Polytope of Type {8,72}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,72}*1152c
Also Known As : {8,72|2}. if this polytope has another name.
Group : SmallGroup(1152,12903)
Rank : 3
Schlafli Type : {8,72}
Number of vertices, edges, etc : 8, 288, 72
Order of s0s1s2 : 72
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 : {4,72}*576a, {8,36}*576a
3-fold quotients : {8,24}*384b
4-fold quotients : {4,36}*288a, {2,72}*288, {8,18}*288
6-fold quotients : {4,24}*192a, {8,12}*192a
8-fold quotients : {2,36}*144, {4,18}*144a
9-fold quotients : {8,8}*128b
12-fold quotients : {4,12}*96a, {2,24}*96, {8,6}*96
16-fold quotients : {2,18}*72
18-fold quotients : {4,8}*64a, {8,4}*64a
24-fold quotients : {2,12}*48, {4,6}*48a
32-fold quotients : {2,9}*36
36-fold quotients : {4,4}*32, {2,8}*32, {8,2}*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 := ( 1,145)( 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)( 37,190)( 38,191)( 39,192)( 40,193)
( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)( 48,183)
( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)( 56,209)
( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)( 64,199)
( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)
( 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)(109,253)(110,254)(111,255)(112,256)
(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)
(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)
(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)
(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)
(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)(325,478)(326,479)(327,480)(328,481)
(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)(336,471)
(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)(344,497)
(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)(352,487)
(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)(360,495)
(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)(397,541)(398,542)(399,543)(400,544)
(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)
(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)
(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)
(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);;
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, 46)( 38, 48)( 39, 47)( 40, 54)( 41, 53)( 42, 52)( 43, 51)( 44, 50)
( 45, 49)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)( 60, 70)( 61, 69)
( 62, 68)( 63, 67)( 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)(109,136)(110,138)(111,137)(112,144)
(113,143)(114,142)(115,141)(116,140)(117,139)(118,127)(119,129)(120,128)
(121,135)(122,134)(123,133)(124,132)(125,131)(126,130)(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)(325,406)(326,408)(327,407)(328,414)(329,413)(330,412)
(331,411)(332,410)(333,409)(334,397)(335,399)(336,398)(337,405)(338,404)
(339,403)(340,402)(341,401)(342,400)(343,424)(344,426)(345,425)(346,432)
(347,431)(348,430)(349,429)(350,428)(351,427)(352,415)(353,417)(354,416)
(355,423)(356,422)(357,421)(358,420)(359,419)(360,418)(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 := ( 1,436)( 2,438)( 3,437)( 4,433)( 5,435)( 6,434)( 7,441)( 8,440)
( 9,439)( 10,445)( 11,447)( 12,446)( 13,442)( 14,444)( 15,443)( 16,450)
( 17,449)( 18,448)( 19,454)( 20,456)( 21,455)( 22,451)( 23,453)( 24,452)
( 25,459)( 26,458)( 27,457)( 28,463)( 29,465)( 30,464)( 31,460)( 32,462)
( 33,461)( 34,468)( 35,467)( 36,466)( 37,472)( 38,474)( 39,473)( 40,469)
( 41,471)( 42,470)( 43,477)( 44,476)( 45,475)( 46,481)( 47,483)( 48,482)
( 49,478)( 50,480)( 51,479)( 52,486)( 53,485)( 54,484)( 55,490)( 56,492)
( 57,491)( 58,487)( 59,489)( 60,488)( 61,495)( 62,494)( 63,493)( 64,499)
( 65,501)( 66,500)( 67,496)( 68,498)( 69,497)( 70,504)( 71,503)( 72,502)
( 73,535)( 74,537)( 75,536)( 76,532)( 77,534)( 78,533)( 79,540)( 80,539)
( 81,538)( 82,526)( 83,528)( 84,527)( 85,523)( 86,525)( 87,524)( 88,531)
( 89,530)( 90,529)( 91,517)( 92,519)( 93,518)( 94,514)( 95,516)( 96,515)
( 97,522)( 98,521)( 99,520)(100,508)(101,510)(102,509)(103,505)(104,507)
(105,506)(106,513)(107,512)(108,511)(109,571)(110,573)(111,572)(112,568)
(113,570)(114,569)(115,576)(116,575)(117,574)(118,562)(119,564)(120,563)
(121,559)(122,561)(123,560)(124,567)(125,566)(126,565)(127,553)(128,555)
(129,554)(130,550)(131,552)(132,551)(133,558)(134,557)(135,556)(136,544)
(137,546)(138,545)(139,541)(140,543)(141,542)(142,549)(143,548)(144,547)
(145,292)(146,294)(147,293)(148,289)(149,291)(150,290)(151,297)(152,296)
(153,295)(154,301)(155,303)(156,302)(157,298)(158,300)(159,299)(160,306)
(161,305)(162,304)(163,310)(164,312)(165,311)(166,307)(167,309)(168,308)
(169,315)(170,314)(171,313)(172,319)(173,321)(174,320)(175,316)(176,318)
(177,317)(178,324)(179,323)(180,322)(181,328)(182,330)(183,329)(184,325)
(185,327)(186,326)(187,333)(188,332)(189,331)(190,337)(191,339)(192,338)
(193,334)(194,336)(195,335)(196,342)(197,341)(198,340)(199,346)(200,348)
(201,347)(202,343)(203,345)(204,344)(205,351)(206,350)(207,349)(208,355)
(209,357)(210,356)(211,352)(212,354)(213,353)(214,360)(215,359)(216,358)
(217,391)(218,393)(219,392)(220,388)(221,390)(222,389)(223,396)(224,395)
(225,394)(226,382)(227,384)(228,383)(229,379)(230,381)(231,380)(232,387)
(233,386)(234,385)(235,373)(236,375)(237,374)(238,370)(239,372)(240,371)
(241,378)(242,377)(243,376)(244,364)(245,366)(246,365)(247,361)(248,363)
(249,362)(250,369)(251,368)(252,367)(253,427)(254,429)(255,428)(256,424)
(257,426)(258,425)(259,432)(260,431)(261,430)(262,418)(263,420)(264,419)
(265,415)(266,417)(267,416)(268,423)(269,422)(270,421)(271,409)(272,411)
(273,410)(274,406)(275,408)(276,407)(277,414)(278,413)(279,412)(280,400)
(281,402)(282,401)(283,397)(284,399)(285,398)(286,405)(287,404)(288,403);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 37,190)( 38,191)( 39,192)
( 40,193)( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)
( 48,183)( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)
( 56,209)( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)
( 64,199)( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)
( 72,207)( 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)(109,253)(110,254)(111,255)
(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)
(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)
(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)
(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)
(144,288)(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)(325,478)(326,479)(327,480)
(328,481)(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)
(336,471)(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)
(344,497)(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)
(352,487)(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)
(360,495)(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)(397,541)(398,542)(399,543)
(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)
(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)
(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)
(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)
(432,576);
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, 46)( 38, 48)( 39, 47)( 40, 54)( 41, 53)( 42, 52)( 43, 51)
( 44, 50)( 45, 49)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)( 60, 70)
( 61, 69)( 62, 68)( 63, 67)( 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)(109,136)(110,138)(111,137)
(112,144)(113,143)(114,142)(115,141)(116,140)(117,139)(118,127)(119,129)
(120,128)(121,135)(122,134)(123,133)(124,132)(125,131)(126,130)(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)(325,406)(326,408)(327,407)(328,414)(329,413)
(330,412)(331,411)(332,410)(333,409)(334,397)(335,399)(336,398)(337,405)
(338,404)(339,403)(340,402)(341,401)(342,400)(343,424)(344,426)(345,425)
(346,432)(347,431)(348,430)(349,429)(350,428)(351,427)(352,415)(353,417)
(354,416)(355,423)(356,422)(357,421)(358,420)(359,419)(360,418)(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)!( 1,436)( 2,438)( 3,437)( 4,433)( 5,435)( 6,434)( 7,441)
( 8,440)( 9,439)( 10,445)( 11,447)( 12,446)( 13,442)( 14,444)( 15,443)
( 16,450)( 17,449)( 18,448)( 19,454)( 20,456)( 21,455)( 22,451)( 23,453)
( 24,452)( 25,459)( 26,458)( 27,457)( 28,463)( 29,465)( 30,464)( 31,460)
( 32,462)( 33,461)( 34,468)( 35,467)( 36,466)( 37,472)( 38,474)( 39,473)
( 40,469)( 41,471)( 42,470)( 43,477)( 44,476)( 45,475)( 46,481)( 47,483)
( 48,482)( 49,478)( 50,480)( 51,479)( 52,486)( 53,485)( 54,484)( 55,490)
( 56,492)( 57,491)( 58,487)( 59,489)( 60,488)( 61,495)( 62,494)( 63,493)
( 64,499)( 65,501)( 66,500)( 67,496)( 68,498)( 69,497)( 70,504)( 71,503)
( 72,502)( 73,535)( 74,537)( 75,536)( 76,532)( 77,534)( 78,533)( 79,540)
( 80,539)( 81,538)( 82,526)( 83,528)( 84,527)( 85,523)( 86,525)( 87,524)
( 88,531)( 89,530)( 90,529)( 91,517)( 92,519)( 93,518)( 94,514)( 95,516)
( 96,515)( 97,522)( 98,521)( 99,520)(100,508)(101,510)(102,509)(103,505)
(104,507)(105,506)(106,513)(107,512)(108,511)(109,571)(110,573)(111,572)
(112,568)(113,570)(114,569)(115,576)(116,575)(117,574)(118,562)(119,564)
(120,563)(121,559)(122,561)(123,560)(124,567)(125,566)(126,565)(127,553)
(128,555)(129,554)(130,550)(131,552)(132,551)(133,558)(134,557)(135,556)
(136,544)(137,546)(138,545)(139,541)(140,543)(141,542)(142,549)(143,548)
(144,547)(145,292)(146,294)(147,293)(148,289)(149,291)(150,290)(151,297)
(152,296)(153,295)(154,301)(155,303)(156,302)(157,298)(158,300)(159,299)
(160,306)(161,305)(162,304)(163,310)(164,312)(165,311)(166,307)(167,309)
(168,308)(169,315)(170,314)(171,313)(172,319)(173,321)(174,320)(175,316)
(176,318)(177,317)(178,324)(179,323)(180,322)(181,328)(182,330)(183,329)
(184,325)(185,327)(186,326)(187,333)(188,332)(189,331)(190,337)(191,339)
(192,338)(193,334)(194,336)(195,335)(196,342)(197,341)(198,340)(199,346)
(200,348)(201,347)(202,343)(203,345)(204,344)(205,351)(206,350)(207,349)
(208,355)(209,357)(210,356)(211,352)(212,354)(213,353)(214,360)(215,359)
(216,358)(217,391)(218,393)(219,392)(220,388)(221,390)(222,389)(223,396)
(224,395)(225,394)(226,382)(227,384)(228,383)(229,379)(230,381)(231,380)
(232,387)(233,386)(234,385)(235,373)(236,375)(237,374)(238,370)(239,372)
(240,371)(241,378)(242,377)(243,376)(244,364)(245,366)(246,365)(247,361)
(248,363)(249,362)(250,369)(251,368)(252,367)(253,427)(254,429)(255,428)
(256,424)(257,426)(258,425)(259,432)(260,431)(261,430)(262,418)(263,420)
(264,419)(265,415)(266,417)(267,416)(268,423)(269,422)(270,421)(271,409)
(272,411)(273,410)(274,406)(275,408)(276,407)(277,414)(278,413)(279,412)
(280,400)(281,402)(282,401)(283,397)(284,399)(285,398)(286,405)(287,404)
(288,403);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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 >;
References : None.
to this polytope