Polytope of Type {12,48}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,48}*1152b
Also Known As : {12,48|2}. if this polytope has another name.
Group : SmallGroup(1152,32078)
Rank : 3
Schlafli Type : {12,48}
Number of vertices, edges, etc : 12, 288, 48
Order of s0s1s2 : 48
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 : {6,48}*576a, {12,24}*576c
3-fold quotients : {4,48}*384a, {12,16}*384a
4-fold quotients : {6,24}*288a, {12,12}*288a
6-fold quotients : {4,24}*192a, {12,8}*192a, {2,48}*192, {6,16}*192
8-fold quotients : {6,12}*144a, {12,6}*144a
9-fold quotients : {4,16}*128a
12-fold quotients : {4,12}*96a, {12,4}*96a, {2,24}*96, {6,8}*96
16-fold quotients : {6,6}*72a
18-fold quotients : {4,8}*64a, {2,16}*64
24-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
36-fold quotients : {4,4}*32, {2,8}*32
48-fold quotients : {2,6}*24, {6,2}*24
72-fold quotients : {2,4}*16, {4,2}*16
96-fold quotients : {2,3}*12, {3,2}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)( 8,147)
( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)
( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)
( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)
( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)( 40,184)
( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)( 48,197)
( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)( 56,204)
( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)( 64,208)
( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)( 72,212)
( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)( 80,219)
( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)( 88,232)
( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)( 96,236)
( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)(104,252)
(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)(112,256)
(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)
(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)
(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)
(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)
(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)
(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)
(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)
(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)
(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)(328,472)
(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)(336,485)
(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)(344,492)
(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)(352,496)
(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)(360,500)
(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)(368,507)
(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)(376,520)
(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)(384,524)
(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)(392,540)
(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)(400,544)
(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)
(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)
(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)
(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);;
s1 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)( 15, 18)
( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)
( 27, 33)( 37, 38)( 40, 44)( 41, 43)( 42, 45)( 46, 47)( 49, 53)( 50, 52)
( 51, 54)( 55, 65)( 56, 64)( 57, 66)( 58, 71)( 59, 70)( 60, 72)( 61, 68)
( 62, 67)( 63, 69)( 73, 92)( 74, 91)( 75, 93)( 76, 98)( 77, 97)( 78, 99)
( 79, 95)( 80, 94)( 81, 96)( 82,101)( 83,100)( 84,102)( 85,107)( 86,106)
( 87,108)( 88,104)( 89,103)( 90,105)(109,128)(110,127)(111,129)(112,134)
(113,133)(114,135)(115,131)(116,130)(117,132)(118,137)(119,136)(120,138)
(121,143)(122,142)(123,144)(124,140)(125,139)(126,141)(145,182)(146,181)
(147,183)(148,188)(149,187)(150,189)(151,185)(152,184)(153,186)(154,191)
(155,190)(156,192)(157,197)(158,196)(159,198)(160,194)(161,193)(162,195)
(163,209)(164,208)(165,210)(166,215)(167,214)(168,216)(169,212)(170,211)
(171,213)(172,200)(173,199)(174,201)(175,206)(176,205)(177,207)(178,203)
(179,202)(180,204)(217,272)(218,271)(219,273)(220,278)(221,277)(222,279)
(223,275)(224,274)(225,276)(226,281)(227,280)(228,282)(229,287)(230,286)
(231,288)(232,284)(233,283)(234,285)(235,254)(236,253)(237,255)(238,260)
(239,259)(240,261)(241,257)(242,256)(243,258)(244,263)(245,262)(246,264)
(247,269)(248,268)(249,270)(250,266)(251,265)(252,267)(289,362)(290,361)
(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)(297,366)(298,371)
(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)(305,373)(306,375)
(307,389)(308,388)(309,390)(310,395)(311,394)(312,396)(313,392)(314,391)
(315,393)(316,380)(317,379)(318,381)(319,386)(320,385)(321,387)(322,383)
(323,382)(324,384)(325,398)(326,397)(327,399)(328,404)(329,403)(330,405)
(331,401)(332,400)(333,402)(334,407)(335,406)(336,408)(337,413)(338,412)
(339,414)(340,410)(341,409)(342,411)(343,425)(344,424)(345,426)(346,431)
(347,430)(348,432)(349,428)(350,427)(351,429)(352,416)(353,415)(354,417)
(355,422)(356,421)(357,423)(358,419)(359,418)(360,420)(433,542)(434,541)
(435,543)(436,548)(437,547)(438,549)(439,545)(440,544)(441,546)(442,551)
(443,550)(444,552)(445,557)(446,556)(447,558)(448,554)(449,553)(450,555)
(451,569)(452,568)(453,570)(454,575)(455,574)(456,576)(457,572)(458,571)
(459,573)(460,560)(461,559)(462,561)(463,566)(464,565)(465,567)(466,563)
(467,562)(468,564)(469,506)(470,505)(471,507)(472,512)(473,511)(474,513)
(475,509)(476,508)(477,510)(478,515)(479,514)(480,516)(481,521)(482,520)
(483,522)(484,518)(485,517)(486,519)(487,533)(488,532)(489,534)(490,539)
(491,538)(492,540)(493,536)(494,535)(495,537)(496,524)(497,523)(498,525)
(499,530)(500,529)(501,531)(502,527)(503,526)(504,528);;
s2 := ( 1,433)( 2,440)( 3,438)( 4,439)( 5,437)( 6,435)( 7,436)( 8,434)
( 9,441)( 10,442)( 11,449)( 12,447)( 13,448)( 14,446)( 15,444)( 16,445)
( 17,443)( 18,450)( 19,460)( 20,467)( 21,465)( 22,466)( 23,464)( 24,462)
( 25,463)( 26,461)( 27,468)( 28,451)( 29,458)( 30,456)( 31,457)( 32,455)
( 33,453)( 34,454)( 35,452)( 36,459)( 37,469)( 38,476)( 39,474)( 40,475)
( 41,473)( 42,471)( 43,472)( 44,470)( 45,477)( 46,478)( 47,485)( 48,483)
( 49,484)( 50,482)( 51,480)( 52,481)( 53,479)( 54,486)( 55,496)( 56,503)
( 57,501)( 58,502)( 59,500)( 60,498)( 61,499)( 62,497)( 63,504)( 64,487)
( 65,494)( 66,492)( 67,493)( 68,491)( 69,489)( 70,490)( 71,488)( 72,495)
( 73,523)( 74,530)( 75,528)( 76,529)( 77,527)( 78,525)( 79,526)( 80,524)
( 81,531)( 82,532)( 83,539)( 84,537)( 85,538)( 86,536)( 87,534)( 88,535)
( 89,533)( 90,540)( 91,505)( 92,512)( 93,510)( 94,511)( 95,509)( 96,507)
( 97,508)( 98,506)( 99,513)(100,514)(101,521)(102,519)(103,520)(104,518)
(105,516)(106,517)(107,515)(108,522)(109,559)(110,566)(111,564)(112,565)
(113,563)(114,561)(115,562)(116,560)(117,567)(118,568)(119,575)(120,573)
(121,574)(122,572)(123,570)(124,571)(125,569)(126,576)(127,541)(128,548)
(129,546)(130,547)(131,545)(132,543)(133,544)(134,542)(135,549)(136,550)
(137,557)(138,555)(139,556)(140,554)(141,552)(142,553)(143,551)(144,558)
(145,289)(146,296)(147,294)(148,295)(149,293)(150,291)(151,292)(152,290)
(153,297)(154,298)(155,305)(156,303)(157,304)(158,302)(159,300)(160,301)
(161,299)(162,306)(163,316)(164,323)(165,321)(166,322)(167,320)(168,318)
(169,319)(170,317)(171,324)(172,307)(173,314)(174,312)(175,313)(176,311)
(177,309)(178,310)(179,308)(180,315)(181,325)(182,332)(183,330)(184,331)
(185,329)(186,327)(187,328)(188,326)(189,333)(190,334)(191,341)(192,339)
(193,340)(194,338)(195,336)(196,337)(197,335)(198,342)(199,352)(200,359)
(201,357)(202,358)(203,356)(204,354)(205,355)(206,353)(207,360)(208,343)
(209,350)(210,348)(211,349)(212,347)(213,345)(214,346)(215,344)(216,351)
(217,379)(218,386)(219,384)(220,385)(221,383)(222,381)(223,382)(224,380)
(225,387)(226,388)(227,395)(228,393)(229,394)(230,392)(231,390)(232,391)
(233,389)(234,396)(235,361)(236,368)(237,366)(238,367)(239,365)(240,363)
(241,364)(242,362)(243,369)(244,370)(245,377)(246,375)(247,376)(248,374)
(249,372)(250,373)(251,371)(252,378)(253,415)(254,422)(255,420)(256,421)
(257,419)(258,417)(259,418)(260,416)(261,423)(262,424)(263,431)(264,429)
(265,430)(266,428)(267,426)(268,427)(269,425)(270,432)(271,397)(272,404)
(273,402)(274,403)(275,401)(276,399)(277,400)(278,398)(279,405)(280,406)
(281,413)(282,411)(283,412)(284,410)(285,408)(286,409)(287,407)(288,414);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)
( 8,147)( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)
( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)
( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)
( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)
( 40,184)( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)
( 48,197)( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)
( 56,204)( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)
( 64,208)( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)
( 72,212)( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)
( 80,219)( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)
( 88,232)( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)
( 96,236)( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)
(104,252)(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)
(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)
(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)
(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)
(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)
(144,284)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)
(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)
(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)
(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)
(320,468)(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)
(328,472)(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)
(336,485)(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)
(344,492)(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)
(352,496)(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)
(360,500)(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)
(368,507)(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)
(376,520)(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)
(384,524)(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)
(392,540)(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)
(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)
(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)
(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)
(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)
(432,572);
s1 := Sym(576)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)
( 15, 18)( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)
( 26, 31)( 27, 33)( 37, 38)( 40, 44)( 41, 43)( 42, 45)( 46, 47)( 49, 53)
( 50, 52)( 51, 54)( 55, 65)( 56, 64)( 57, 66)( 58, 71)( 59, 70)( 60, 72)
( 61, 68)( 62, 67)( 63, 69)( 73, 92)( 74, 91)( 75, 93)( 76, 98)( 77, 97)
( 78, 99)( 79, 95)( 80, 94)( 81, 96)( 82,101)( 83,100)( 84,102)( 85,107)
( 86,106)( 87,108)( 88,104)( 89,103)( 90,105)(109,128)(110,127)(111,129)
(112,134)(113,133)(114,135)(115,131)(116,130)(117,132)(118,137)(119,136)
(120,138)(121,143)(122,142)(123,144)(124,140)(125,139)(126,141)(145,182)
(146,181)(147,183)(148,188)(149,187)(150,189)(151,185)(152,184)(153,186)
(154,191)(155,190)(156,192)(157,197)(158,196)(159,198)(160,194)(161,193)
(162,195)(163,209)(164,208)(165,210)(166,215)(167,214)(168,216)(169,212)
(170,211)(171,213)(172,200)(173,199)(174,201)(175,206)(176,205)(177,207)
(178,203)(179,202)(180,204)(217,272)(218,271)(219,273)(220,278)(221,277)
(222,279)(223,275)(224,274)(225,276)(226,281)(227,280)(228,282)(229,287)
(230,286)(231,288)(232,284)(233,283)(234,285)(235,254)(236,253)(237,255)
(238,260)(239,259)(240,261)(241,257)(242,256)(243,258)(244,263)(245,262)
(246,264)(247,269)(248,268)(249,270)(250,266)(251,265)(252,267)(289,362)
(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)(297,366)
(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)(305,373)
(306,375)(307,389)(308,388)(309,390)(310,395)(311,394)(312,396)(313,392)
(314,391)(315,393)(316,380)(317,379)(318,381)(319,386)(320,385)(321,387)
(322,383)(323,382)(324,384)(325,398)(326,397)(327,399)(328,404)(329,403)
(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)(336,408)(337,413)
(338,412)(339,414)(340,410)(341,409)(342,411)(343,425)(344,424)(345,426)
(346,431)(347,430)(348,432)(349,428)(350,427)(351,429)(352,416)(353,415)
(354,417)(355,422)(356,421)(357,423)(358,419)(359,418)(360,420)(433,542)
(434,541)(435,543)(436,548)(437,547)(438,549)(439,545)(440,544)(441,546)
(442,551)(443,550)(444,552)(445,557)(446,556)(447,558)(448,554)(449,553)
(450,555)(451,569)(452,568)(453,570)(454,575)(455,574)(456,576)(457,572)
(458,571)(459,573)(460,560)(461,559)(462,561)(463,566)(464,565)(465,567)
(466,563)(467,562)(468,564)(469,506)(470,505)(471,507)(472,512)(473,511)
(474,513)(475,509)(476,508)(477,510)(478,515)(479,514)(480,516)(481,521)
(482,520)(483,522)(484,518)(485,517)(486,519)(487,533)(488,532)(489,534)
(490,539)(491,538)(492,540)(493,536)(494,535)(495,537)(496,524)(497,523)
(498,525)(499,530)(500,529)(501,531)(502,527)(503,526)(504,528);
s2 := Sym(576)!( 1,433)( 2,440)( 3,438)( 4,439)( 5,437)( 6,435)( 7,436)
( 8,434)( 9,441)( 10,442)( 11,449)( 12,447)( 13,448)( 14,446)( 15,444)
( 16,445)( 17,443)( 18,450)( 19,460)( 20,467)( 21,465)( 22,466)( 23,464)
( 24,462)( 25,463)( 26,461)( 27,468)( 28,451)( 29,458)( 30,456)( 31,457)
( 32,455)( 33,453)( 34,454)( 35,452)( 36,459)( 37,469)( 38,476)( 39,474)
( 40,475)( 41,473)( 42,471)( 43,472)( 44,470)( 45,477)( 46,478)( 47,485)
( 48,483)( 49,484)( 50,482)( 51,480)( 52,481)( 53,479)( 54,486)( 55,496)
( 56,503)( 57,501)( 58,502)( 59,500)( 60,498)( 61,499)( 62,497)( 63,504)
( 64,487)( 65,494)( 66,492)( 67,493)( 68,491)( 69,489)( 70,490)( 71,488)
( 72,495)( 73,523)( 74,530)( 75,528)( 76,529)( 77,527)( 78,525)( 79,526)
( 80,524)( 81,531)( 82,532)( 83,539)( 84,537)( 85,538)( 86,536)( 87,534)
( 88,535)( 89,533)( 90,540)( 91,505)( 92,512)( 93,510)( 94,511)( 95,509)
( 96,507)( 97,508)( 98,506)( 99,513)(100,514)(101,521)(102,519)(103,520)
(104,518)(105,516)(106,517)(107,515)(108,522)(109,559)(110,566)(111,564)
(112,565)(113,563)(114,561)(115,562)(116,560)(117,567)(118,568)(119,575)
(120,573)(121,574)(122,572)(123,570)(124,571)(125,569)(126,576)(127,541)
(128,548)(129,546)(130,547)(131,545)(132,543)(133,544)(134,542)(135,549)
(136,550)(137,557)(138,555)(139,556)(140,554)(141,552)(142,553)(143,551)
(144,558)(145,289)(146,296)(147,294)(148,295)(149,293)(150,291)(151,292)
(152,290)(153,297)(154,298)(155,305)(156,303)(157,304)(158,302)(159,300)
(160,301)(161,299)(162,306)(163,316)(164,323)(165,321)(166,322)(167,320)
(168,318)(169,319)(170,317)(171,324)(172,307)(173,314)(174,312)(175,313)
(176,311)(177,309)(178,310)(179,308)(180,315)(181,325)(182,332)(183,330)
(184,331)(185,329)(186,327)(187,328)(188,326)(189,333)(190,334)(191,341)
(192,339)(193,340)(194,338)(195,336)(196,337)(197,335)(198,342)(199,352)
(200,359)(201,357)(202,358)(203,356)(204,354)(205,355)(206,353)(207,360)
(208,343)(209,350)(210,348)(211,349)(212,347)(213,345)(214,346)(215,344)
(216,351)(217,379)(218,386)(219,384)(220,385)(221,383)(222,381)(223,382)
(224,380)(225,387)(226,388)(227,395)(228,393)(229,394)(230,392)(231,390)
(232,391)(233,389)(234,396)(235,361)(236,368)(237,366)(238,367)(239,365)
(240,363)(241,364)(242,362)(243,369)(244,370)(245,377)(246,375)(247,376)
(248,374)(249,372)(250,373)(251,371)(252,378)(253,415)(254,422)(255,420)
(256,421)(257,419)(258,417)(259,418)(260,416)(261,423)(262,424)(263,431)
(264,429)(265,430)(266,428)(267,426)(268,427)(269,425)(270,432)(271,397)
(272,404)(273,402)(274,403)(275,401)(276,399)(277,400)(278,398)(279,405)
(280,406)(281,413)(282,411)(283,412)(284,410)(285,408)(286,409)(287,407)
(288,414);
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*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 >;
References : None.
to this polytope