Polytope of Type {4,8,22}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,22}*1408a
Also Known As : {{4,8|2},{8,22|2}}. if this polytope has another name.
Group : SmallGroup(1408,13683)
Rank : 4
Schlafli Type : {4,8,22}
Number of vertices, edges, etc : 4, 16, 88, 22
Order of s0s1s2s3 : 88
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {4,4,22}*704, {2,8,22}*704
4-fold quotients : {2,4,22}*352, {4,2,22}*352
8-fold quotients : {4,2,11}*176, {2,2,22}*176
11-fold quotients : {4,8,2}*128a
16-fold quotients : {2,2,11}*88
22-fold quotients : {4,4,2}*64, {2,8,2}*64
44-fold quotients : {2,4,2}*32, {4,2,2}*32
88-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,177)( 2,178)( 3,179)( 4,180)( 5,181)( 6,182)( 7,183)( 8,184)
( 9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)( 16,192)
( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)( 24,200)
( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)( 32,208)
( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)( 40,216)
( 41,217)( 42,218)( 43,219)( 44,220)( 45,221)( 46,222)( 47,223)( 48,224)
( 49,225)( 50,226)( 51,227)( 52,228)( 53,229)( 54,230)( 55,231)( 56,232)
( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)( 64,240)
( 65,241)( 66,242)( 67,243)( 68,244)( 69,245)( 70,246)( 71,247)( 72,248)
( 73,249)( 74,250)( 75,251)( 76,252)( 77,253)( 78,254)( 79,255)( 80,256)
( 81,257)( 82,258)( 83,259)( 84,260)( 85,261)( 86,262)( 87,263)( 88,264)
( 89,265)( 90,266)( 91,267)( 92,268)( 93,269)( 94,270)( 95,271)( 96,272)
( 97,273)( 98,274)( 99,275)(100,276)(101,277)(102,278)(103,279)(104,280)
(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)(112,288)
(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)(120,296)
(121,297)(122,298)(123,299)(124,300)(125,301)(126,302)(127,303)(128,304)
(129,305)(130,306)(131,307)(132,308)(133,309)(134,310)(135,311)(136,312)
(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)(144,320)
(145,321)(146,322)(147,323)(148,324)(149,325)(150,326)(151,327)(152,328)
(153,329)(154,330)(155,331)(156,332)(157,333)(158,334)(159,335)(160,336)
(161,337)(162,338)(163,339)(164,340)(165,341)(166,342)(167,343)(168,344)
(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)(176,352)
(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)(360,536)
(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)(368,544)
(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)(376,552)
(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)(384,560)
(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)(392,568)
(393,569)(394,570)(395,571)(396,572)(397,573)(398,574)(399,575)(400,576)
(401,577)(402,578)(403,579)(404,580)(405,581)(406,582)(407,583)(408,584)
(409,585)(410,586)(411,587)(412,588)(413,589)(414,590)(415,591)(416,592)
(417,593)(418,594)(419,595)(420,596)(421,597)(422,598)(423,599)(424,600)
(425,601)(426,602)(427,603)(428,604)(429,605)(430,606)(431,607)(432,608)
(433,609)(434,610)(435,611)(436,612)(437,613)(438,614)(439,615)(440,616)
(441,617)(442,618)(443,619)(444,620)(445,621)(446,622)(447,623)(448,624)
(449,625)(450,626)(451,627)(452,628)(453,629)(454,630)(455,631)(456,632)
(457,633)(458,634)(459,635)(460,636)(461,637)(462,638)(463,639)(464,640)
(465,641)(466,642)(467,643)(468,644)(469,645)(470,646)(471,647)(472,648)
(473,649)(474,650)(475,651)(476,652)(477,653)(478,654)(479,655)(480,656)
(481,657)(482,658)(483,659)(484,660)(485,661)(486,662)(487,663)(488,664)
(489,665)(490,666)(491,667)(492,668)(493,669)(494,670)(495,671)(496,672)
(497,673)(498,674)(499,675)(500,676)(501,677)(502,678)(503,679)(504,680)
(505,681)(506,682)(507,683)(508,684)(509,685)(510,686)(511,687)(512,688)
(513,689)(514,690)(515,691)(516,692)(517,693)(518,694)(519,695)(520,696)
(521,697)(522,698)(523,699)(524,700)(525,701)(526,702)(527,703)(528,704);;
s1 := ( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)
( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)
( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(133,144)(134,145)
(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)(142,153)
(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)
(162,173)(163,174)(164,175)(165,176)(177,199)(178,200)(179,201)(180,202)
(181,203)(182,204)(183,205)(184,206)(185,207)(186,208)(187,209)(188,210)
(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)
(197,219)(198,220)(221,254)(222,255)(223,256)(224,257)(225,258)(226,259)
(227,260)(228,261)(229,262)(230,263)(231,264)(232,243)(233,244)(234,245)
(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)
(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)
(273,295)(274,296)(275,297)(276,298)(277,299)(278,300)(279,301)(280,302)
(281,303)(282,304)(283,305)(284,306)(285,307)(286,308)(309,342)(310,343)
(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)(318,351)
(319,352)(320,331)(321,332)(322,333)(323,334)(324,335)(325,336)(326,337)
(327,338)(328,339)(329,340)(330,341)(353,397)(354,398)(355,399)(356,400)
(357,401)(358,402)(359,403)(360,404)(361,405)(362,406)(363,407)(364,408)
(365,409)(366,410)(367,411)(368,412)(369,413)(370,414)(371,415)(372,416)
(373,417)(374,418)(375,419)(376,420)(377,421)(378,422)(379,423)(380,424)
(381,425)(382,426)(383,427)(384,428)(385,429)(386,430)(387,431)(388,432)
(389,433)(390,434)(391,435)(392,436)(393,437)(394,438)(395,439)(396,440)
(441,485)(442,486)(443,487)(444,488)(445,489)(446,490)(447,491)(448,492)
(449,493)(450,494)(451,495)(452,496)(453,497)(454,498)(455,499)(456,500)
(457,501)(458,502)(459,503)(460,504)(461,505)(462,506)(463,507)(464,508)
(465,509)(466,510)(467,511)(468,512)(469,513)(470,514)(471,515)(472,516)
(473,517)(474,518)(475,519)(476,520)(477,521)(478,522)(479,523)(480,524)
(481,525)(482,526)(483,527)(484,528)(529,595)(530,596)(531,597)(532,598)
(533,599)(534,600)(535,601)(536,602)(537,603)(538,604)(539,605)(540,606)
(541,607)(542,608)(543,609)(544,610)(545,611)(546,612)(547,613)(548,614)
(549,615)(550,616)(551,573)(552,574)(553,575)(554,576)(555,577)(556,578)
(557,579)(558,580)(559,581)(560,582)(561,583)(562,584)(563,585)(564,586)
(565,587)(566,588)(567,589)(568,590)(569,591)(570,592)(571,593)(572,594)
(617,683)(618,684)(619,685)(620,686)(621,687)(622,688)(623,689)(624,690)
(625,691)(626,692)(627,693)(628,694)(629,695)(630,696)(631,697)(632,698)
(633,699)(634,700)(635,701)(636,702)(637,703)(638,704)(639,661)(640,662)
(641,663)(642,664)(643,665)(644,666)(645,667)(646,668)(647,669)(648,670)
(649,671)(650,672)(651,673)(652,674)(653,675)(654,676)(655,677)(656,678)
(657,679)(658,680)(659,681)(660,682);;
s2 := ( 1,441)( 2,451)( 3,450)( 4,449)( 5,448)( 6,447)( 7,446)( 8,445)
( 9,444)( 10,443)( 11,442)( 12,452)( 13,462)( 14,461)( 15,460)( 16,459)
( 17,458)( 18,457)( 19,456)( 20,455)( 21,454)( 22,453)( 23,463)( 24,473)
( 25,472)( 26,471)( 27,470)( 28,469)( 29,468)( 30,467)( 31,466)( 32,465)
( 33,464)( 34,474)( 35,484)( 36,483)( 37,482)( 38,481)( 39,480)( 40,479)
( 41,478)( 42,477)( 43,476)( 44,475)( 45,496)( 46,506)( 47,505)( 48,504)
( 49,503)( 50,502)( 51,501)( 52,500)( 53,499)( 54,498)( 55,497)( 56,485)
( 57,495)( 58,494)( 59,493)( 60,492)( 61,491)( 62,490)( 63,489)( 64,488)
( 65,487)( 66,486)( 67,518)( 68,528)( 69,527)( 70,526)( 71,525)( 72,524)
( 73,523)( 74,522)( 75,521)( 76,520)( 77,519)( 78,507)( 79,517)( 80,516)
( 81,515)( 82,514)( 83,513)( 84,512)( 85,511)( 86,510)( 87,509)( 88,508)
( 89,353)( 90,363)( 91,362)( 92,361)( 93,360)( 94,359)( 95,358)( 96,357)
( 97,356)( 98,355)( 99,354)(100,364)(101,374)(102,373)(103,372)(104,371)
(105,370)(106,369)(107,368)(108,367)(109,366)(110,365)(111,375)(112,385)
(113,384)(114,383)(115,382)(116,381)(117,380)(118,379)(119,378)(120,377)
(121,376)(122,386)(123,396)(124,395)(125,394)(126,393)(127,392)(128,391)
(129,390)(130,389)(131,388)(132,387)(133,408)(134,418)(135,417)(136,416)
(137,415)(138,414)(139,413)(140,412)(141,411)(142,410)(143,409)(144,397)
(145,407)(146,406)(147,405)(148,404)(149,403)(150,402)(151,401)(152,400)
(153,399)(154,398)(155,430)(156,440)(157,439)(158,438)(159,437)(160,436)
(161,435)(162,434)(163,433)(164,432)(165,431)(166,419)(167,429)(168,428)
(169,427)(170,426)(171,425)(172,424)(173,423)(174,422)(175,421)(176,420)
(177,617)(178,627)(179,626)(180,625)(181,624)(182,623)(183,622)(184,621)
(185,620)(186,619)(187,618)(188,628)(189,638)(190,637)(191,636)(192,635)
(193,634)(194,633)(195,632)(196,631)(197,630)(198,629)(199,639)(200,649)
(201,648)(202,647)(203,646)(204,645)(205,644)(206,643)(207,642)(208,641)
(209,640)(210,650)(211,660)(212,659)(213,658)(214,657)(215,656)(216,655)
(217,654)(218,653)(219,652)(220,651)(221,672)(222,682)(223,681)(224,680)
(225,679)(226,678)(227,677)(228,676)(229,675)(230,674)(231,673)(232,661)
(233,671)(234,670)(235,669)(236,668)(237,667)(238,666)(239,665)(240,664)
(241,663)(242,662)(243,694)(244,704)(245,703)(246,702)(247,701)(248,700)
(249,699)(250,698)(251,697)(252,696)(253,695)(254,683)(255,693)(256,692)
(257,691)(258,690)(259,689)(260,688)(261,687)(262,686)(263,685)(264,684)
(265,529)(266,539)(267,538)(268,537)(269,536)(270,535)(271,534)(272,533)
(273,532)(274,531)(275,530)(276,540)(277,550)(278,549)(279,548)(280,547)
(281,546)(282,545)(283,544)(284,543)(285,542)(286,541)(287,551)(288,561)
(289,560)(290,559)(291,558)(292,557)(293,556)(294,555)(295,554)(296,553)
(297,552)(298,562)(299,572)(300,571)(301,570)(302,569)(303,568)(304,567)
(305,566)(306,565)(307,564)(308,563)(309,584)(310,594)(311,593)(312,592)
(313,591)(314,590)(315,589)(316,588)(317,587)(318,586)(319,585)(320,573)
(321,583)(322,582)(323,581)(324,580)(325,579)(326,578)(327,577)(328,576)
(329,575)(330,574)(331,606)(332,616)(333,615)(334,614)(335,613)(336,612)
(337,611)(338,610)(339,609)(340,608)(341,607)(342,595)(343,605)(344,604)
(345,603)(346,602)(347,601)(348,600)(349,599)(350,598)(351,597)(352,596);;
s3 := ( 1, 90)( 2, 89)( 3, 99)( 4, 98)( 5, 97)( 6, 96)( 7, 95)( 8, 94)
( 9, 93)( 10, 92)( 11, 91)( 12,101)( 13,100)( 14,110)( 15,109)( 16,108)
( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,112)( 24,111)
( 25,121)( 26,120)( 27,119)( 28,118)( 29,117)( 30,116)( 31,115)( 32,114)
( 33,113)( 34,123)( 35,122)( 36,132)( 37,131)( 38,130)( 39,129)( 40,128)
( 41,127)( 42,126)( 43,125)( 44,124)( 45,134)( 46,133)( 47,143)( 48,142)
( 49,141)( 50,140)( 51,139)( 52,138)( 53,137)( 54,136)( 55,135)( 56,145)
( 57,144)( 58,154)( 59,153)( 60,152)( 61,151)( 62,150)( 63,149)( 64,148)
( 65,147)( 66,146)( 67,156)( 68,155)( 69,165)( 70,164)( 71,163)( 72,162)
( 73,161)( 74,160)( 75,159)( 76,158)( 77,157)( 78,167)( 79,166)( 80,176)
( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)( 88,168)
(177,266)(178,265)(179,275)(180,274)(181,273)(182,272)(183,271)(184,270)
(185,269)(186,268)(187,267)(188,277)(189,276)(190,286)(191,285)(192,284)
(193,283)(194,282)(195,281)(196,280)(197,279)(198,278)(199,288)(200,287)
(201,297)(202,296)(203,295)(204,294)(205,293)(206,292)(207,291)(208,290)
(209,289)(210,299)(211,298)(212,308)(213,307)(214,306)(215,305)(216,304)
(217,303)(218,302)(219,301)(220,300)(221,310)(222,309)(223,319)(224,318)
(225,317)(226,316)(227,315)(228,314)(229,313)(230,312)(231,311)(232,321)
(233,320)(234,330)(235,329)(236,328)(237,327)(238,326)(239,325)(240,324)
(241,323)(242,322)(243,332)(244,331)(245,341)(246,340)(247,339)(248,338)
(249,337)(250,336)(251,335)(252,334)(253,333)(254,343)(255,342)(256,352)
(257,351)(258,350)(259,349)(260,348)(261,347)(262,346)(263,345)(264,344)
(353,442)(354,441)(355,451)(356,450)(357,449)(358,448)(359,447)(360,446)
(361,445)(362,444)(363,443)(364,453)(365,452)(366,462)(367,461)(368,460)
(369,459)(370,458)(371,457)(372,456)(373,455)(374,454)(375,464)(376,463)
(377,473)(378,472)(379,471)(380,470)(381,469)(382,468)(383,467)(384,466)
(385,465)(386,475)(387,474)(388,484)(389,483)(390,482)(391,481)(392,480)
(393,479)(394,478)(395,477)(396,476)(397,486)(398,485)(399,495)(400,494)
(401,493)(402,492)(403,491)(404,490)(405,489)(406,488)(407,487)(408,497)
(409,496)(410,506)(411,505)(412,504)(413,503)(414,502)(415,501)(416,500)
(417,499)(418,498)(419,508)(420,507)(421,517)(422,516)(423,515)(424,514)
(425,513)(426,512)(427,511)(428,510)(429,509)(430,519)(431,518)(432,528)
(433,527)(434,526)(435,525)(436,524)(437,523)(438,522)(439,521)(440,520)
(529,618)(530,617)(531,627)(532,626)(533,625)(534,624)(535,623)(536,622)
(537,621)(538,620)(539,619)(540,629)(541,628)(542,638)(543,637)(544,636)
(545,635)(546,634)(547,633)(548,632)(549,631)(550,630)(551,640)(552,639)
(553,649)(554,648)(555,647)(556,646)(557,645)(558,644)(559,643)(560,642)
(561,641)(562,651)(563,650)(564,660)(565,659)(566,658)(567,657)(568,656)
(569,655)(570,654)(571,653)(572,652)(573,662)(574,661)(575,671)(576,670)
(577,669)(578,668)(579,667)(580,666)(581,665)(582,664)(583,663)(584,673)
(585,672)(586,682)(587,681)(588,680)(589,679)(590,678)(591,677)(592,676)
(593,675)(594,674)(595,684)(596,683)(597,693)(598,692)(599,691)(600,690)
(601,689)(602,688)(603,687)(604,686)(605,685)(606,695)(607,694)(608,704)
(609,703)(610,702)(611,701)(612,700)(613,699)(614,698)(615,697)(616,696);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(704)!( 1,177)( 2,178)( 3,179)( 4,180)( 5,181)( 6,182)( 7,183)
( 8,184)( 9,185)( 10,186)( 11,187)( 12,188)( 13,189)( 14,190)( 15,191)
( 16,192)( 17,193)( 18,194)( 19,195)( 20,196)( 21,197)( 22,198)( 23,199)
( 24,200)( 25,201)( 26,202)( 27,203)( 28,204)( 29,205)( 30,206)( 31,207)
( 32,208)( 33,209)( 34,210)( 35,211)( 36,212)( 37,213)( 38,214)( 39,215)
( 40,216)( 41,217)( 42,218)( 43,219)( 44,220)( 45,221)( 46,222)( 47,223)
( 48,224)( 49,225)( 50,226)( 51,227)( 52,228)( 53,229)( 54,230)( 55,231)
( 56,232)( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)
( 64,240)( 65,241)( 66,242)( 67,243)( 68,244)( 69,245)( 70,246)( 71,247)
( 72,248)( 73,249)( 74,250)( 75,251)( 76,252)( 77,253)( 78,254)( 79,255)
( 80,256)( 81,257)( 82,258)( 83,259)( 84,260)( 85,261)( 86,262)( 87,263)
( 88,264)( 89,265)( 90,266)( 91,267)( 92,268)( 93,269)( 94,270)( 95,271)
( 96,272)( 97,273)( 98,274)( 99,275)(100,276)(101,277)(102,278)(103,279)
(104,280)(105,281)(106,282)(107,283)(108,284)(109,285)(110,286)(111,287)
(112,288)(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)
(120,296)(121,297)(122,298)(123,299)(124,300)(125,301)(126,302)(127,303)
(128,304)(129,305)(130,306)(131,307)(132,308)(133,309)(134,310)(135,311)
(136,312)(137,313)(138,314)(139,315)(140,316)(141,317)(142,318)(143,319)
(144,320)(145,321)(146,322)(147,323)(148,324)(149,325)(150,326)(151,327)
(152,328)(153,329)(154,330)(155,331)(156,332)(157,333)(158,334)(159,335)
(160,336)(161,337)(162,338)(163,339)(164,340)(165,341)(166,342)(167,343)
(168,344)(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)
(176,352)(353,529)(354,530)(355,531)(356,532)(357,533)(358,534)(359,535)
(360,536)(361,537)(362,538)(363,539)(364,540)(365,541)(366,542)(367,543)
(368,544)(369,545)(370,546)(371,547)(372,548)(373,549)(374,550)(375,551)
(376,552)(377,553)(378,554)(379,555)(380,556)(381,557)(382,558)(383,559)
(384,560)(385,561)(386,562)(387,563)(388,564)(389,565)(390,566)(391,567)
(392,568)(393,569)(394,570)(395,571)(396,572)(397,573)(398,574)(399,575)
(400,576)(401,577)(402,578)(403,579)(404,580)(405,581)(406,582)(407,583)
(408,584)(409,585)(410,586)(411,587)(412,588)(413,589)(414,590)(415,591)
(416,592)(417,593)(418,594)(419,595)(420,596)(421,597)(422,598)(423,599)
(424,600)(425,601)(426,602)(427,603)(428,604)(429,605)(430,606)(431,607)
(432,608)(433,609)(434,610)(435,611)(436,612)(437,613)(438,614)(439,615)
(440,616)(441,617)(442,618)(443,619)(444,620)(445,621)(446,622)(447,623)
(448,624)(449,625)(450,626)(451,627)(452,628)(453,629)(454,630)(455,631)
(456,632)(457,633)(458,634)(459,635)(460,636)(461,637)(462,638)(463,639)
(464,640)(465,641)(466,642)(467,643)(468,644)(469,645)(470,646)(471,647)
(472,648)(473,649)(474,650)(475,651)(476,652)(477,653)(478,654)(479,655)
(480,656)(481,657)(482,658)(483,659)(484,660)(485,661)(486,662)(487,663)
(488,664)(489,665)(490,666)(491,667)(492,668)(493,669)(494,670)(495,671)
(496,672)(497,673)(498,674)(499,675)(500,676)(501,677)(502,678)(503,679)
(504,680)(505,681)(506,682)(507,683)(508,684)(509,685)(510,686)(511,687)
(512,688)(513,689)(514,690)(515,691)(516,692)(517,693)(518,694)(519,695)
(520,696)(521,697)(522,698)(523,699)(524,700)(525,701)(526,702)(527,703)
(528,704);
s1 := Sym(704)!( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)
( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)
( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(133,144)
(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)
(142,153)(143,154)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)
(161,172)(162,173)(163,174)(164,175)(165,176)(177,199)(178,200)(179,201)
(180,202)(181,203)(182,204)(183,205)(184,206)(185,207)(186,208)(187,209)
(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)
(196,218)(197,219)(198,220)(221,254)(222,255)(223,256)(224,257)(225,258)
(226,259)(227,260)(228,261)(229,262)(230,263)(231,264)(232,243)(233,244)
(234,245)(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)
(242,253)(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)
(272,294)(273,295)(274,296)(275,297)(276,298)(277,299)(278,300)(279,301)
(280,302)(281,303)(282,304)(283,305)(284,306)(285,307)(286,308)(309,342)
(310,343)(311,344)(312,345)(313,346)(314,347)(315,348)(316,349)(317,350)
(318,351)(319,352)(320,331)(321,332)(322,333)(323,334)(324,335)(325,336)
(326,337)(327,338)(328,339)(329,340)(330,341)(353,397)(354,398)(355,399)
(356,400)(357,401)(358,402)(359,403)(360,404)(361,405)(362,406)(363,407)
(364,408)(365,409)(366,410)(367,411)(368,412)(369,413)(370,414)(371,415)
(372,416)(373,417)(374,418)(375,419)(376,420)(377,421)(378,422)(379,423)
(380,424)(381,425)(382,426)(383,427)(384,428)(385,429)(386,430)(387,431)
(388,432)(389,433)(390,434)(391,435)(392,436)(393,437)(394,438)(395,439)
(396,440)(441,485)(442,486)(443,487)(444,488)(445,489)(446,490)(447,491)
(448,492)(449,493)(450,494)(451,495)(452,496)(453,497)(454,498)(455,499)
(456,500)(457,501)(458,502)(459,503)(460,504)(461,505)(462,506)(463,507)
(464,508)(465,509)(466,510)(467,511)(468,512)(469,513)(470,514)(471,515)
(472,516)(473,517)(474,518)(475,519)(476,520)(477,521)(478,522)(479,523)
(480,524)(481,525)(482,526)(483,527)(484,528)(529,595)(530,596)(531,597)
(532,598)(533,599)(534,600)(535,601)(536,602)(537,603)(538,604)(539,605)
(540,606)(541,607)(542,608)(543,609)(544,610)(545,611)(546,612)(547,613)
(548,614)(549,615)(550,616)(551,573)(552,574)(553,575)(554,576)(555,577)
(556,578)(557,579)(558,580)(559,581)(560,582)(561,583)(562,584)(563,585)
(564,586)(565,587)(566,588)(567,589)(568,590)(569,591)(570,592)(571,593)
(572,594)(617,683)(618,684)(619,685)(620,686)(621,687)(622,688)(623,689)
(624,690)(625,691)(626,692)(627,693)(628,694)(629,695)(630,696)(631,697)
(632,698)(633,699)(634,700)(635,701)(636,702)(637,703)(638,704)(639,661)
(640,662)(641,663)(642,664)(643,665)(644,666)(645,667)(646,668)(647,669)
(648,670)(649,671)(650,672)(651,673)(652,674)(653,675)(654,676)(655,677)
(656,678)(657,679)(658,680)(659,681)(660,682);
s2 := Sym(704)!( 1,441)( 2,451)( 3,450)( 4,449)( 5,448)( 6,447)( 7,446)
( 8,445)( 9,444)( 10,443)( 11,442)( 12,452)( 13,462)( 14,461)( 15,460)
( 16,459)( 17,458)( 18,457)( 19,456)( 20,455)( 21,454)( 22,453)( 23,463)
( 24,473)( 25,472)( 26,471)( 27,470)( 28,469)( 29,468)( 30,467)( 31,466)
( 32,465)( 33,464)( 34,474)( 35,484)( 36,483)( 37,482)( 38,481)( 39,480)
( 40,479)( 41,478)( 42,477)( 43,476)( 44,475)( 45,496)( 46,506)( 47,505)
( 48,504)( 49,503)( 50,502)( 51,501)( 52,500)( 53,499)( 54,498)( 55,497)
( 56,485)( 57,495)( 58,494)( 59,493)( 60,492)( 61,491)( 62,490)( 63,489)
( 64,488)( 65,487)( 66,486)( 67,518)( 68,528)( 69,527)( 70,526)( 71,525)
( 72,524)( 73,523)( 74,522)( 75,521)( 76,520)( 77,519)( 78,507)( 79,517)
( 80,516)( 81,515)( 82,514)( 83,513)( 84,512)( 85,511)( 86,510)( 87,509)
( 88,508)( 89,353)( 90,363)( 91,362)( 92,361)( 93,360)( 94,359)( 95,358)
( 96,357)( 97,356)( 98,355)( 99,354)(100,364)(101,374)(102,373)(103,372)
(104,371)(105,370)(106,369)(107,368)(108,367)(109,366)(110,365)(111,375)
(112,385)(113,384)(114,383)(115,382)(116,381)(117,380)(118,379)(119,378)
(120,377)(121,376)(122,386)(123,396)(124,395)(125,394)(126,393)(127,392)
(128,391)(129,390)(130,389)(131,388)(132,387)(133,408)(134,418)(135,417)
(136,416)(137,415)(138,414)(139,413)(140,412)(141,411)(142,410)(143,409)
(144,397)(145,407)(146,406)(147,405)(148,404)(149,403)(150,402)(151,401)
(152,400)(153,399)(154,398)(155,430)(156,440)(157,439)(158,438)(159,437)
(160,436)(161,435)(162,434)(163,433)(164,432)(165,431)(166,419)(167,429)
(168,428)(169,427)(170,426)(171,425)(172,424)(173,423)(174,422)(175,421)
(176,420)(177,617)(178,627)(179,626)(180,625)(181,624)(182,623)(183,622)
(184,621)(185,620)(186,619)(187,618)(188,628)(189,638)(190,637)(191,636)
(192,635)(193,634)(194,633)(195,632)(196,631)(197,630)(198,629)(199,639)
(200,649)(201,648)(202,647)(203,646)(204,645)(205,644)(206,643)(207,642)
(208,641)(209,640)(210,650)(211,660)(212,659)(213,658)(214,657)(215,656)
(216,655)(217,654)(218,653)(219,652)(220,651)(221,672)(222,682)(223,681)
(224,680)(225,679)(226,678)(227,677)(228,676)(229,675)(230,674)(231,673)
(232,661)(233,671)(234,670)(235,669)(236,668)(237,667)(238,666)(239,665)
(240,664)(241,663)(242,662)(243,694)(244,704)(245,703)(246,702)(247,701)
(248,700)(249,699)(250,698)(251,697)(252,696)(253,695)(254,683)(255,693)
(256,692)(257,691)(258,690)(259,689)(260,688)(261,687)(262,686)(263,685)
(264,684)(265,529)(266,539)(267,538)(268,537)(269,536)(270,535)(271,534)
(272,533)(273,532)(274,531)(275,530)(276,540)(277,550)(278,549)(279,548)
(280,547)(281,546)(282,545)(283,544)(284,543)(285,542)(286,541)(287,551)
(288,561)(289,560)(290,559)(291,558)(292,557)(293,556)(294,555)(295,554)
(296,553)(297,552)(298,562)(299,572)(300,571)(301,570)(302,569)(303,568)
(304,567)(305,566)(306,565)(307,564)(308,563)(309,584)(310,594)(311,593)
(312,592)(313,591)(314,590)(315,589)(316,588)(317,587)(318,586)(319,585)
(320,573)(321,583)(322,582)(323,581)(324,580)(325,579)(326,578)(327,577)
(328,576)(329,575)(330,574)(331,606)(332,616)(333,615)(334,614)(335,613)
(336,612)(337,611)(338,610)(339,609)(340,608)(341,607)(342,595)(343,605)
(344,604)(345,603)(346,602)(347,601)(348,600)(349,599)(350,598)(351,597)
(352,596);
s3 := Sym(704)!( 1, 90)( 2, 89)( 3, 99)( 4, 98)( 5, 97)( 6, 96)( 7, 95)
( 8, 94)( 9, 93)( 10, 92)( 11, 91)( 12,101)( 13,100)( 14,110)( 15,109)
( 16,108)( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,112)
( 24,111)( 25,121)( 26,120)( 27,119)( 28,118)( 29,117)( 30,116)( 31,115)
( 32,114)( 33,113)( 34,123)( 35,122)( 36,132)( 37,131)( 38,130)( 39,129)
( 40,128)( 41,127)( 42,126)( 43,125)( 44,124)( 45,134)( 46,133)( 47,143)
( 48,142)( 49,141)( 50,140)( 51,139)( 52,138)( 53,137)( 54,136)( 55,135)
( 56,145)( 57,144)( 58,154)( 59,153)( 60,152)( 61,151)( 62,150)( 63,149)
( 64,148)( 65,147)( 66,146)( 67,156)( 68,155)( 69,165)( 70,164)( 71,163)
( 72,162)( 73,161)( 74,160)( 75,159)( 76,158)( 77,157)( 78,167)( 79,166)
( 80,176)( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)
( 88,168)(177,266)(178,265)(179,275)(180,274)(181,273)(182,272)(183,271)
(184,270)(185,269)(186,268)(187,267)(188,277)(189,276)(190,286)(191,285)
(192,284)(193,283)(194,282)(195,281)(196,280)(197,279)(198,278)(199,288)
(200,287)(201,297)(202,296)(203,295)(204,294)(205,293)(206,292)(207,291)
(208,290)(209,289)(210,299)(211,298)(212,308)(213,307)(214,306)(215,305)
(216,304)(217,303)(218,302)(219,301)(220,300)(221,310)(222,309)(223,319)
(224,318)(225,317)(226,316)(227,315)(228,314)(229,313)(230,312)(231,311)
(232,321)(233,320)(234,330)(235,329)(236,328)(237,327)(238,326)(239,325)
(240,324)(241,323)(242,322)(243,332)(244,331)(245,341)(246,340)(247,339)
(248,338)(249,337)(250,336)(251,335)(252,334)(253,333)(254,343)(255,342)
(256,352)(257,351)(258,350)(259,349)(260,348)(261,347)(262,346)(263,345)
(264,344)(353,442)(354,441)(355,451)(356,450)(357,449)(358,448)(359,447)
(360,446)(361,445)(362,444)(363,443)(364,453)(365,452)(366,462)(367,461)
(368,460)(369,459)(370,458)(371,457)(372,456)(373,455)(374,454)(375,464)
(376,463)(377,473)(378,472)(379,471)(380,470)(381,469)(382,468)(383,467)
(384,466)(385,465)(386,475)(387,474)(388,484)(389,483)(390,482)(391,481)
(392,480)(393,479)(394,478)(395,477)(396,476)(397,486)(398,485)(399,495)
(400,494)(401,493)(402,492)(403,491)(404,490)(405,489)(406,488)(407,487)
(408,497)(409,496)(410,506)(411,505)(412,504)(413,503)(414,502)(415,501)
(416,500)(417,499)(418,498)(419,508)(420,507)(421,517)(422,516)(423,515)
(424,514)(425,513)(426,512)(427,511)(428,510)(429,509)(430,519)(431,518)
(432,528)(433,527)(434,526)(435,525)(436,524)(437,523)(438,522)(439,521)
(440,520)(529,618)(530,617)(531,627)(532,626)(533,625)(534,624)(535,623)
(536,622)(537,621)(538,620)(539,619)(540,629)(541,628)(542,638)(543,637)
(544,636)(545,635)(546,634)(547,633)(548,632)(549,631)(550,630)(551,640)
(552,639)(553,649)(554,648)(555,647)(556,646)(557,645)(558,644)(559,643)
(560,642)(561,641)(562,651)(563,650)(564,660)(565,659)(566,658)(567,657)
(568,656)(569,655)(570,654)(571,653)(572,652)(573,662)(574,661)(575,671)
(576,670)(577,669)(578,668)(579,667)(580,666)(581,665)(582,664)(583,663)
(584,673)(585,672)(586,682)(587,681)(588,680)(589,679)(590,678)(591,677)
(592,676)(593,675)(594,674)(595,684)(596,683)(597,693)(598,692)(599,691)
(600,690)(601,689)(602,688)(603,687)(604,686)(605,685)(606,695)(607,694)
(608,704)(609,703)(610,702)(611,701)(612,700)(613,699)(614,698)(615,697)
(616,696);
poly := sub<Sym(704)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope