Polytope of Type {4,152}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,152}*1216b
if this polytope has a name.
Group : SmallGroup(1216,719)
Rank : 3
Schlafli Type : {4,152}
Number of vertices, edges, etc : 4, 304, 152
Order of s0s1s2 : 152
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 : {4,76}*608
4-fold quotients : {2,76}*304, {4,38}*304
8-fold quotients : {2,38}*152
16-fold quotients : {2,19}*76
19-fold quotients : {4,8}*64b
38-fold quotients : {4,4}*32
76-fold quotients : {2,4}*16, {4,2}*16
152-fold quotients : {2,2}*8
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)
( 9,161)( 10,162)( 11,163)( 12,164)( 13,165)( 14,166)( 15,167)( 16,168)
( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)( 24,176)
( 25,177)( 26,178)( 27,179)( 28,180)( 29,181)( 30,182)( 31,183)( 32,184)
( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)( 40,192)
( 41,193)( 42,194)( 43,195)( 44,196)( 45,197)( 46,198)( 47,199)( 48,200)
( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)( 56,208)
( 57,209)( 58,210)( 59,211)( 60,212)( 61,213)( 62,214)( 63,215)( 64,216)
( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)( 72,224)
( 73,225)( 74,226)( 75,227)( 76,228)( 77,248)( 78,249)( 79,250)( 80,251)
( 81,252)( 82,253)( 83,254)( 84,255)( 85,256)( 86,257)( 87,258)( 88,259)
( 89,260)( 90,261)( 91,262)( 92,263)( 93,264)( 94,265)( 95,266)( 96,229)
( 97,230)( 98,231)( 99,232)(100,233)(101,234)(102,235)(103,236)(104,237)
(105,238)(106,239)(107,240)(108,241)(109,242)(110,243)(111,244)(112,245)
(113,246)(114,247)(115,286)(116,287)(117,288)(118,289)(119,290)(120,291)
(121,292)(122,293)(123,294)(124,295)(125,296)(126,297)(127,298)(128,299)
(129,300)(130,301)(131,302)(132,303)(133,304)(134,267)(135,268)(136,269)
(137,270)(138,271)(139,272)(140,273)(141,274)(142,275)(143,276)(144,277)
(145,278)(146,279)(147,280)(148,281)(149,282)(150,283)(151,284)(152,285)
(305,457)(306,458)(307,459)(308,460)(309,461)(310,462)(311,463)(312,464)
(313,465)(314,466)(315,467)(316,468)(317,469)(318,470)(319,471)(320,472)
(321,473)(322,474)(323,475)(324,476)(325,477)(326,478)(327,479)(328,480)
(329,481)(330,482)(331,483)(332,484)(333,485)(334,486)(335,487)(336,488)
(337,489)(338,490)(339,491)(340,492)(341,493)(342,494)(343,495)(344,496)
(345,497)(346,498)(347,499)(348,500)(349,501)(350,502)(351,503)(352,504)
(353,505)(354,506)(355,507)(356,508)(357,509)(358,510)(359,511)(360,512)
(361,513)(362,514)(363,515)(364,516)(365,517)(366,518)(367,519)(368,520)
(369,521)(370,522)(371,523)(372,524)(373,525)(374,526)(375,527)(376,528)
(377,529)(378,530)(379,531)(380,532)(381,552)(382,553)(383,554)(384,555)
(385,556)(386,557)(387,558)(388,559)(389,560)(390,561)(391,562)(392,563)
(393,564)(394,565)(395,566)(396,567)(397,568)(398,569)(399,570)(400,533)
(401,534)(402,535)(403,536)(404,537)(405,538)(406,539)(407,540)(408,541)
(409,542)(410,543)(411,544)(412,545)(413,546)(414,547)(415,548)(416,549)
(417,550)(418,551)(419,590)(420,591)(421,592)(422,593)(423,594)(424,595)
(425,596)(426,597)(427,598)(428,599)(429,600)(430,601)(431,602)(432,603)
(433,604)(434,605)(435,606)(436,607)(437,608)(438,571)(439,572)(440,573)
(441,574)(442,575)(443,576)(444,577)(445,578)(446,579)(447,580)(448,581)
(449,582)(450,583)(451,584)(452,585)(453,586)(454,587)(455,588)(456,589);;
s1 := ( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)
( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)( 80,112)
( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)( 88,104)
( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)(115,134)
(116,152)(117,151)(118,150)(119,149)(120,148)(121,147)(122,146)(123,145)
(124,144)(125,143)(126,142)(127,141)(128,140)(129,139)(130,138)(131,137)
(132,136)(133,135)(153,191)(154,209)(155,208)(156,207)(157,206)(158,205)
(159,204)(160,203)(161,202)(162,201)(163,200)(164,199)(165,198)(166,197)
(167,196)(168,195)(169,194)(170,193)(171,192)(172,210)(173,228)(174,227)
(175,226)(176,225)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)
(183,218)(184,217)(185,216)(186,215)(187,214)(188,213)(189,212)(190,211)
(229,286)(230,304)(231,303)(232,302)(233,301)(234,300)(235,299)(236,298)
(237,297)(238,296)(239,295)(240,294)(241,293)(242,292)(243,291)(244,290)
(245,289)(246,288)(247,287)(248,267)(249,285)(250,284)(251,283)(252,282)
(253,281)(254,280)(255,279)(256,278)(257,277)(258,276)(259,275)(260,274)
(261,273)(262,272)(263,271)(264,270)(265,269)(266,268)(305,381)(306,399)
(307,398)(308,397)(309,396)(310,395)(311,394)(312,393)(313,392)(314,391)
(315,390)(316,389)(317,388)(318,387)(319,386)(320,385)(321,384)(322,383)
(323,382)(324,400)(325,418)(326,417)(327,416)(328,415)(329,414)(330,413)
(331,412)(332,411)(333,410)(334,409)(335,408)(336,407)(337,406)(338,405)
(339,404)(340,403)(341,402)(342,401)(343,419)(344,437)(345,436)(346,435)
(347,434)(348,433)(349,432)(350,431)(351,430)(352,429)(353,428)(354,427)
(355,426)(356,425)(357,424)(358,423)(359,422)(360,421)(361,420)(362,438)
(363,456)(364,455)(365,454)(366,453)(367,452)(368,451)(369,450)(370,449)
(371,448)(372,447)(373,446)(374,445)(375,444)(376,443)(377,442)(378,441)
(379,440)(380,439)(457,590)(458,608)(459,607)(460,606)(461,605)(462,604)
(463,603)(464,602)(465,601)(466,600)(467,599)(468,598)(469,597)(470,596)
(471,595)(472,594)(473,593)(474,592)(475,591)(476,571)(477,589)(478,588)
(479,587)(480,586)(481,585)(482,584)(483,583)(484,582)(485,581)(486,580)
(487,579)(488,578)(489,577)(490,576)(491,575)(492,574)(493,573)(494,572)
(495,552)(496,570)(497,569)(498,568)(499,567)(500,566)(501,565)(502,564)
(503,563)(504,562)(505,561)(506,560)(507,559)(508,558)(509,557)(510,556)
(511,555)(512,554)(513,553)(514,533)(515,551)(516,550)(517,549)(518,548)
(519,547)(520,546)(521,545)(522,544)(523,543)(524,542)(525,541)(526,540)
(527,539)(528,538)(529,537)(530,536)(531,535)(532,534);;
s2 := ( 1,306)( 2,305)( 3,323)( 4,322)( 5,321)( 6,320)( 7,319)( 8,318)
( 9,317)( 10,316)( 11,315)( 12,314)( 13,313)( 14,312)( 15,311)( 16,310)
( 17,309)( 18,308)( 19,307)( 20,325)( 21,324)( 22,342)( 23,341)( 24,340)
( 25,339)( 26,338)( 27,337)( 28,336)( 29,335)( 30,334)( 31,333)( 32,332)
( 33,331)( 34,330)( 35,329)( 36,328)( 37,327)( 38,326)( 39,363)( 40,362)
( 41,380)( 42,379)( 43,378)( 44,377)( 45,376)( 46,375)( 47,374)( 48,373)
( 49,372)( 50,371)( 51,370)( 52,369)( 53,368)( 54,367)( 55,366)( 56,365)
( 57,364)( 58,344)( 59,343)( 60,361)( 61,360)( 62,359)( 63,358)( 64,357)
( 65,356)( 66,355)( 67,354)( 68,353)( 69,352)( 70,351)( 71,350)( 72,349)
( 73,348)( 74,347)( 75,346)( 76,345)( 77,401)( 78,400)( 79,418)( 80,417)
( 81,416)( 82,415)( 83,414)( 84,413)( 85,412)( 86,411)( 87,410)( 88,409)
( 89,408)( 90,407)( 91,406)( 92,405)( 93,404)( 94,403)( 95,402)( 96,382)
( 97,381)( 98,399)( 99,398)(100,397)(101,396)(102,395)(103,394)(104,393)
(105,392)(106,391)(107,390)(108,389)(109,388)(110,387)(111,386)(112,385)
(113,384)(114,383)(115,420)(116,419)(117,437)(118,436)(119,435)(120,434)
(121,433)(122,432)(123,431)(124,430)(125,429)(126,428)(127,427)(128,426)
(129,425)(130,424)(131,423)(132,422)(133,421)(134,439)(135,438)(136,456)
(137,455)(138,454)(139,453)(140,452)(141,451)(142,450)(143,449)(144,448)
(145,447)(146,446)(147,445)(148,444)(149,443)(150,442)(151,441)(152,440)
(153,458)(154,457)(155,475)(156,474)(157,473)(158,472)(159,471)(160,470)
(161,469)(162,468)(163,467)(164,466)(165,465)(166,464)(167,463)(168,462)
(169,461)(170,460)(171,459)(172,477)(173,476)(174,494)(175,493)(176,492)
(177,491)(178,490)(179,489)(180,488)(181,487)(182,486)(183,485)(184,484)
(185,483)(186,482)(187,481)(188,480)(189,479)(190,478)(191,515)(192,514)
(193,532)(194,531)(195,530)(196,529)(197,528)(198,527)(199,526)(200,525)
(201,524)(202,523)(203,522)(204,521)(205,520)(206,519)(207,518)(208,517)
(209,516)(210,496)(211,495)(212,513)(213,512)(214,511)(215,510)(216,509)
(217,508)(218,507)(219,506)(220,505)(221,504)(222,503)(223,502)(224,501)
(225,500)(226,499)(227,498)(228,497)(229,553)(230,552)(231,570)(232,569)
(233,568)(234,567)(235,566)(236,565)(237,564)(238,563)(239,562)(240,561)
(241,560)(242,559)(243,558)(244,557)(245,556)(246,555)(247,554)(248,534)
(249,533)(250,551)(251,550)(252,549)(253,548)(254,547)(255,546)(256,545)
(257,544)(258,543)(259,542)(260,541)(261,540)(262,539)(263,538)(264,537)
(265,536)(266,535)(267,572)(268,571)(269,589)(270,588)(271,587)(272,586)
(273,585)(274,584)(275,583)(276,582)(277,581)(278,580)(279,579)(280,578)
(281,577)(282,576)(283,575)(284,574)(285,573)(286,591)(287,590)(288,608)
(289,607)(290,606)(291,605)(292,604)(293,603)(294,602)(295,601)(296,600)
(297,599)(298,598)(299,597)(300,596)(301,595)(302,594)(303,593)(304,592);;
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,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*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*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(608)!( 1,153)( 2,154)( 3,155)( 4,156)( 5,157)( 6,158)( 7,159)
( 8,160)( 9,161)( 10,162)( 11,163)( 12,164)( 13,165)( 14,166)( 15,167)
( 16,168)( 17,169)( 18,170)( 19,171)( 20,172)( 21,173)( 22,174)( 23,175)
( 24,176)( 25,177)( 26,178)( 27,179)( 28,180)( 29,181)( 30,182)( 31,183)
( 32,184)( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)
( 40,192)( 41,193)( 42,194)( 43,195)( 44,196)( 45,197)( 46,198)( 47,199)
( 48,200)( 49,201)( 50,202)( 51,203)( 52,204)( 53,205)( 54,206)( 55,207)
( 56,208)( 57,209)( 58,210)( 59,211)( 60,212)( 61,213)( 62,214)( 63,215)
( 64,216)( 65,217)( 66,218)( 67,219)( 68,220)( 69,221)( 70,222)( 71,223)
( 72,224)( 73,225)( 74,226)( 75,227)( 76,228)( 77,248)( 78,249)( 79,250)
( 80,251)( 81,252)( 82,253)( 83,254)( 84,255)( 85,256)( 86,257)( 87,258)
( 88,259)( 89,260)( 90,261)( 91,262)( 92,263)( 93,264)( 94,265)( 95,266)
( 96,229)( 97,230)( 98,231)( 99,232)(100,233)(101,234)(102,235)(103,236)
(104,237)(105,238)(106,239)(107,240)(108,241)(109,242)(110,243)(111,244)
(112,245)(113,246)(114,247)(115,286)(116,287)(117,288)(118,289)(119,290)
(120,291)(121,292)(122,293)(123,294)(124,295)(125,296)(126,297)(127,298)
(128,299)(129,300)(130,301)(131,302)(132,303)(133,304)(134,267)(135,268)
(136,269)(137,270)(138,271)(139,272)(140,273)(141,274)(142,275)(143,276)
(144,277)(145,278)(146,279)(147,280)(148,281)(149,282)(150,283)(151,284)
(152,285)(305,457)(306,458)(307,459)(308,460)(309,461)(310,462)(311,463)
(312,464)(313,465)(314,466)(315,467)(316,468)(317,469)(318,470)(319,471)
(320,472)(321,473)(322,474)(323,475)(324,476)(325,477)(326,478)(327,479)
(328,480)(329,481)(330,482)(331,483)(332,484)(333,485)(334,486)(335,487)
(336,488)(337,489)(338,490)(339,491)(340,492)(341,493)(342,494)(343,495)
(344,496)(345,497)(346,498)(347,499)(348,500)(349,501)(350,502)(351,503)
(352,504)(353,505)(354,506)(355,507)(356,508)(357,509)(358,510)(359,511)
(360,512)(361,513)(362,514)(363,515)(364,516)(365,517)(366,518)(367,519)
(368,520)(369,521)(370,522)(371,523)(372,524)(373,525)(374,526)(375,527)
(376,528)(377,529)(378,530)(379,531)(380,532)(381,552)(382,553)(383,554)
(384,555)(385,556)(386,557)(387,558)(388,559)(389,560)(390,561)(391,562)
(392,563)(393,564)(394,565)(395,566)(396,567)(397,568)(398,569)(399,570)
(400,533)(401,534)(402,535)(403,536)(404,537)(405,538)(406,539)(407,540)
(408,541)(409,542)(410,543)(411,544)(412,545)(413,546)(414,547)(415,548)
(416,549)(417,550)(418,551)(419,590)(420,591)(421,592)(422,593)(423,594)
(424,595)(425,596)(426,597)(427,598)(428,599)(429,600)(430,601)(431,602)
(432,603)(433,604)(434,605)(435,606)(436,607)(437,608)(438,571)(439,572)
(440,573)(441,574)(442,575)(443,576)(444,577)(445,578)(446,579)(447,580)
(448,581)(449,582)(450,583)(451,584)(452,585)(453,586)(454,587)(455,588)
(456,589);
s1 := Sym(608)!( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)
( 9, 12)( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)
( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)
( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)
(115,134)(116,152)(117,151)(118,150)(119,149)(120,148)(121,147)(122,146)
(123,145)(124,144)(125,143)(126,142)(127,141)(128,140)(129,139)(130,138)
(131,137)(132,136)(133,135)(153,191)(154,209)(155,208)(156,207)(157,206)
(158,205)(159,204)(160,203)(161,202)(162,201)(163,200)(164,199)(165,198)
(166,197)(167,196)(168,195)(169,194)(170,193)(171,192)(172,210)(173,228)
(174,227)(175,226)(176,225)(177,224)(178,223)(179,222)(180,221)(181,220)
(182,219)(183,218)(184,217)(185,216)(186,215)(187,214)(188,213)(189,212)
(190,211)(229,286)(230,304)(231,303)(232,302)(233,301)(234,300)(235,299)
(236,298)(237,297)(238,296)(239,295)(240,294)(241,293)(242,292)(243,291)
(244,290)(245,289)(246,288)(247,287)(248,267)(249,285)(250,284)(251,283)
(252,282)(253,281)(254,280)(255,279)(256,278)(257,277)(258,276)(259,275)
(260,274)(261,273)(262,272)(263,271)(264,270)(265,269)(266,268)(305,381)
(306,399)(307,398)(308,397)(309,396)(310,395)(311,394)(312,393)(313,392)
(314,391)(315,390)(316,389)(317,388)(318,387)(319,386)(320,385)(321,384)
(322,383)(323,382)(324,400)(325,418)(326,417)(327,416)(328,415)(329,414)
(330,413)(331,412)(332,411)(333,410)(334,409)(335,408)(336,407)(337,406)
(338,405)(339,404)(340,403)(341,402)(342,401)(343,419)(344,437)(345,436)
(346,435)(347,434)(348,433)(349,432)(350,431)(351,430)(352,429)(353,428)
(354,427)(355,426)(356,425)(357,424)(358,423)(359,422)(360,421)(361,420)
(362,438)(363,456)(364,455)(365,454)(366,453)(367,452)(368,451)(369,450)
(370,449)(371,448)(372,447)(373,446)(374,445)(375,444)(376,443)(377,442)
(378,441)(379,440)(380,439)(457,590)(458,608)(459,607)(460,606)(461,605)
(462,604)(463,603)(464,602)(465,601)(466,600)(467,599)(468,598)(469,597)
(470,596)(471,595)(472,594)(473,593)(474,592)(475,591)(476,571)(477,589)
(478,588)(479,587)(480,586)(481,585)(482,584)(483,583)(484,582)(485,581)
(486,580)(487,579)(488,578)(489,577)(490,576)(491,575)(492,574)(493,573)
(494,572)(495,552)(496,570)(497,569)(498,568)(499,567)(500,566)(501,565)
(502,564)(503,563)(504,562)(505,561)(506,560)(507,559)(508,558)(509,557)
(510,556)(511,555)(512,554)(513,553)(514,533)(515,551)(516,550)(517,549)
(518,548)(519,547)(520,546)(521,545)(522,544)(523,543)(524,542)(525,541)
(526,540)(527,539)(528,538)(529,537)(530,536)(531,535)(532,534);
s2 := Sym(608)!( 1,306)( 2,305)( 3,323)( 4,322)( 5,321)( 6,320)( 7,319)
( 8,318)( 9,317)( 10,316)( 11,315)( 12,314)( 13,313)( 14,312)( 15,311)
( 16,310)( 17,309)( 18,308)( 19,307)( 20,325)( 21,324)( 22,342)( 23,341)
( 24,340)( 25,339)( 26,338)( 27,337)( 28,336)( 29,335)( 30,334)( 31,333)
( 32,332)( 33,331)( 34,330)( 35,329)( 36,328)( 37,327)( 38,326)( 39,363)
( 40,362)( 41,380)( 42,379)( 43,378)( 44,377)( 45,376)( 46,375)( 47,374)
( 48,373)( 49,372)( 50,371)( 51,370)( 52,369)( 53,368)( 54,367)( 55,366)
( 56,365)( 57,364)( 58,344)( 59,343)( 60,361)( 61,360)( 62,359)( 63,358)
( 64,357)( 65,356)( 66,355)( 67,354)( 68,353)( 69,352)( 70,351)( 71,350)
( 72,349)( 73,348)( 74,347)( 75,346)( 76,345)( 77,401)( 78,400)( 79,418)
( 80,417)( 81,416)( 82,415)( 83,414)( 84,413)( 85,412)( 86,411)( 87,410)
( 88,409)( 89,408)( 90,407)( 91,406)( 92,405)( 93,404)( 94,403)( 95,402)
( 96,382)( 97,381)( 98,399)( 99,398)(100,397)(101,396)(102,395)(103,394)
(104,393)(105,392)(106,391)(107,390)(108,389)(109,388)(110,387)(111,386)
(112,385)(113,384)(114,383)(115,420)(116,419)(117,437)(118,436)(119,435)
(120,434)(121,433)(122,432)(123,431)(124,430)(125,429)(126,428)(127,427)
(128,426)(129,425)(130,424)(131,423)(132,422)(133,421)(134,439)(135,438)
(136,456)(137,455)(138,454)(139,453)(140,452)(141,451)(142,450)(143,449)
(144,448)(145,447)(146,446)(147,445)(148,444)(149,443)(150,442)(151,441)
(152,440)(153,458)(154,457)(155,475)(156,474)(157,473)(158,472)(159,471)
(160,470)(161,469)(162,468)(163,467)(164,466)(165,465)(166,464)(167,463)
(168,462)(169,461)(170,460)(171,459)(172,477)(173,476)(174,494)(175,493)
(176,492)(177,491)(178,490)(179,489)(180,488)(181,487)(182,486)(183,485)
(184,484)(185,483)(186,482)(187,481)(188,480)(189,479)(190,478)(191,515)
(192,514)(193,532)(194,531)(195,530)(196,529)(197,528)(198,527)(199,526)
(200,525)(201,524)(202,523)(203,522)(204,521)(205,520)(206,519)(207,518)
(208,517)(209,516)(210,496)(211,495)(212,513)(213,512)(214,511)(215,510)
(216,509)(217,508)(218,507)(219,506)(220,505)(221,504)(222,503)(223,502)
(224,501)(225,500)(226,499)(227,498)(228,497)(229,553)(230,552)(231,570)
(232,569)(233,568)(234,567)(235,566)(236,565)(237,564)(238,563)(239,562)
(240,561)(241,560)(242,559)(243,558)(244,557)(245,556)(246,555)(247,554)
(248,534)(249,533)(250,551)(251,550)(252,549)(253,548)(254,547)(255,546)
(256,545)(257,544)(258,543)(259,542)(260,541)(261,540)(262,539)(263,538)
(264,537)(265,536)(266,535)(267,572)(268,571)(269,589)(270,588)(271,587)
(272,586)(273,585)(274,584)(275,583)(276,582)(277,581)(278,580)(279,579)
(280,578)(281,577)(282,576)(283,575)(284,574)(285,573)(286,591)(287,590)
(288,608)(289,607)(290,606)(291,605)(292,604)(293,603)(294,602)(295,601)
(296,600)(297,599)(298,598)(299,597)(300,596)(301,595)(302,594)(303,593)
(304,592);
poly := sub<Sym(608)|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,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*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*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*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 >;
References : None.
to this polytope