474)(332,473)(333,472)(334,478)(335,480)
(336,479)(337,486)(338,485)(339,484)(340,483)(341,482)(342,481)(343,487)
(344,489)(345,488)(346,495)(347,494)(348,493)(349,492)(350,491)(351,490)
(352,496)(353,498)(354,497)(355,504)(356,503)(357,502)(358,501)(359,500)
(360,499)(361,505)(362,507)(363,506)(364,513)(365,512)(366,511)(367,510)
(368,509)(369,508)(370,514)(371,516)(372,515)(373,522)(374,521)(375,520)
(376,519)(377,518)(378,517)(379,523)(380,525)(381,524)(382,531)(383,530)
(384,529)(385,528)(386,527)(387,526)(388,532)(389,534)(390,533)(391,540)
(392,539)(393,538)(394,537)(395,536)(396,535)(397,541)(398,543)(399,542)
(400,549)(401,548)(402,547)(403,546)(404,545)(405,544)(406,550)(407,552)
(408,551)(409,558)(410,557)(411,556)(412,555)(413,554)(414,553)(415,559)
(416,561)(417,560)(418,567)(419,566)(420,565)(421,564)(422,563)(423,562)
(424,568)(425,570)(426,569)(427,576)(428,575)(429,574)(430,573)(431,572)
(432,571);
s1 := Sym(576)!( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 13)( 11, 15)( 12, 14)
( 16, 18)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)
( 26, 35)( 27, 34)( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)
( 48, 50)( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)
( 61, 72)( 62, 71)( 63, 70)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)
( 78, 92)( 79, 99)( 80, 98)( 81, 97)( 82,103)( 83,105)( 84,104)( 85,100)
( 86,102)( 87,101)( 88,108)( 89,107)( 90,106)(109,130)(110,132)(111,131)
(112,127)(113,129)(114,128)(115,135)(116,134)(117,133)(118,139)(119,141)
(120,140)(121,136)(122,138)(123,137)(124,144)(125,143)(126,142)(145,184)
(146,186)(147,185)(148,181)(149,183)(150,182)(151,189)(152,188)(153,187)
(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,198)(161,197)
(162,196)(163,211)(164,213)(165,212)(166,208)(167,210)(168,209)(169,216)
(170,215)(171,214)(172,202)(173,204)(174,203)(175,199)(176,201)(177,200)
(178,207)(179,206)(180,205)(217,274)(218,276)(219,275)(220,271)(221,273)
(222,272)(223,279)(224,278)(225,277)(226,283)(227,285)(228,284)(229,280)
(230,282)(231,281)(232,288)(233,287)(234,286)(235,256)(236,258)(237,257)
(238,253)(239,255)(240,254)(241,261)(242,260)(243,259)(244,265)(245,267)
(246,266)(247,262)(248,264)(249,263)(250,270)(251,269)(252,268)(289,364)
(290,366)(291,365)(292,361)(293,363)(294,362)(295,369)(296,368)(297,367)
(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,378)(305,377)
(306,376)(307,391)(308,393)(309,392)(310,388)(311,390)(312,389)(313,396)
(314,395)(315,394)(316,382)(317,384)(318,383)(319,379)(320,381)(321,380)
(322,387)(323,386)(324,385)(325,400)(326,402)(327,401)(328,397)(329,399)
(330,398)(331,405)(332,404)(333,403)(334,409)(335,411)(336,410)(337,406)
(338,408)(339,407)(340,414)(341,413)(342,412)(343,427)(344,429)(345,428)
(346,424)(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)
(354,419)(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(433,544)
(434,546)(435,545)(436,541)(437,543)(438,542)(439,549)(440,548)(441,547)
(442,553)(443,555)(444,554)(445,550)(446,552)(447,551)(448,558)(449,557)
(450,556)(451,571)(452,573)(453,572)(454,568)(455,570)(456,569)(457,576)
(458,575)(459,574)(460,562)(461,564)(462,563)(463,559)(464,561)(465,560)
(466,567)(467,566)(468,565)(469,508)(470,510)(471,509)(472,505)(473,507)
(474,506)(475,513)(476,512)(477,511)(478,517)(479,519)(480,518)(481,514)
(482,516)(483,515)(484,522)(485,521)(486,520)(487,535)(488,537)(489,536)
(490,532)(491,534)(492,533)(493,540)(494,539)(495,538)(496,526)(497,528)
(498,527)(499,523)(500,525)(501,524)(502,531)(503,530)(504,529);
s2 := Sym(576)!( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)
( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)
( 16,304)( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)
( 24,321)( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)
( 32,311)( 33,312)( 34,313)( 35,314)( 36,315)( 37,325)( 38,326)( 39,327)
( 40,328)( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)
( 48,336)( 49,337)( 50,338)( 51,339)( 52,340)( 53,341)( 54,342)( 55,352)
( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)
( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)
( 72,351)( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)
( 80,386)( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)
( 88,394)( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)
( 96,366)( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)
(104,374)(105,375)(106,376)(107,377)(108,378)(109,415)(110,416)(111,417)
(112,418)(113,419)(114,420)(115,421)(116,422)(117,423)(118,424)(119,425)
(120,426)(121,427)(122,428)(123,429)(124,430)(125,431)(126,432)(127,397)
(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)
(136,406)(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)
(144,414)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)
(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)
(160,448)(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)
(168,465)(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)
(176,455)(177,456)(178,457)(179,458)(180,459)(181,469)(182,470)(183,471)
(184,472)(185,473)(186,474)(187,475)(188,476)(189,477)(190,478)(191,479)
(192,480)(193,481)(194,482)(195,483)(196,484)(197,485)(198,486)(199,496)
(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)
(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)
(216,495)(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)
(224,530)(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)
(232,538)(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)
(240,510)(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)
(248,518)(249,519)(250,520)(251,521)(252,522)(253,559)(254,560)(255,561)
(256,562)(257,563)(258,564)(259,565)(260,566)(261,567)(262,568)(263,569)
(264,570)(265,571)(266,572)(267,573)(268,574)(269,575)(270,576)(271,541)
(272,542)(273,543)(274,544)(275,545)(276,546)(277,547)(278,548)(279,549)
(280,550)(281,551)(282,552)(283,553)(284,554)(285,555)(286,556)(287,557)
(288,558);
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*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope