Polytope of Type {72,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {72,8}*1152c
Also Known As : {72,8|2}. if this polytope has another name.
Group : SmallGroup(1152,12903)
Rank : 3
Schlafli Type : {72,8}
Number of vertices, edges, etc : 72, 288, 8
Order of s0s1s2 : 72
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {72,4}*576a, {36,8}*576a
3-fold quotients : {24,8}*384b
4-fold quotients : {36,4}*288a, {72,2}*288, {18,8}*288
6-fold quotients : {24,4}*192a, {12,8}*192a
8-fold quotients : {36,2}*144, {18,4}*144a
9-fold quotients : {8,8}*128b
12-fold quotients : {12,4}*96a, {24,2}*96, {6,8}*96
16-fold quotients : {18,2}*72
18-fold quotients : {4,8}*64a, {8,4}*64a
24-fold quotients : {12,2}*48, {6,4}*48a
32-fold quotients : {9,2}*36
36-fold quotients : {4,4}*32, {2,8}*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 := ( 1,433)( 2,435)( 3,434)( 4,441)( 5,440)( 6,439)( 7,438)( 8,437)
( 9,436)( 10,442)( 11,444)( 12,443)( 13,450)( 14,449)( 15,448)( 16,447)
( 17,446)( 18,445)( 19,451)( 20,453)( 21,452)( 22,459)( 23,458)( 24,457)
( 25,456)( 26,455)( 27,454)( 28,460)( 29,462)( 30,461)( 31,468)( 32,467)
( 33,466)( 34,465)( 35,464)( 36,463)( 37,469)( 38,471)( 39,470)( 40,477)
( 41,476)( 42,475)( 43,474)( 44,473)( 45,472)( 46,478)( 47,480)( 48,479)
( 49,486)( 50,485)( 51,484)( 52,483)( 53,482)( 54,481)( 55,487)( 56,489)
( 57,488)( 58,495)( 59,494)( 60,493)( 61,492)( 62,491)( 63,490)( 64,496)
( 65,498)( 66,497)( 67,504)( 68,503)( 69,502)( 70,501)( 71,500)( 72,499)
( 73,532)( 74,534)( 75,533)( 76,540)( 77,539)( 78,538)( 79,537)( 80,536)
( 81,535)( 82,523)( 83,525)( 84,524)( 85,531)( 86,530)( 87,529)( 88,528)
( 89,527)( 90,526)( 91,514)( 92,516)( 93,515)( 94,522)( 95,521)( 96,520)
( 97,519)( 98,518)( 99,517)(100,505)(101,507)(102,506)(103,513)(104,512)
(105,511)(106,510)(107,509)(108,508)(109,568)(110,570)(111,569)(112,576)
(113,575)(114,574)(115,573)(116,572)(117,571)(118,559)(119,561)(120,560)
(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,550)(128,552)
(129,551)(130,558)(131,557)(132,556)(133,555)(134,554)(135,553)(136,541)
(137,543)(138,542)(139,549)(140,548)(141,547)(142,546)(143,545)(144,544)
(145,289)(146,291)(147,290)(148,297)(149,296)(150,295)(151,294)(152,293)
(153,292)(154,298)(155,300)(156,299)(157,306)(158,305)(159,304)(160,303)
(161,302)(162,301)(163,307)(164,309)(165,308)(166,315)(167,314)(168,313)
(169,312)(170,311)(171,310)(172,316)(173,318)(174,317)(175,324)(176,323)
(177,322)(178,321)(179,320)(180,319)(181,325)(182,327)(183,326)(184,333)
(185,332)(186,331)(187,330)(188,329)(189,328)(190,334)(191,336)(192,335)
(193,342)(194,341)(195,340)(196,339)(197,338)(198,337)(199,343)(200,345)
(201,344)(202,351)(203,350)(204,349)(205,348)(206,347)(207,346)(208,352)
(209,354)(210,353)(211,360)(212,359)(213,358)(214,357)(215,356)(216,355)
(217,388)(218,390)(219,389)(220,396)(221,395)(222,394)(223,393)(224,392)
(225,391)(226,379)(227,381)(228,380)(229,387)(230,386)(231,385)(232,384)
(233,383)(234,382)(235,370)(236,372)(237,371)(238,378)(239,377)(240,376)
(241,375)(242,374)(243,373)(244,361)(245,363)(246,362)(247,369)(248,368)
(249,367)(250,366)(251,365)(252,364)(253,424)(254,426)(255,425)(256,432)
(257,431)(258,430)(259,429)(260,428)(261,427)(262,415)(263,417)(264,416)
(265,423)(266,422)(267,421)(268,420)(269,419)(270,418)(271,406)(272,408)
(273,407)(274,414)(275,413)(276,412)(277,411)(278,410)(279,409)(280,397)
(281,399)(282,398)(283,405)(284,404)(285,403)(286,402)(287,401)(288,400);;
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, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 54)( 44, 53)
( 45, 52)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)
( 62, 71)( 63, 70)( 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)(109,139)(110,141)(111,140)(112,136)
(113,138)(114,137)(115,144)(116,143)(117,142)(118,130)(119,132)(120,131)
(121,127)(122,129)(123,128)(124,135)(125,134)(126,133)(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)(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)
(331,414)(332,413)(333,412)(334,400)(335,402)(336,401)(337,397)(338,399)
(339,398)(340,405)(341,404)(342,403)(343,427)(344,429)(345,428)(346,424)
(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)(354,419)
(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(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)( 37,190)( 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);;
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,
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*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)!( 1,433)( 2,435)( 3,434)( 4,441)( 5,440)( 6,439)( 7,438)
( 8,437)( 9,436)( 10,442)( 11,444)( 12,443)( 13,450)( 14,449)( 15,448)
( 16,447)( 17,446)( 18,445)( 19,451)( 20,453)( 21,452)( 22,459)( 23,458)
( 24,457)( 25,456)( 26,455)( 27,454)( 28,460)( 29,462)( 30,461)( 31,468)
( 32,467)( 33,466)( 34,465)( 35,464)( 36,463)( 37,469)( 38,471)( 39,470)
( 40,477)( 41,476)( 42,475)( 43,474)( 44,473)( 45,472)( 46,478)( 47,480)
( 48,479)( 49,486)( 50,485)( 51,484)( 52,483)( 53,482)( 54,481)( 55,487)
( 56,489)( 57,488)( 58,495)( 59,494)( 60,493)( 61,492)( 62,491)( 63,490)
( 64,496)( 65,498)( 66,497)( 67,504)( 68,503)( 69,502)( 70,501)( 71,500)
( 72,499)( 73,532)( 74,534)( 75,533)( 76,540)( 77,539)( 78,538)( 79,537)
( 80,536)( 81,535)( 82,523)( 83,525)( 84,524)( 85,531)( 86,530)( 87,529)
( 88,528)( 89,527)( 90,526)( 91,514)( 92,516)( 93,515)( 94,522)( 95,521)
( 96,520)( 97,519)( 98,518)( 99,517)(100,505)(101,507)(102,506)(103,513)
(104,512)(105,511)(106,510)(107,509)(108,508)(109,568)(110,570)(111,569)
(112,576)(113,575)(114,574)(115,573)(116,572)(117,571)(118,559)(119,561)
(120,560)(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,550)
(128,552)(129,551)(130,558)(131,557)(132,556)(133,555)(134,554)(135,553)
(136,541)(137,543)(138,542)(139,549)(140,548)(141,547)(142,546)(143,545)
(144,544)(145,289)(146,291)(147,290)(148,297)(149,296)(150,295)(151,294)
(152,293)(153,292)(154,298)(155,300)(156,299)(157,306)(158,305)(159,304)
(160,303)(161,302)(162,301)(163,307)(164,309)(165,308)(166,315)(167,314)
(168,313)(169,312)(170,311)(171,310)(172,316)(173,318)(174,317)(175,324)
(176,323)(177,322)(178,321)(179,320)(180,319)(181,325)(182,327)(183,326)
(184,333)(185,332)(186,331)(187,330)(188,329)(189,328)(190,334)(191,336)
(192,335)(193,342)(194,341)(195,340)(196,339)(197,338)(198,337)(199,343)
(200,345)(201,344)(202,351)(203,350)(204,349)(205,348)(206,347)(207,346)
(208,352)(209,354)(210,353)(211,360)(212,359)(213,358)(214,357)(215,356)
(216,355)(217,388)(218,390)(219,389)(220,396)(221,395)(222,394)(223,393)
(224,392)(225,391)(226,379)(227,381)(228,380)(229,387)(230,386)(231,385)
(232,384)(233,383)(234,382)(235,370)(236,372)(237,371)(238,378)(239,377)
(240,376)(241,375)(242,374)(243,373)(244,361)(245,363)(246,362)(247,369)
(248,368)(249,367)(250,366)(251,365)(252,364)(253,424)(254,426)(255,425)
(256,432)(257,431)(258,430)(259,429)(260,428)(261,427)(262,415)(263,417)
(264,416)(265,423)(266,422)(267,421)(268,420)(269,419)(270,418)(271,406)
(272,408)(273,407)(274,414)(275,413)(276,412)(277,411)(278,410)(279,409)
(280,397)(281,399)(282,398)(283,405)(284,404)(285,403)(286,402)(287,401)
(288,400);
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, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 54)
( 44, 53)( 45, 52)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)
( 61, 72)( 62, 71)( 63, 70)( 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)(109,139)(110,141)(111,140)
(112,136)(113,138)(114,137)(115,144)(116,143)(117,142)(118,130)(119,132)
(120,131)(121,127)(122,129)(123,128)(124,135)(125,134)(126,133)(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)(325,409)(326,411)(327,410)(328,406)(329,408)
(330,407)(331,414)(332,413)(333,412)(334,400)(335,402)(336,401)(337,397)
(338,399)(339,398)(340,405)(341,404)(342,403)(343,427)(344,429)(345,428)
(346,424)(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)
(354,419)(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(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)( 37,190)( 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);
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,
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*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