Polytope of Type {8,72}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,72}*1152d
if this polytope has a name.
Group : SmallGroup(1152,14477)
Rank : 3
Schlafli Type : {8,72}
Number of vertices, edges, etc : 8, 288, 72
Order of s0s1s2 : 72
Order of s0s1s2s1 : 4
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 : {4,72}*576b, {8,36}*576b
3-fold quotients : {8,24}*384c
4-fold quotients : {4,36}*288a
6-fold quotients : {4,24}*192b, {8,12}*192b
8-fold quotients : {2,36}*144, {4,18}*144a
9-fold quotients : {8,8}*128d
12-fold quotients : {4,12}*96a
16-fold quotients : {2,18}*72
18-fold quotients : {4,8}*64b, {8,4}*64b
24-fold quotients : {2,12}*48, {4,6}*48a
32-fold quotients : {2,9}*36
36-fold quotients : {4,4}*32
48-fold quotients : {2,6}*24
72-fold quotients : {2,4}*16, {4,2}*16
96-fold quotients : {2,3}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)
( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)
( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)( 40,337)
( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)
( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 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)(109,424)(110,425)(111,426)(112,427)
(113,428)(114,429)(115,430)(116,431)(117,432)(118,415)(119,416)(120,417)
(121,418)(122,419)(123,420)(124,421)(125,422)(126,423)(127,406)(128,407)
(129,408)(130,409)(131,410)(132,411)(133,412)(134,413)(135,414)(136,397)
(137,398)(138,399)(139,400)(140,401)(141,402)(142,403)(143,404)(144,405)
(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)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)
(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)
(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)(184,481)
(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)
(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(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)(253,568)(254,569)(255,570)(256,571)
(257,572)(258,573)(259,574)(260,575)(261,576)(262,559)(263,560)(264,561)
(265,562)(266,563)(267,564)(268,565)(269,566)(270,567)(271,550)(272,551)
(273,552)(274,553)(275,554)(276,555)(277,556)(278,557)(279,558)(280,541)
(281,542)(282,543)(283,544)(284,545)(285,546)(286,547)(287,548)(288,549);;
s1 := ( 2, 3)( 4, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)( 15, 16)
( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)( 33, 34)
( 37, 64)( 38, 66)( 39, 65)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)
( 45, 67)( 46, 55)( 47, 57)( 48, 56)( 49, 63)( 50, 62)( 51, 61)( 52, 60)
( 53, 59)( 54, 58)( 73, 91)( 74, 93)( 75, 92)( 76, 99)( 77, 98)( 78, 97)
( 79, 96)( 80, 95)( 81, 94)( 82,100)( 83,102)( 84,101)( 85,108)( 86,107)
( 87,106)( 88,105)( 89,104)( 90,103)(109,118)(110,120)(111,119)(112,126)
(113,125)(114,124)(115,123)(116,122)(117,121)(127,136)(128,138)(129,137)
(130,144)(131,143)(132,142)(133,141)(134,140)(135,139)(145,181)(146,183)
(147,182)(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)(154,190)
(155,192)(156,191)(157,198)(158,197)(159,196)(160,195)(161,194)(162,193)
(163,199)(164,201)(165,200)(166,207)(167,206)(168,205)(169,204)(170,203)
(171,202)(172,208)(173,210)(174,209)(175,216)(176,215)(177,214)(178,213)
(179,212)(180,211)(217,271)(218,273)(219,272)(220,279)(221,278)(222,277)
(223,276)(224,275)(225,274)(226,280)(227,282)(228,281)(229,288)(230,287)
(231,286)(232,285)(233,284)(234,283)(235,253)(236,255)(237,254)(238,261)
(239,260)(240,259)(241,258)(242,257)(243,256)(244,262)(245,264)(246,263)
(247,270)(248,269)(249,268)(250,267)(251,266)(252,265)(289,361)(290,363)
(291,362)(292,369)(293,368)(294,367)(295,366)(296,365)(297,364)(298,370)
(299,372)(300,371)(301,378)(302,377)(303,376)(304,375)(305,374)(306,373)
(307,379)(308,381)(309,380)(310,387)(311,386)(312,385)(313,384)(314,383)
(315,382)(316,388)(317,390)(318,389)(319,396)(320,395)(321,394)(322,393)
(323,392)(324,391)(325,424)(326,426)(327,425)(328,432)(329,431)(330,430)
(331,429)(332,428)(333,427)(334,415)(335,417)(336,416)(337,423)(338,422)
(339,421)(340,420)(341,419)(342,418)(343,406)(344,408)(345,407)(346,414)
(347,413)(348,412)(349,411)(350,410)(351,409)(352,397)(353,399)(354,398)
(355,405)(356,404)(357,403)(358,402)(359,401)(360,400)(433,550)(434,552)
(435,551)(436,558)(437,557)(438,556)(439,555)(440,554)(441,553)(442,541)
(443,543)(444,542)(445,549)(446,548)(447,547)(448,546)(449,545)(450,544)
(451,568)(452,570)(453,569)(454,576)(455,575)(456,574)(457,573)(458,572)
(459,571)(460,559)(461,561)(462,560)(463,567)(464,566)(465,565)(466,564)
(467,563)(468,562)(469,514)(470,516)(471,515)(472,522)(473,521)(474,520)
(475,519)(476,518)(477,517)(478,505)(479,507)(480,506)(481,513)(482,512)
(483,511)(484,510)(485,509)(486,508)(487,532)(488,534)(489,533)(490,540)
(491,539)(492,538)(493,537)(494,536)(495,535)(496,523)(497,525)(498,524)
(499,531)(500,530)(501,529)(502,528)(503,527)(504,526);;
s2 := ( 1,148)( 2,150)( 3,149)( 4,145)( 5,147)( 6,146)( 7,153)( 8,152)
( 9,151)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,162)
( 17,161)( 18,160)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)
( 25,171)( 26,170)( 27,169)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)
( 33,173)( 34,180)( 35,179)( 36,178)( 37,211)( 38,213)( 39,212)( 40,208)
( 41,210)( 42,209)( 43,216)( 44,215)( 45,214)( 46,202)( 47,204)( 48,203)
( 49,199)( 50,201)( 51,200)( 52,207)( 53,206)( 54,205)( 55,193)( 56,195)
( 57,194)( 58,190)( 59,192)( 60,191)( 61,198)( 62,197)( 63,196)( 64,184)
( 65,186)( 66,185)( 67,181)( 68,183)( 69,182)( 70,189)( 71,188)( 72,187)
( 73,229)( 74,231)( 75,230)( 76,226)( 77,228)( 78,227)( 79,234)( 80,233)
( 81,232)( 82,220)( 83,222)( 84,221)( 85,217)( 86,219)( 87,218)( 88,225)
( 89,224)( 90,223)( 91,247)( 92,249)( 93,248)( 94,244)( 95,246)( 96,245)
( 97,252)( 98,251)( 99,250)(100,238)(101,240)(102,239)(103,235)(104,237)
(105,236)(106,243)(107,242)(108,241)(109,274)(110,276)(111,275)(112,271)
(113,273)(114,272)(115,279)(116,278)(117,277)(118,283)(119,285)(120,284)
(121,280)(122,282)(123,281)(124,288)(125,287)(126,286)(127,256)(128,258)
(129,257)(130,253)(131,255)(132,254)(133,261)(134,260)(135,259)(136,265)
(137,267)(138,266)(139,262)(140,264)(141,263)(142,270)(143,269)(144,268)
(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,441)(296,440)
(297,439)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)(304,450)
(305,449)(306,448)(307,454)(308,456)(309,455)(310,451)(311,453)(312,452)
(313,459)(314,458)(315,457)(316,463)(317,465)(318,464)(319,460)(320,462)
(321,461)(322,468)(323,467)(324,466)(325,499)(326,501)(327,500)(328,496)
(329,498)(330,497)(331,504)(332,503)(333,502)(334,490)(335,492)(336,491)
(337,487)(338,489)(339,488)(340,495)(341,494)(342,493)(343,481)(344,483)
(345,482)(346,478)(347,480)(348,479)(349,486)(350,485)(351,484)(352,472)
(353,474)(354,473)(355,469)(356,471)(357,470)(358,477)(359,476)(360,475)
(361,517)(362,519)(363,518)(364,514)(365,516)(366,515)(367,522)(368,521)
(369,520)(370,508)(371,510)(372,509)(373,505)(374,507)(375,506)(376,513)
(377,512)(378,511)(379,535)(380,537)(381,536)(382,532)(383,534)(384,533)
(385,540)(386,539)(387,538)(388,526)(389,528)(390,527)(391,523)(392,525)
(393,524)(394,531)(395,530)(396,529)(397,562)(398,564)(399,563)(400,559)
(401,561)(402,560)(403,567)(404,566)(405,565)(406,571)(407,573)(408,572)
(409,568)(410,570)(411,569)(412,576)(413,575)(414,574)(415,544)(416,546)
(417,545)(418,541)(419,543)(420,542)(421,549)(422,548)(423,547)(424,553)
(425,555)(426,554)(427,550)(428,552)(429,551)(430,558)(431,557)(432,556);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*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*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*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)
( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)
( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)
( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)
( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 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)(109,424)(110,425)(111,426)
(112,427)(113,428)(114,429)(115,430)(116,431)(117,432)(118,415)(119,416)
(120,417)(121,418)(122,419)(123,420)(124,421)(125,422)(126,423)(127,406)
(128,407)(129,408)(130,409)(131,410)(132,411)(133,412)(134,413)(135,414)
(136,397)(137,398)(138,399)(139,400)(140,401)(141,402)(142,403)(143,404)
(144,405)(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)(163,451)(164,452)(165,453)(166,454)(167,455)
(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)
(176,464)(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)
(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)
(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(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)(253,568)(254,569)(255,570)
(256,571)(257,572)(258,573)(259,574)(260,575)(261,576)(262,559)(263,560)
(264,561)(265,562)(266,563)(267,564)(268,565)(269,566)(270,567)(271,550)
(272,551)(273,552)(274,553)(275,554)(276,555)(277,556)(278,557)(279,558)
(280,541)(281,542)(282,543)(283,544)(284,545)(285,546)(286,547)(287,548)
(288,549);
s1 := Sym(576)!( 2, 3)( 4, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)
( 15, 16)( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 29, 30)( 31, 36)( 32, 35)
( 33, 34)( 37, 64)( 38, 66)( 39, 65)( 40, 72)( 41, 71)( 42, 70)( 43, 69)
( 44, 68)( 45, 67)( 46, 55)( 47, 57)( 48, 56)( 49, 63)( 50, 62)( 51, 61)
( 52, 60)( 53, 59)( 54, 58)( 73, 91)( 74, 93)( 75, 92)( 76, 99)( 77, 98)
( 78, 97)( 79, 96)( 80, 95)( 81, 94)( 82,100)( 83,102)( 84,101)( 85,108)
( 86,107)( 87,106)( 88,105)( 89,104)( 90,103)(109,118)(110,120)(111,119)
(112,126)(113,125)(114,124)(115,123)(116,122)(117,121)(127,136)(128,138)
(129,137)(130,144)(131,143)(132,142)(133,141)(134,140)(135,139)(145,181)
(146,183)(147,182)(148,189)(149,188)(150,187)(151,186)(152,185)(153,184)
(154,190)(155,192)(156,191)(157,198)(158,197)(159,196)(160,195)(161,194)
(162,193)(163,199)(164,201)(165,200)(166,207)(167,206)(168,205)(169,204)
(170,203)(171,202)(172,208)(173,210)(174,209)(175,216)(176,215)(177,214)
(178,213)(179,212)(180,211)(217,271)(218,273)(219,272)(220,279)(221,278)
(222,277)(223,276)(224,275)(225,274)(226,280)(227,282)(228,281)(229,288)
(230,287)(231,286)(232,285)(233,284)(234,283)(235,253)(236,255)(237,254)
(238,261)(239,260)(240,259)(241,258)(242,257)(243,256)(244,262)(245,264)
(246,263)(247,270)(248,269)(249,268)(250,267)(251,266)(252,265)(289,361)
(290,363)(291,362)(292,369)(293,368)(294,367)(295,366)(296,365)(297,364)
(298,370)(299,372)(300,371)(301,378)(302,377)(303,376)(304,375)(305,374)
(306,373)(307,379)(308,381)(309,380)(310,387)(311,386)(312,385)(313,384)
(314,383)(315,382)(316,388)(317,390)(318,389)(319,396)(320,395)(321,394)
(322,393)(323,392)(324,391)(325,424)(326,426)(327,425)(328,432)(329,431)
(330,430)(331,429)(332,428)(333,427)(334,415)(335,417)(336,416)(337,423)
(338,422)(339,421)(340,420)(341,419)(342,418)(343,406)(344,408)(345,407)
(346,414)(347,413)(348,412)(349,411)(350,410)(351,409)(352,397)(353,399)
(354,398)(355,405)(356,404)(357,403)(358,402)(359,401)(360,400)(433,550)
(434,552)(435,551)(436,558)(437,557)(438,556)(439,555)(440,554)(441,553)
(442,541)(443,543)(444,542)(445,549)(446,548)(447,547)(448,546)(449,545)
(450,544)(451,568)(452,570)(453,569)(454,576)(455,575)(456,574)(457,573)
(458,572)(459,571)(460,559)(461,561)(462,560)(463,567)(464,566)(465,565)
(466,564)(467,563)(468,562)(469,514)(470,516)(471,515)(472,522)(473,521)
(474,520)(475,519)(476,518)(477,517)(478,505)(479,507)(480,506)(481,513)
(482,512)(483,511)(484,510)(485,509)(486,508)(487,532)(488,534)(489,533)
(490,540)(491,539)(492,538)(493,537)(494,536)(495,535)(496,523)(497,525)
(498,524)(499,531)(500,530)(501,529)(502,528)(503,527)(504,526);
s2 := Sym(576)!( 1,148)( 2,150)( 3,149)( 4,145)( 5,147)( 6,146)( 7,153)
( 8,152)( 9,151)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)
( 16,162)( 17,161)( 18,160)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)
( 24,164)( 25,171)( 26,170)( 27,169)( 28,175)( 29,177)( 30,176)( 31,172)
( 32,174)( 33,173)( 34,180)( 35,179)( 36,178)( 37,211)( 38,213)( 39,212)
( 40,208)( 41,210)( 42,209)( 43,216)( 44,215)( 45,214)( 46,202)( 47,204)
( 48,203)( 49,199)( 50,201)( 51,200)( 52,207)( 53,206)( 54,205)( 55,193)
( 56,195)( 57,194)( 58,190)( 59,192)( 60,191)( 61,198)( 62,197)( 63,196)
( 64,184)( 65,186)( 66,185)( 67,181)( 68,183)( 69,182)( 70,189)( 71,188)
( 72,187)( 73,229)( 74,231)( 75,230)( 76,226)( 77,228)( 78,227)( 79,234)
( 80,233)( 81,232)( 82,220)( 83,222)( 84,221)( 85,217)( 86,219)( 87,218)
( 88,225)( 89,224)( 90,223)( 91,247)( 92,249)( 93,248)( 94,244)( 95,246)
( 96,245)( 97,252)( 98,251)( 99,250)(100,238)(101,240)(102,239)(103,235)
(104,237)(105,236)(106,243)(107,242)(108,241)(109,274)(110,276)(111,275)
(112,271)(113,273)(114,272)(115,279)(116,278)(117,277)(118,283)(119,285)
(120,284)(121,280)(122,282)(123,281)(124,288)(125,287)(126,286)(127,256)
(128,258)(129,257)(130,253)(131,255)(132,254)(133,261)(134,260)(135,259)
(136,265)(137,267)(138,266)(139,262)(140,264)(141,263)(142,270)(143,269)
(144,268)(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,441)
(296,440)(297,439)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)
(304,450)(305,449)(306,448)(307,454)(308,456)(309,455)(310,451)(311,453)
(312,452)(313,459)(314,458)(315,457)(316,463)(317,465)(318,464)(319,460)
(320,462)(321,461)(322,468)(323,467)(324,466)(325,499)(326,501)(327,500)
(328,496)(329,498)(330,497)(331,504)(332,503)(333,502)(334,490)(335,492)
(336,491)(337,487)(338,489)(339,488)(340,495)(341,494)(342,493)(343,481)
(344,483)(345,482)(346,478)(347,480)(348,479)(349,486)(350,485)(351,484)
(352,472)(353,474)(354,473)(355,469)(356,471)(357,470)(358,477)(359,476)
(360,475)(361,517)(362,519)(363,518)(364,514)(365,516)(366,515)(367,522)
(368,521)(369,520)(370,508)(371,510)(372,509)(373,505)(374,507)(375,506)
(376,513)(377,512)(378,511)(379,535)(380,537)(381,536)(382,532)(383,534)
(384,533)(385,540)(386,539)(387,538)(388,526)(389,528)(390,527)(391,523)
(392,525)(393,524)(394,531)(395,530)(396,529)(397,562)(398,564)(399,563)
(400,559)(401,561)(402,560)(403,567)(404,566)(405,565)(406,571)(407,573)
(408,572)(409,568)(410,570)(411,569)(412,576)(413,575)(414,574)(415,544)
(416,546)(417,545)(418,541)(419,543)(420,542)(421,549)(422,548)(423,547)
(424,553)(425,555)(426,554)(427,550)(428,552)(429,551)(430,558)(431,557)
(432,556);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*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*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*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;
References : None.
to this polytope