Polytope of Type {24,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,12010)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 48, 288, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,12}*576a, {24,12}*576c, {24,12}*576e
3-fold quotients : {24,4}*384a, {8,12}*384a
4-fold quotients : {24,6}*288a, {12,12}*288a
6-fold quotients : {24,4}*192a, {4,12}*192a, {12,4}*192a, {24,4}*192b, {8,12}*192a, {8,12}*192b
8-fold quotients : {6,12}*144a, {12,6}*144a
9-fold quotients : {8,4}*128a
12-fold quotients : {4,12}*96a, {12,4}*96a, {24,2}*96, {8,6}*96
16-fold quotients : {6,6}*72a
18-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
24-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
36-fold quotients : {4,4}*32, {8,2}*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 := ( 1,433)( 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)( 19,451)( 20,458)( 21,456)( 22,457)( 23,455)( 24,453)
( 25,454)( 26,452)( 27,459)( 28,460)( 29,467)( 30,465)( 31,466)( 32,464)
( 33,462)( 34,463)( 35,461)( 36,468)( 37,478)( 38,485)( 39,483)( 40,484)
( 41,482)( 42,480)( 43,481)( 44,479)( 45,486)( 46,469)( 47,476)( 48,474)
( 49,475)( 50,473)( 51,471)( 52,472)( 53,470)( 54,477)( 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)
( 73,532)( 74,539)( 75,537)( 76,538)( 77,536)( 78,534)( 79,535)( 80,533)
( 81,540)( 82,523)( 83,530)( 84,528)( 85,529)( 86,527)( 87,525)( 88,526)
( 89,524)( 90,531)( 91,514)( 92,521)( 93,519)( 94,520)( 95,518)( 96,516)
( 97,517)( 98,515)( 99,522)(100,505)(101,512)(102,510)(103,511)(104,509)
(105,507)(106,508)(107,506)(108,513)(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)(163,307)(164,314)(165,312)(166,313)(167,311)(168,309)
(169,310)(170,308)(171,315)(172,316)(173,323)(174,321)(175,322)(176,320)
(177,318)(178,319)(179,317)(180,324)(181,334)(182,341)(183,339)(184,340)
(185,338)(186,336)(187,337)(188,335)(189,342)(190,325)(191,332)(192,330)
(193,331)(194,329)(195,327)(196,328)(197,326)(198,333)(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)
(217,388)(218,395)(219,393)(220,394)(221,392)(222,390)(223,391)(224,389)
(225,396)(226,379)(227,386)(228,384)(229,385)(230,383)(231,381)(232,382)
(233,380)(234,387)(235,370)(236,377)(237,375)(238,376)(239,374)(240,372)
(241,373)(242,371)(243,378)(244,361)(245,368)(246,366)(247,367)(248,365)
(249,363)(250,364)(251,362)(252,369)(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);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)
( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)( 35, 36)
( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)( 53, 54)
( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)( 65, 69)( 66, 68)( 71, 72)
( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 97)( 80, 99)
( 81, 98)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)( 88,106)
( 89,108)( 90,107)(109,130)(110,132)(111,131)(112,127)(113,129)(114,128)
(115,133)(116,135)(117,134)(118,139)(119,141)(120,140)(121,136)(122,138)
(123,137)(124,142)(125,144)(126,143)(145,184)(146,186)(147,185)(148,181)
(149,183)(150,182)(151,187)(152,189)(153,188)(154,193)(155,195)(156,194)
(157,190)(158,192)(159,191)(160,196)(161,198)(162,197)(163,202)(164,204)
(165,203)(166,199)(167,201)(168,200)(169,205)(170,207)(171,206)(172,211)
(173,213)(174,212)(175,208)(176,210)(177,209)(178,214)(179,216)(180,215)
(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,277)(224,279)
(225,278)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)(232,286)
(233,288)(234,287)(235,256)(236,258)(237,257)(238,253)(239,255)(240,254)
(241,259)(242,261)(243,260)(244,265)(245,267)(246,266)(247,262)(248,264)
(249,263)(250,268)(251,270)(252,269)(289,364)(290,366)(291,365)(292,361)
(293,363)(294,362)(295,367)(296,369)(297,368)(298,373)(299,375)(300,374)
(301,370)(302,372)(303,371)(304,376)(305,378)(306,377)(307,382)(308,384)
(309,383)(310,379)(311,381)(312,380)(313,385)(314,387)(315,386)(316,391)
(317,393)(318,392)(319,388)(320,390)(321,389)(322,394)(323,396)(324,395)
(325,400)(326,402)(327,401)(328,397)(329,399)(330,398)(331,403)(332,405)
(333,404)(334,409)(335,411)(336,410)(337,406)(338,408)(339,407)(340,412)
(341,414)(342,413)(343,418)(344,420)(345,419)(346,415)(347,417)(348,416)
(349,421)(350,423)(351,422)(352,427)(353,429)(354,428)(355,424)(356,426)
(357,425)(358,430)(359,432)(360,431)(433,553)(434,555)(435,554)(436,550)
(437,552)(438,551)(439,556)(440,558)(441,557)(442,544)(443,546)(444,545)
(445,541)(446,543)(447,542)(448,547)(449,549)(450,548)(451,571)(452,573)
(453,572)(454,568)(455,570)(456,569)(457,574)(458,576)(459,575)(460,562)
(461,564)(462,563)(463,559)(464,561)(465,560)(466,565)(467,567)(468,566)
(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,520)(476,522)
(477,521)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,511)
(485,513)(486,512)(487,535)(488,537)(489,536)(490,532)(491,534)(492,533)
(493,538)(494,540)(495,539)(496,526)(497,528)(498,527)(499,523)(500,525)
(501,524)(502,529)(503,531)(504,530);;
s2 := ( 1,149)( 2,151)( 3,147)( 4,152)( 5,145)( 6,150)( 7,146)( 8,148)
( 9,153)( 10,158)( 11,160)( 12,156)( 13,161)( 14,154)( 15,159)( 16,155)
( 17,157)( 18,162)( 19,167)( 20,169)( 21,165)( 22,170)( 23,163)( 24,168)
( 25,164)( 26,166)( 27,171)( 28,176)( 29,178)( 30,174)( 31,179)( 32,172)
( 33,177)( 34,173)( 35,175)( 36,180)( 37,185)( 38,187)( 39,183)( 40,188)
( 41,181)( 42,186)( 43,182)( 44,184)( 45,189)( 46,194)( 47,196)( 48,192)
( 49,197)( 50,190)( 51,195)( 52,191)( 53,193)( 54,198)( 55,203)( 56,205)
( 57,201)( 58,206)( 59,199)( 60,204)( 61,200)( 62,202)( 63,207)( 64,212)
( 65,214)( 66,210)( 67,215)( 68,208)( 69,213)( 70,209)( 71,211)( 72,216)
( 73,230)( 74,232)( 75,228)( 76,233)( 77,226)( 78,231)( 79,227)( 80,229)
( 81,234)( 82,221)( 83,223)( 84,219)( 85,224)( 86,217)( 87,222)( 88,218)
( 89,220)( 90,225)( 91,248)( 92,250)( 93,246)( 94,251)( 95,244)( 96,249)
( 97,245)( 98,247)( 99,252)(100,239)(101,241)(102,237)(103,242)(104,235)
(105,240)(106,236)(107,238)(108,243)(109,266)(110,268)(111,264)(112,269)
(113,262)(114,267)(115,263)(116,265)(117,270)(118,257)(119,259)(120,255)
(121,260)(122,253)(123,258)(124,254)(125,256)(126,261)(127,284)(128,286)
(129,282)(130,287)(131,280)(132,285)(133,281)(134,283)(135,288)(136,275)
(137,277)(138,273)(139,278)(140,271)(141,276)(142,272)(143,274)(144,279)
(289,437)(290,439)(291,435)(292,440)(293,433)(294,438)(295,434)(296,436)
(297,441)(298,446)(299,448)(300,444)(301,449)(302,442)(303,447)(304,443)
(305,445)(306,450)(307,455)(308,457)(309,453)(310,458)(311,451)(312,456)
(313,452)(314,454)(315,459)(316,464)(317,466)(318,462)(319,467)(320,460)
(321,465)(322,461)(323,463)(324,468)(325,473)(326,475)(327,471)(328,476)
(329,469)(330,474)(331,470)(332,472)(333,477)(334,482)(335,484)(336,480)
(337,485)(338,478)(339,483)(340,479)(341,481)(342,486)(343,491)(344,493)
(345,489)(346,494)(347,487)(348,492)(349,488)(350,490)(351,495)(352,500)
(353,502)(354,498)(355,503)(356,496)(357,501)(358,497)(359,499)(360,504)
(361,518)(362,520)(363,516)(364,521)(365,514)(366,519)(367,515)(368,517)
(369,522)(370,509)(371,511)(372,507)(373,512)(374,505)(375,510)(376,506)
(377,508)(378,513)(379,536)(380,538)(381,534)(382,539)(383,532)(384,537)
(385,533)(386,535)(387,540)(388,527)(389,529)(390,525)(391,530)(392,523)
(393,528)(394,524)(395,526)(396,531)(397,554)(398,556)(399,552)(400,557)
(401,550)(402,555)(403,551)(404,553)(405,558)(406,545)(407,547)(408,543)
(409,548)(410,541)(411,546)(412,542)(413,544)(414,549)(415,572)(416,574)
(417,570)(418,575)(419,568)(420,573)(421,569)(422,571)(423,576)(424,563)
(425,565)(426,561)(427,566)(428,559)(429,564)(430,560)(431,562)(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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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,
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)!( 1,433)( 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)( 19,451)( 20,458)( 21,456)( 22,457)( 23,455)
( 24,453)( 25,454)( 26,452)( 27,459)( 28,460)( 29,467)( 30,465)( 31,466)
( 32,464)( 33,462)( 34,463)( 35,461)( 36,468)( 37,478)( 38,485)( 39,483)
( 40,484)( 41,482)( 42,480)( 43,481)( 44,479)( 45,486)( 46,469)( 47,476)
( 48,474)( 49,475)( 50,473)( 51,471)( 52,472)( 53,470)( 54,477)( 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)( 73,532)( 74,539)( 75,537)( 76,538)( 77,536)( 78,534)( 79,535)
( 80,533)( 81,540)( 82,523)( 83,530)( 84,528)( 85,529)( 86,527)( 87,525)
( 88,526)( 89,524)( 90,531)( 91,514)( 92,521)( 93,519)( 94,520)( 95,518)
( 96,516)( 97,517)( 98,515)( 99,522)(100,505)(101,512)(102,510)(103,511)
(104,509)(105,507)(106,508)(107,506)(108,513)(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)(163,307)(164,314)(165,312)(166,313)(167,311)
(168,309)(169,310)(170,308)(171,315)(172,316)(173,323)(174,321)(175,322)
(176,320)(177,318)(178,319)(179,317)(180,324)(181,334)(182,341)(183,339)
(184,340)(185,338)(186,336)(187,337)(188,335)(189,342)(190,325)(191,332)
(192,330)(193,331)(194,329)(195,327)(196,328)(197,326)(198,333)(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)(217,388)(218,395)(219,393)(220,394)(221,392)(222,390)(223,391)
(224,389)(225,396)(226,379)(227,386)(228,384)(229,385)(230,383)(231,381)
(232,382)(233,380)(234,387)(235,370)(236,377)(237,375)(238,376)(239,374)
(240,372)(241,373)(242,371)(243,378)(244,361)(245,368)(246,366)(247,367)
(248,365)(249,363)(250,364)(251,362)(252,369)(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);
s1 := Sym(576)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 13)( 11, 15)( 12, 14)
( 17, 18)( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)
( 35, 36)( 37, 40)( 38, 42)( 39, 41)( 44, 45)( 46, 49)( 47, 51)( 48, 50)
( 53, 54)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)( 65, 69)( 66, 68)
( 71, 72)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 97)
( 80, 99)( 81, 98)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)
( 88,106)( 89,108)( 90,107)(109,130)(110,132)(111,131)(112,127)(113,129)
(114,128)(115,133)(116,135)(117,134)(118,139)(119,141)(120,140)(121,136)
(122,138)(123,137)(124,142)(125,144)(126,143)(145,184)(146,186)(147,185)
(148,181)(149,183)(150,182)(151,187)(152,189)(153,188)(154,193)(155,195)
(156,194)(157,190)(158,192)(159,191)(160,196)(161,198)(162,197)(163,202)
(164,204)(165,203)(166,199)(167,201)(168,200)(169,205)(170,207)(171,206)
(172,211)(173,213)(174,212)(175,208)(176,210)(177,209)(178,214)(179,216)
(180,215)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,277)
(224,279)(225,278)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)
(232,286)(233,288)(234,287)(235,256)(236,258)(237,257)(238,253)(239,255)
(240,254)(241,259)(242,261)(243,260)(244,265)(245,267)(246,266)(247,262)
(248,264)(249,263)(250,268)(251,270)(252,269)(289,364)(290,366)(291,365)
(292,361)(293,363)(294,362)(295,367)(296,369)(297,368)(298,373)(299,375)
(300,374)(301,370)(302,372)(303,371)(304,376)(305,378)(306,377)(307,382)
(308,384)(309,383)(310,379)(311,381)(312,380)(313,385)(314,387)(315,386)
(316,391)(317,393)(318,392)(319,388)(320,390)(321,389)(322,394)(323,396)
(324,395)(325,400)(326,402)(327,401)(328,397)(329,399)(330,398)(331,403)
(332,405)(333,404)(334,409)(335,411)(336,410)(337,406)(338,408)(339,407)
(340,412)(341,414)(342,413)(343,418)(344,420)(345,419)(346,415)(347,417)
(348,416)(349,421)(350,423)(351,422)(352,427)(353,429)(354,428)(355,424)
(356,426)(357,425)(358,430)(359,432)(360,431)(433,553)(434,555)(435,554)
(436,550)(437,552)(438,551)(439,556)(440,558)(441,557)(442,544)(443,546)
(444,545)(445,541)(446,543)(447,542)(448,547)(449,549)(450,548)(451,571)
(452,573)(453,572)(454,568)(455,570)(456,569)(457,574)(458,576)(459,575)
(460,562)(461,564)(462,563)(463,559)(464,561)(465,560)(466,565)(467,567)
(468,566)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,520)
(476,522)(477,521)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)
(484,511)(485,513)(486,512)(487,535)(488,537)(489,536)(490,532)(491,534)
(492,533)(493,538)(494,540)(495,539)(496,526)(497,528)(498,527)(499,523)
(500,525)(501,524)(502,529)(503,531)(504,530);
s2 := Sym(576)!( 1,149)( 2,151)( 3,147)( 4,152)( 5,145)( 6,150)( 7,146)
( 8,148)( 9,153)( 10,158)( 11,160)( 12,156)( 13,161)( 14,154)( 15,159)
( 16,155)( 17,157)( 18,162)( 19,167)( 20,169)( 21,165)( 22,170)( 23,163)
( 24,168)( 25,164)( 26,166)( 27,171)( 28,176)( 29,178)( 30,174)( 31,179)
( 32,172)( 33,177)( 34,173)( 35,175)( 36,180)( 37,185)( 38,187)( 39,183)
( 40,188)( 41,181)( 42,186)( 43,182)( 44,184)( 45,189)( 46,194)( 47,196)
( 48,192)( 49,197)( 50,190)( 51,195)( 52,191)( 53,193)( 54,198)( 55,203)
( 56,205)( 57,201)( 58,206)( 59,199)( 60,204)( 61,200)( 62,202)( 63,207)
( 64,212)( 65,214)( 66,210)( 67,215)( 68,208)( 69,213)( 70,209)( 71,211)
( 72,216)( 73,230)( 74,232)( 75,228)( 76,233)( 77,226)( 78,231)( 79,227)
( 80,229)( 81,234)( 82,221)( 83,223)( 84,219)( 85,224)( 86,217)( 87,222)
( 88,218)( 89,220)( 90,225)( 91,248)( 92,250)( 93,246)( 94,251)( 95,244)
( 96,249)( 97,245)( 98,247)( 99,252)(100,239)(101,241)(102,237)(103,242)
(104,235)(105,240)(106,236)(107,238)(108,243)(109,266)(110,268)(111,264)
(112,269)(113,262)(114,267)(115,263)(116,265)(117,270)(118,257)(119,259)
(120,255)(121,260)(122,253)(123,258)(124,254)(125,256)(126,261)(127,284)
(128,286)(129,282)(130,287)(131,280)(132,285)(133,281)(134,283)(135,288)
(136,275)(137,277)(138,273)(139,278)(140,271)(141,276)(142,272)(143,274)
(144,279)(289,437)(290,439)(291,435)(292,440)(293,433)(294,438)(295,434)
(296,436)(297,441)(298,446)(299,448)(300,444)(301,449)(302,442)(303,447)
(304,443)(305,445)(306,450)(307,455)(308,457)(309,453)(310,458)(311,451)
(312,456)(313,452)(314,454)(315,459)(316,464)(317,466)(318,462)(319,467)
(320,460)(321,465)(322,461)(323,463)(324,468)(325,473)(326,475)(327,471)
(328,476)(329,469)(330,474)(331,470)(332,472)(333,477)(334,482)(335,484)
(336,480)(337,485)(338,478)(339,483)(340,479)(341,481)(342,486)(343,491)
(344,493)(345,489)(346,494)(347,487)(348,492)(349,488)(350,490)(351,495)
(352,500)(353,502)(354,498)(355,503)(356,496)(357,501)(358,497)(359,499)
(360,504)(361,518)(362,520)(363,516)(364,521)(365,514)(366,519)(367,515)
(368,517)(369,522)(370,509)(371,511)(372,507)(373,512)(374,505)(375,510)
(376,506)(377,508)(378,513)(379,536)(380,538)(381,534)(382,539)(383,532)
(384,537)(385,533)(386,535)(387,540)(388,527)(389,529)(390,525)(391,530)
(392,523)(393,528)(394,524)(395,526)(396,531)(397,554)(398,556)(399,552)
(400,557)(401,550)(402,555)(403,551)(404,553)(405,558)(406,545)(407,547)
(408,543)(409,548)(410,541)(411,546)(412,542)(413,544)(414,549)(415,572)
(416,574)(417,570)(418,575)(419,568)(420,573)(421,569)(422,571)(423,576)
(424,563)(425,565)(426,561)(427,566)(428,559)(429,564)(430,560)(431,562)
(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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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,
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