Polytope of Type {72,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {72,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,11999)
Rank : 3
Schlafli Type : {72,4}
Number of vertices, edges, etc : 144, 288, 8
Order of s0s1s2 : 72
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {72,4}*576a, {36,4}*576a, {72,4}*576b
3-fold quotients : {24,4}*384a
4-fold quotients : {36,4}*288a, {72,2}*288
6-fold quotients : {24,4}*192a, {12,4}*192a, {24,4}*192b
8-fold quotients : {36,2}*144, {18,4}*144a
9-fold quotients : {8,4}*128a
12-fold quotients : {12,4}*96a, {24,2}*96
16-fold quotients : {18,2}*72
18-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
24-fold quotients : {12,2}*48, {6,4}*48a
32-fold quotients : {9,2}*36
36-fold quotients : {4,4}*32, {8,2}*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 := ( 1,289)( 2,291)( 3,290)( 4,297)( 5,296)( 6,295)( 7,294)( 8,293)
( 9,292)( 10,298)( 11,300)( 12,299)( 13,306)( 14,305)( 15,304)( 16,303)
( 17,302)( 18,301)( 19,307)( 20,309)( 21,308)( 22,315)( 23,314)( 24,313)
( 25,312)( 26,311)( 27,310)( 28,316)( 29,318)( 30,317)( 31,324)( 32,323)
( 33,322)( 34,321)( 35,320)( 36,319)( 37,334)( 38,336)( 39,335)( 40,342)
( 41,341)( 42,340)( 43,339)( 44,338)( 45,337)( 46,325)( 47,327)( 48,326)
( 49,333)( 50,332)( 51,331)( 52,330)( 53,329)( 54,328)( 55,352)( 56,354)
( 57,353)( 58,360)( 59,359)( 60,358)( 61,357)( 62,356)( 63,355)( 64,343)
( 65,345)( 66,344)( 67,351)( 68,350)( 69,349)( 70,348)( 71,347)( 72,346)
( 73,379)( 74,381)( 75,380)( 76,387)( 77,386)( 78,385)( 79,384)( 80,383)
( 81,382)( 82,388)( 83,390)( 84,389)( 85,396)( 86,395)( 87,394)( 88,393)
( 89,392)( 90,391)( 91,361)( 92,363)( 93,362)( 94,369)( 95,368)( 96,367)
( 97,366)( 98,365)( 99,364)(100,370)(101,372)(102,371)(103,378)(104,377)
(105,376)(106,375)(107,374)(108,373)(109,424)(110,426)(111,425)(112,432)
(113,431)(114,430)(115,429)(116,428)(117,427)(118,415)(119,417)(120,416)
(121,423)(122,422)(123,421)(124,420)(125,419)(126,418)(127,406)(128,408)
(129,407)(130,414)(131,413)(132,412)(133,411)(134,410)(135,409)(136,397)
(137,399)(138,398)(139,405)(140,404)(141,403)(142,402)(143,401)(144,400)
(145,433)(146,435)(147,434)(148,441)(149,440)(150,439)(151,438)(152,437)
(153,436)(154,442)(155,444)(156,443)(157,450)(158,449)(159,448)(160,447)
(161,446)(162,445)(163,451)(164,453)(165,452)(166,459)(167,458)(168,457)
(169,456)(170,455)(171,454)(172,460)(173,462)(174,461)(175,468)(176,467)
(177,466)(178,465)(179,464)(180,463)(181,478)(182,480)(183,479)(184,486)
(185,485)(186,484)(187,483)(188,482)(189,481)(190,469)(191,471)(192,470)
(193,477)(194,476)(195,475)(196,474)(197,473)(198,472)(199,496)(200,498)
(201,497)(202,504)(203,503)(204,502)(205,501)(206,500)(207,499)(208,487)
(209,489)(210,488)(211,495)(212,494)(213,493)(214,492)(215,491)(216,490)
(217,523)(218,525)(219,524)(220,531)(221,530)(222,529)(223,528)(224,527)
(225,526)(226,532)(227,534)(228,533)(229,540)(230,539)(231,538)(232,537)
(233,536)(234,535)(235,505)(236,507)(237,506)(238,513)(239,512)(240,511)
(241,510)(242,509)(243,508)(244,514)(245,516)(246,515)(247,522)(248,521)
(249,520)(250,519)(251,518)(252,517)(253,568)(254,570)(255,569)(256,576)
(257,575)(258,574)(259,573)(260,572)(261,571)(262,559)(263,561)(264,560)
(265,567)(266,566)(267,565)(268,564)(269,563)(270,562)(271,550)(272,552)
(273,551)(274,558)(275,557)(276,556)(277,555)(278,554)(279,553)(280,541)
(281,543)(282,542)(283,549)(284,548)(285,547)(286,546)(287,545)(288,544);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)
( 19, 22)( 20, 24)( 21, 23)( 25, 27)( 28, 31)( 29, 33)( 30, 32)( 34, 36)
( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)( 48, 50)( 52, 54)
( 55, 58)( 56, 60)( 57, 59)( 61, 63)( 64, 67)( 65, 69)( 66, 68)( 70, 72)
( 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)(163,202)(164,204)
(165,203)(166,199)(167,201)(168,200)(169,207)(170,206)(171,205)(172,211)
(173,213)(174,212)(175,208)(176,210)(177,209)(178,216)(179,215)(180,214)
(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)(307,382)(308,384)
(309,383)(310,379)(311,381)(312,380)(313,387)(314,386)(315,385)(316,391)
(317,393)(318,392)(319,388)(320,390)(321,389)(322,396)(323,395)(324,394)
(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)(343,418)(344,420)(345,419)(346,415)(347,417)(348,416)
(349,423)(350,422)(351,421)(352,427)(353,429)(354,428)(355,424)(356,426)
(357,425)(358,432)(359,431)(360,430)(433,553)(434,555)(435,554)(436,550)
(437,552)(438,551)(439,558)(440,557)(441,556)(442,544)(443,546)(444,545)
(445,541)(446,543)(447,542)(448,549)(449,548)(450,547)(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)
(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,522)(476,521)
(477,520)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,513)
(485,512)(486,511)(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 := ( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)( 8,152)
( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,226)( 74,227)( 75,228)( 76,229)( 77,230)( 78,231)( 79,232)( 80,233)
( 81,234)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)( 88,223)
( 89,224)( 90,225)( 91,244)( 92,245)( 93,246)( 94,247)( 95,248)( 96,249)
( 97,250)( 98,251)( 99,252)(100,235)(101,236)(102,237)(103,238)(104,239)
(105,240)(106,241)(107,242)(108,243)(109,262)(110,263)(111,264)(112,265)
(113,266)(114,267)(115,268)(116,269)(117,270)(118,253)(119,254)(120,255)
(121,256)(122,257)(123,258)(124,259)(125,260)(126,261)(127,280)(128,281)
(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)(136,271)
(137,272)(138,273)(139,274)(140,275)(141,276)(142,277)(143,278)(144,279)
(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)
(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)
(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)
(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)
(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)(328,472)
(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)
(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)(344,488)
(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)(352,496)
(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)(360,504)
(361,514)(362,515)(363,516)(364,517)(365,518)(366,519)(367,520)(368,521)
(369,522)(370,505)(371,506)(372,507)(373,508)(374,509)(375,510)(376,511)
(377,512)(378,513)(379,532)(380,533)(381,534)(382,535)(383,536)(384,537)
(385,538)(386,539)(387,540)(388,523)(389,524)(390,525)(391,526)(392,527)
(393,528)(394,529)(395,530)(396,531)(397,550)(398,551)(399,552)(400,553)
(401,554)(402,555)(403,556)(404,557)(405,558)(406,541)(407,542)(408,543)
(409,544)(410,545)(411,546)(412,547)(413,548)(414,549)(415,568)(416,569)
(417,570)(418,571)(419,572)(420,573)(421,574)(422,575)(423,576)(424,559)
(425,560)(426,561)(427,562)(428,563)(429,564)(430,565)(431,566)(432,567);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,289)( 2,291)( 3,290)( 4,297)( 5,296)( 6,295)( 7,294)
( 8,293)( 9,292)( 10,298)( 11,300)( 12,299)( 13,306)( 14,305)( 15,304)
( 16,303)( 17,302)( 18,301)( 19,307)( 20,309)( 21,308)( 22,315)( 23,314)
( 24,313)( 25,312)( 26,311)( 27,310)( 28,316)( 29,318)( 30,317)( 31,324)
( 32,323)( 33,322)( 34,321)( 35,320)( 36,319)( 37,334)( 38,336)( 39,335)
( 40,342)( 41,341)( 42,340)( 43,339)( 44,338)( 45,337)( 46,325)( 47,327)
( 48,326)( 49,333)( 50,332)( 51,331)( 52,330)( 53,329)( 54,328)( 55,352)
( 56,354)( 57,353)( 58,360)( 59,359)( 60,358)( 61,357)( 62,356)( 63,355)
( 64,343)( 65,345)( 66,344)( 67,351)( 68,350)( 69,349)( 70,348)( 71,347)
( 72,346)( 73,379)( 74,381)( 75,380)( 76,387)( 77,386)( 78,385)( 79,384)
( 80,383)( 81,382)( 82,388)( 83,390)( 84,389)( 85,396)( 86,395)( 87,394)
( 88,393)( 89,392)( 90,391)( 91,361)( 92,363)( 93,362)( 94,369)( 95,368)
( 96,367)( 97,366)( 98,365)( 99,364)(100,370)(101,372)(102,371)(103,378)
(104,377)(105,376)(106,375)(107,374)(108,373)(109,424)(110,426)(111,425)
(112,432)(113,431)(114,430)(115,429)(116,428)(117,427)(118,415)(119,417)
(120,416)(121,423)(122,422)(123,421)(124,420)(125,419)(126,418)(127,406)
(128,408)(129,407)(130,414)(131,413)(132,412)(133,411)(134,410)(135,409)
(136,397)(137,399)(138,398)(139,405)(140,404)(141,403)(142,402)(143,401)
(144,400)(145,433)(146,435)(147,434)(148,441)(149,440)(150,439)(151,438)
(152,437)(153,436)(154,442)(155,444)(156,443)(157,450)(158,449)(159,448)
(160,447)(161,446)(162,445)(163,451)(164,453)(165,452)(166,459)(167,458)
(168,457)(169,456)(170,455)(171,454)(172,460)(173,462)(174,461)(175,468)
(176,467)(177,466)(178,465)(179,464)(180,463)(181,478)(182,480)(183,479)
(184,486)(185,485)(186,484)(187,483)(188,482)(189,481)(190,469)(191,471)
(192,470)(193,477)(194,476)(195,475)(196,474)(197,473)(198,472)(199,496)
(200,498)(201,497)(202,504)(203,503)(204,502)(205,501)(206,500)(207,499)
(208,487)(209,489)(210,488)(211,495)(212,494)(213,493)(214,492)(215,491)
(216,490)(217,523)(218,525)(219,524)(220,531)(221,530)(222,529)(223,528)
(224,527)(225,526)(226,532)(227,534)(228,533)(229,540)(230,539)(231,538)
(232,537)(233,536)(234,535)(235,505)(236,507)(237,506)(238,513)(239,512)
(240,511)(241,510)(242,509)(243,508)(244,514)(245,516)(246,515)(247,522)
(248,521)(249,520)(250,519)(251,518)(252,517)(253,568)(254,570)(255,569)
(256,576)(257,575)(258,574)(259,573)(260,572)(261,571)(262,559)(263,561)
(264,560)(265,567)(266,566)(267,565)(268,564)(269,563)(270,562)(271,550)
(272,552)(273,551)(274,558)(275,557)(276,556)(277,555)(278,554)(279,553)
(280,541)(281,543)(282,542)(283,549)(284,548)(285,547)(286,546)(287,545)
(288,544);
s1 := Sym(576)!( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 13)( 11, 15)( 12, 14)
( 16, 18)( 19, 22)( 20, 24)( 21, 23)( 25, 27)( 28, 31)( 29, 33)( 30, 32)
( 34, 36)( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)( 48, 50)
( 52, 54)( 55, 58)( 56, 60)( 57, 59)( 61, 63)( 64, 67)( 65, 69)( 66, 68)
( 70, 72)( 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)(163,202)
(164,204)(165,203)(166,199)(167,201)(168,200)(169,207)(170,206)(171,205)
(172,211)(173,213)(174,212)(175,208)(176,210)(177,209)(178,216)(179,215)
(180,214)(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)(307,382)
(308,384)(309,383)(310,379)(311,381)(312,380)(313,387)(314,386)(315,385)
(316,391)(317,393)(318,392)(319,388)(320,390)(321,389)(322,396)(323,395)
(324,394)(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)(343,418)(344,420)(345,419)(346,415)(347,417)
(348,416)(349,423)(350,422)(351,421)(352,427)(353,429)(354,428)(355,424)
(356,426)(357,425)(358,432)(359,431)(360,430)(433,553)(434,555)(435,554)
(436,550)(437,552)(438,551)(439,558)(440,557)(441,556)(442,544)(443,546)
(444,545)(445,541)(446,543)(447,542)(448,549)(449,548)(450,547)(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)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,522)
(476,521)(477,520)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)
(484,513)(485,512)(486,511)(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)!( 1,145)( 2,146)( 3,147)( 4,148)( 5,149)( 6,150)( 7,151)
( 8,152)( 9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,226)( 74,227)( 75,228)( 76,229)( 77,230)( 78,231)( 79,232)
( 80,233)( 81,234)( 82,217)( 83,218)( 84,219)( 85,220)( 86,221)( 87,222)
( 88,223)( 89,224)( 90,225)( 91,244)( 92,245)( 93,246)( 94,247)( 95,248)
( 96,249)( 97,250)( 98,251)( 99,252)(100,235)(101,236)(102,237)(103,238)
(104,239)(105,240)(106,241)(107,242)(108,243)(109,262)(110,263)(111,264)
(112,265)(113,266)(114,267)(115,268)(116,269)(117,270)(118,253)(119,254)
(120,255)(121,256)(122,257)(123,258)(124,259)(125,260)(126,261)(127,280)
(128,281)(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)
(136,271)(137,272)(138,273)(139,274)(140,275)(141,276)(142,277)(143,278)
(144,279)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)
(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)
(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)
(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)
(320,464)(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)
(328,472)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)
(336,480)(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)
(344,488)(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)
(352,496)(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)
(360,504)(361,514)(362,515)(363,516)(364,517)(365,518)(366,519)(367,520)
(368,521)(369,522)(370,505)(371,506)(372,507)(373,508)(374,509)(375,510)
(376,511)(377,512)(378,513)(379,532)(380,533)(381,534)(382,535)(383,536)
(384,537)(385,538)(386,539)(387,540)(388,523)(389,524)(390,525)(391,526)
(392,527)(393,528)(394,529)(395,530)(396,531)(397,550)(398,551)(399,552)
(400,553)(401,554)(402,555)(403,556)(404,557)(405,558)(406,541)(407,542)
(408,543)(409,544)(410,545)(411,546)(412,547)(413,548)(414,549)(415,568)
(416,569)(417,570)(418,571)(419,572)(420,573)(421,574)(422,575)(423,576)
(424,559)(425,560)(426,561)(427,562)(428,563)(429,564)(430,565)(431,566)
(432,567);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*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*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*s0*s1*s0*s1 >;
References : None.
to this polytope