Polytope of Type {26,32}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,32}*1664
Also Known As : {26,32|2}. if this polytope has another name.
Group : SmallGroup(1664,6806)
Rank : 3
Schlafli Type : {26,32}
Number of vertices, edges, etc : 26, 416, 32
Order of s0s1s2 : 416
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 : {26,16}*832
4-fold quotients : {26,8}*416
8-fold quotients : {26,4}*208
13-fold quotients : {2,32}*128
16-fold quotients : {26,2}*104
26-fold quotients : {2,16}*64
32-fold quotients : {13,2}*52
52-fold quotients : {2,8}*32
104-fold quotients : {2,4}*16
208-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,209)( 2,221)( 3,220)( 4,219)( 5,218)( 6,217)( 7,216)( 8,215)
( 9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,222)( 15,234)( 16,233)
( 17,232)( 18,231)( 19,230)( 20,229)( 21,228)( 22,227)( 23,226)( 24,225)
( 25,224)( 26,223)( 27,235)( 28,247)( 29,246)( 30,245)( 31,244)( 32,243)
( 33,242)( 34,241)( 35,240)( 36,239)( 37,238)( 38,237)( 39,236)( 40,248)
( 41,260)( 42,259)( 43,258)( 44,257)( 45,256)( 46,255)( 47,254)( 48,253)
( 49,252)( 50,251)( 51,250)( 52,249)( 53,261)( 54,273)( 55,272)( 56,271)
( 57,270)( 58,269)( 59,268)( 60,267)( 61,266)( 62,265)( 63,264)( 64,263)
( 65,262)( 66,274)( 67,286)( 68,285)( 69,284)( 70,283)( 71,282)( 72,281)
( 73,280)( 74,279)( 75,278)( 76,277)( 77,276)( 78,275)( 79,287)( 80,299)
( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)( 88,291)
( 89,290)( 90,289)( 91,288)( 92,300)( 93,312)( 94,311)( 95,310)( 96,309)
( 97,308)( 98,307)( 99,306)(100,305)(101,304)(102,303)(103,302)(104,301)
(105,313)(106,325)(107,324)(108,323)(109,322)(110,321)(111,320)(112,319)
(113,318)(114,317)(115,316)(116,315)(117,314)(118,326)(119,338)(120,337)
(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,330)(128,329)
(129,328)(130,327)(131,339)(132,351)(133,350)(134,349)(135,348)(136,347)
(137,346)(138,345)(139,344)(140,343)(141,342)(142,341)(143,340)(144,352)
(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)
(153,356)(154,355)(155,354)(156,353)(157,365)(158,377)(159,376)(160,375)
(161,374)(162,373)(163,372)(164,371)(165,370)(166,369)(167,368)(168,367)
(169,366)(170,378)(171,390)(172,389)(173,388)(174,387)(175,386)(176,385)
(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,391)(184,403)
(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)(192,395)
(193,394)(194,393)(195,392)(196,404)(197,416)(198,415)(199,414)(200,413)
(201,412)(202,411)(203,410)(204,409)(205,408)(206,407)(207,406)(208,405)
(417,625)(418,637)(419,636)(420,635)(421,634)(422,633)(423,632)(424,631)
(425,630)(426,629)(427,628)(428,627)(429,626)(430,638)(431,650)(432,649)
(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)(440,641)
(441,640)(442,639)(443,651)(444,663)(445,662)(446,661)(447,660)(448,659)
(449,658)(450,657)(451,656)(452,655)(453,654)(454,653)(455,652)(456,664)
(457,676)(458,675)(459,674)(460,673)(461,672)(462,671)(463,670)(464,669)
(465,668)(466,667)(467,666)(468,665)(469,677)(470,689)(471,688)(472,687)
(473,686)(474,685)(475,684)(476,683)(477,682)(478,681)(479,680)(480,679)
(481,678)(482,690)(483,702)(484,701)(485,700)(486,699)(487,698)(488,697)
(489,696)(490,695)(491,694)(492,693)(493,692)(494,691)(495,703)(496,715)
(497,714)(498,713)(499,712)(500,711)(501,710)(502,709)(503,708)(504,707)
(505,706)(506,705)(507,704)(508,716)(509,728)(510,727)(511,726)(512,725)
(513,724)(514,723)(515,722)(516,721)(517,720)(518,719)(519,718)(520,717)
(521,729)(522,741)(523,740)(524,739)(525,738)(526,737)(527,736)(528,735)
(529,734)(530,733)(531,732)(532,731)(533,730)(534,742)(535,754)(536,753)
(537,752)(538,751)(539,750)(540,749)(541,748)(542,747)(543,746)(544,745)
(545,744)(546,743)(547,755)(548,767)(549,766)(550,765)(551,764)(552,763)
(553,762)(554,761)(555,760)(556,759)(557,758)(558,757)(559,756)(560,768)
(561,780)(562,779)(563,778)(564,777)(565,776)(566,775)(567,774)(568,773)
(569,772)(570,771)(571,770)(572,769)(573,781)(574,793)(575,792)(576,791)
(577,790)(578,789)(579,788)(580,787)(581,786)(582,785)(583,784)(584,783)
(585,782)(586,794)(587,806)(588,805)(589,804)(590,803)(591,802)(592,801)
(593,800)(594,799)(595,798)(596,797)(597,796)(598,795)(599,807)(600,819)
(601,818)(602,817)(603,816)(604,815)(605,814)(606,813)(607,812)(608,811)
(609,810)(610,809)(611,808)(612,820)(613,832)(614,831)(615,830)(616,829)
(617,828)(618,827)(619,826)(620,825)(621,824)(622,823)(623,822)(624,821);;
s1 := ( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)( 8,216)
( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)( 16,234)
( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)
( 25,225)( 26,224)( 27,249)( 28,248)( 29,260)( 30,259)( 31,258)( 32,257)
( 33,256)( 34,255)( 35,254)( 36,253)( 37,252)( 38,251)( 39,250)( 40,236)
( 41,235)( 42,247)( 43,246)( 44,245)( 45,244)( 46,243)( 47,242)( 48,241)
( 49,240)( 50,239)( 51,238)( 52,237)( 53,288)( 54,287)( 55,299)( 56,298)
( 57,297)( 58,296)( 59,295)( 60,294)( 61,293)( 62,292)( 63,291)( 64,290)
( 65,289)( 66,301)( 67,300)( 68,312)( 69,311)( 70,310)( 71,309)( 72,308)
( 73,307)( 74,306)( 75,305)( 76,304)( 77,303)( 78,302)( 79,262)( 80,261)
( 81,273)( 82,272)( 83,271)( 84,270)( 85,269)( 86,268)( 87,267)( 88,266)
( 89,265)( 90,264)( 91,263)( 92,275)( 93,274)( 94,286)( 95,285)( 96,284)
( 97,283)( 98,282)( 99,281)(100,280)(101,279)(102,278)(103,277)(104,276)
(105,366)(106,365)(107,377)(108,376)(109,375)(110,374)(111,373)(112,372)
(113,371)(114,370)(115,369)(116,368)(117,367)(118,379)(119,378)(120,390)
(121,389)(122,388)(123,387)(124,386)(125,385)(126,384)(127,383)(128,382)
(129,381)(130,380)(131,405)(132,404)(133,416)(134,415)(135,414)(136,413)
(137,412)(138,411)(139,410)(140,409)(141,408)(142,407)(143,406)(144,392)
(145,391)(146,403)(147,402)(148,401)(149,400)(150,399)(151,398)(152,397)
(153,396)(154,395)(155,394)(156,393)(157,314)(158,313)(159,325)(160,324)
(161,323)(162,322)(163,321)(164,320)(165,319)(166,318)(167,317)(168,316)
(169,315)(170,327)(171,326)(172,338)(173,337)(174,336)(175,335)(176,334)
(177,333)(178,332)(179,331)(180,330)(181,329)(182,328)(183,353)(184,352)
(185,364)(186,363)(187,362)(188,361)(189,360)(190,359)(191,358)(192,357)
(193,356)(194,355)(195,354)(196,340)(197,339)(198,351)(199,350)(200,349)
(201,348)(202,347)(203,346)(204,345)(205,344)(206,343)(207,342)(208,341)
(417,730)(418,729)(419,741)(420,740)(421,739)(422,738)(423,737)(424,736)
(425,735)(426,734)(427,733)(428,732)(429,731)(430,743)(431,742)(432,754)
(433,753)(434,752)(435,751)(436,750)(437,749)(438,748)(439,747)(440,746)
(441,745)(442,744)(443,769)(444,768)(445,780)(446,779)(447,778)(448,777)
(449,776)(450,775)(451,774)(452,773)(453,772)(454,771)(455,770)(456,756)
(457,755)(458,767)(459,766)(460,765)(461,764)(462,763)(463,762)(464,761)
(465,760)(466,759)(467,758)(468,757)(469,808)(470,807)(471,819)(472,818)
(473,817)(474,816)(475,815)(476,814)(477,813)(478,812)(479,811)(480,810)
(481,809)(482,821)(483,820)(484,832)(485,831)(486,830)(487,829)(488,828)
(489,827)(490,826)(491,825)(492,824)(493,823)(494,822)(495,782)(496,781)
(497,793)(498,792)(499,791)(500,790)(501,789)(502,788)(503,787)(504,786)
(505,785)(506,784)(507,783)(508,795)(509,794)(510,806)(511,805)(512,804)
(513,803)(514,802)(515,801)(516,800)(517,799)(518,798)(519,797)(520,796)
(521,626)(522,625)(523,637)(524,636)(525,635)(526,634)(527,633)(528,632)
(529,631)(530,630)(531,629)(532,628)(533,627)(534,639)(535,638)(536,650)
(537,649)(538,648)(539,647)(540,646)(541,645)(542,644)(543,643)(544,642)
(545,641)(546,640)(547,665)(548,664)(549,676)(550,675)(551,674)(552,673)
(553,672)(554,671)(555,670)(556,669)(557,668)(558,667)(559,666)(560,652)
(561,651)(562,663)(563,662)(564,661)(565,660)(566,659)(567,658)(568,657)
(569,656)(570,655)(571,654)(572,653)(573,704)(574,703)(575,715)(576,714)
(577,713)(578,712)(579,711)(580,710)(581,709)(582,708)(583,707)(584,706)
(585,705)(586,717)(587,716)(588,728)(589,727)(590,726)(591,725)(592,724)
(593,723)(594,722)(595,721)(596,720)(597,719)(598,718)(599,678)(600,677)
(601,689)(602,688)(603,687)(604,686)(605,685)(606,684)(607,683)(608,682)
(609,681)(610,680)(611,679)(612,691)(613,690)(614,702)(615,701)(616,700)
(617,699)(618,698)(619,697)(620,696)(621,695)(622,694)(623,693)(624,692);;
s2 := ( 1,417)( 2,418)( 3,419)( 4,420)( 5,421)( 6,422)( 7,423)( 8,424)
( 9,425)( 10,426)( 11,427)( 12,428)( 13,429)( 14,430)( 15,431)( 16,432)
( 17,433)( 18,434)( 19,435)( 20,436)( 21,437)( 22,438)( 23,439)( 24,440)
( 25,441)( 26,442)( 27,456)( 28,457)( 29,458)( 30,459)( 31,460)( 32,461)
( 33,462)( 34,463)( 35,464)( 36,465)( 37,466)( 38,467)( 39,468)( 40,443)
( 41,444)( 42,445)( 43,446)( 44,447)( 45,448)( 46,449)( 47,450)( 48,451)
( 49,452)( 50,453)( 51,454)( 52,455)( 53,495)( 54,496)( 55,497)( 56,498)
( 57,499)( 58,500)( 59,501)( 60,502)( 61,503)( 62,504)( 63,505)( 64,506)
( 65,507)( 66,508)( 67,509)( 68,510)( 69,511)( 70,512)( 71,513)( 72,514)
( 73,515)( 74,516)( 75,517)( 76,518)( 77,519)( 78,520)( 79,469)( 80,470)
( 81,471)( 82,472)( 83,473)( 84,474)( 85,475)( 86,476)( 87,477)( 88,478)
( 89,479)( 90,480)( 91,481)( 92,482)( 93,483)( 94,484)( 95,485)( 96,486)
( 97,487)( 98,488)( 99,489)(100,490)(101,491)(102,492)(103,493)(104,494)
(105,573)(106,574)(107,575)(108,576)(109,577)(110,578)(111,579)(112,580)
(113,581)(114,582)(115,583)(116,584)(117,585)(118,586)(119,587)(120,588)
(121,589)(122,590)(123,591)(124,592)(125,593)(126,594)(127,595)(128,596)
(129,597)(130,598)(131,612)(132,613)(133,614)(134,615)(135,616)(136,617)
(137,618)(138,619)(139,620)(140,621)(141,622)(142,623)(143,624)(144,599)
(145,600)(146,601)(147,602)(148,603)(149,604)(150,605)(151,606)(152,607)
(153,608)(154,609)(155,610)(156,611)(157,521)(158,522)(159,523)(160,524)
(161,525)(162,526)(163,527)(164,528)(165,529)(166,530)(167,531)(168,532)
(169,533)(170,534)(171,535)(172,536)(173,537)(174,538)(175,539)(176,540)
(177,541)(178,542)(179,543)(180,544)(181,545)(182,546)(183,560)(184,561)
(185,562)(186,563)(187,564)(188,565)(189,566)(190,567)(191,568)(192,569)
(193,570)(194,571)(195,572)(196,547)(197,548)(198,549)(199,550)(200,551)
(201,552)(202,553)(203,554)(204,555)(205,556)(206,557)(207,558)(208,559)
(209,625)(210,626)(211,627)(212,628)(213,629)(214,630)(215,631)(216,632)
(217,633)(218,634)(219,635)(220,636)(221,637)(222,638)(223,639)(224,640)
(225,641)(226,642)(227,643)(228,644)(229,645)(230,646)(231,647)(232,648)
(233,649)(234,650)(235,664)(236,665)(237,666)(238,667)(239,668)(240,669)
(241,670)(242,671)(243,672)(244,673)(245,674)(246,675)(247,676)(248,651)
(249,652)(250,653)(251,654)(252,655)(253,656)(254,657)(255,658)(256,659)
(257,660)(258,661)(259,662)(260,663)(261,703)(262,704)(263,705)(264,706)
(265,707)(266,708)(267,709)(268,710)(269,711)(270,712)(271,713)(272,714)
(273,715)(274,716)(275,717)(276,718)(277,719)(278,720)(279,721)(280,722)
(281,723)(282,724)(283,725)(284,726)(285,727)(286,728)(287,677)(288,678)
(289,679)(290,680)(291,681)(292,682)(293,683)(294,684)(295,685)(296,686)
(297,687)(298,688)(299,689)(300,690)(301,691)(302,692)(303,693)(304,694)
(305,695)(306,696)(307,697)(308,698)(309,699)(310,700)(311,701)(312,702)
(313,781)(314,782)(315,783)(316,784)(317,785)(318,786)(319,787)(320,788)
(321,789)(322,790)(323,791)(324,792)(325,793)(326,794)(327,795)(328,796)
(329,797)(330,798)(331,799)(332,800)(333,801)(334,802)(335,803)(336,804)
(337,805)(338,806)(339,820)(340,821)(341,822)(342,823)(343,824)(344,825)
(345,826)(346,827)(347,828)(348,829)(349,830)(350,831)(351,832)(352,807)
(353,808)(354,809)(355,810)(356,811)(357,812)(358,813)(359,814)(360,815)
(361,816)(362,817)(363,818)(364,819)(365,729)(366,730)(367,731)(368,732)
(369,733)(370,734)(371,735)(372,736)(373,737)(374,738)(375,739)(376,740)
(377,741)(378,742)(379,743)(380,744)(381,745)(382,746)(383,747)(384,748)
(385,749)(386,750)(387,751)(388,752)(389,753)(390,754)(391,768)(392,769)
(393,770)(394,771)(395,772)(396,773)(397,774)(398,775)(399,776)(400,777)
(401,778)(402,779)(403,780)(404,755)(405,756)(406,757)(407,758)(408,759)
(409,760)(410,761)(411,762)(412,763)(413,764)(414,765)(415,766)(416,767);;
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*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,
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(832)!( 1,209)( 2,221)( 3,220)( 4,219)( 5,218)( 6,217)( 7,216)
( 8,215)( 9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,222)( 15,234)
( 16,233)( 17,232)( 18,231)( 19,230)( 20,229)( 21,228)( 22,227)( 23,226)
( 24,225)( 25,224)( 26,223)( 27,235)( 28,247)( 29,246)( 30,245)( 31,244)
( 32,243)( 33,242)( 34,241)( 35,240)( 36,239)( 37,238)( 38,237)( 39,236)
( 40,248)( 41,260)( 42,259)( 43,258)( 44,257)( 45,256)( 46,255)( 47,254)
( 48,253)( 49,252)( 50,251)( 51,250)( 52,249)( 53,261)( 54,273)( 55,272)
( 56,271)( 57,270)( 58,269)( 59,268)( 60,267)( 61,266)( 62,265)( 63,264)
( 64,263)( 65,262)( 66,274)( 67,286)( 68,285)( 69,284)( 70,283)( 71,282)
( 72,281)( 73,280)( 74,279)( 75,278)( 76,277)( 77,276)( 78,275)( 79,287)
( 80,299)( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)
( 88,291)( 89,290)( 90,289)( 91,288)( 92,300)( 93,312)( 94,311)( 95,310)
( 96,309)( 97,308)( 98,307)( 99,306)(100,305)(101,304)(102,303)(103,302)
(104,301)(105,313)(106,325)(107,324)(108,323)(109,322)(110,321)(111,320)
(112,319)(113,318)(114,317)(115,316)(116,315)(117,314)(118,326)(119,338)
(120,337)(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,330)
(128,329)(129,328)(130,327)(131,339)(132,351)(133,350)(134,349)(135,348)
(136,347)(137,346)(138,345)(139,344)(140,343)(141,342)(142,341)(143,340)
(144,352)(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)
(152,357)(153,356)(154,355)(155,354)(156,353)(157,365)(158,377)(159,376)
(160,375)(161,374)(162,373)(163,372)(164,371)(165,370)(166,369)(167,368)
(168,367)(169,366)(170,378)(171,390)(172,389)(173,388)(174,387)(175,386)
(176,385)(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,391)
(184,403)(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)
(192,395)(193,394)(194,393)(195,392)(196,404)(197,416)(198,415)(199,414)
(200,413)(201,412)(202,411)(203,410)(204,409)(205,408)(206,407)(207,406)
(208,405)(417,625)(418,637)(419,636)(420,635)(421,634)(422,633)(423,632)
(424,631)(425,630)(426,629)(427,628)(428,627)(429,626)(430,638)(431,650)
(432,649)(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)
(440,641)(441,640)(442,639)(443,651)(444,663)(445,662)(446,661)(447,660)
(448,659)(449,658)(450,657)(451,656)(452,655)(453,654)(454,653)(455,652)
(456,664)(457,676)(458,675)(459,674)(460,673)(461,672)(462,671)(463,670)
(464,669)(465,668)(466,667)(467,666)(468,665)(469,677)(470,689)(471,688)
(472,687)(473,686)(474,685)(475,684)(476,683)(477,682)(478,681)(479,680)
(480,679)(481,678)(482,690)(483,702)(484,701)(485,700)(486,699)(487,698)
(488,697)(489,696)(490,695)(491,694)(492,693)(493,692)(494,691)(495,703)
(496,715)(497,714)(498,713)(499,712)(500,711)(501,710)(502,709)(503,708)
(504,707)(505,706)(506,705)(507,704)(508,716)(509,728)(510,727)(511,726)
(512,725)(513,724)(514,723)(515,722)(516,721)(517,720)(518,719)(519,718)
(520,717)(521,729)(522,741)(523,740)(524,739)(525,738)(526,737)(527,736)
(528,735)(529,734)(530,733)(531,732)(532,731)(533,730)(534,742)(535,754)
(536,753)(537,752)(538,751)(539,750)(540,749)(541,748)(542,747)(543,746)
(544,745)(545,744)(546,743)(547,755)(548,767)(549,766)(550,765)(551,764)
(552,763)(553,762)(554,761)(555,760)(556,759)(557,758)(558,757)(559,756)
(560,768)(561,780)(562,779)(563,778)(564,777)(565,776)(566,775)(567,774)
(568,773)(569,772)(570,771)(571,770)(572,769)(573,781)(574,793)(575,792)
(576,791)(577,790)(578,789)(579,788)(580,787)(581,786)(582,785)(583,784)
(584,783)(585,782)(586,794)(587,806)(588,805)(589,804)(590,803)(591,802)
(592,801)(593,800)(594,799)(595,798)(596,797)(597,796)(598,795)(599,807)
(600,819)(601,818)(602,817)(603,816)(604,815)(605,814)(606,813)(607,812)
(608,811)(609,810)(610,809)(611,808)(612,820)(613,832)(614,831)(615,830)
(616,829)(617,828)(618,827)(619,826)(620,825)(621,824)(622,823)(623,822)
(624,821);
s1 := Sym(832)!( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)
( 8,216)( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)
( 16,234)( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)
( 24,226)( 25,225)( 26,224)( 27,249)( 28,248)( 29,260)( 30,259)( 31,258)
( 32,257)( 33,256)( 34,255)( 35,254)( 36,253)( 37,252)( 38,251)( 39,250)
( 40,236)( 41,235)( 42,247)( 43,246)( 44,245)( 45,244)( 46,243)( 47,242)
( 48,241)( 49,240)( 50,239)( 51,238)( 52,237)( 53,288)( 54,287)( 55,299)
( 56,298)( 57,297)( 58,296)( 59,295)( 60,294)( 61,293)( 62,292)( 63,291)
( 64,290)( 65,289)( 66,301)( 67,300)( 68,312)( 69,311)( 70,310)( 71,309)
( 72,308)( 73,307)( 74,306)( 75,305)( 76,304)( 77,303)( 78,302)( 79,262)
( 80,261)( 81,273)( 82,272)( 83,271)( 84,270)( 85,269)( 86,268)( 87,267)
( 88,266)( 89,265)( 90,264)( 91,263)( 92,275)( 93,274)( 94,286)( 95,285)
( 96,284)( 97,283)( 98,282)( 99,281)(100,280)(101,279)(102,278)(103,277)
(104,276)(105,366)(106,365)(107,377)(108,376)(109,375)(110,374)(111,373)
(112,372)(113,371)(114,370)(115,369)(116,368)(117,367)(118,379)(119,378)
(120,390)(121,389)(122,388)(123,387)(124,386)(125,385)(126,384)(127,383)
(128,382)(129,381)(130,380)(131,405)(132,404)(133,416)(134,415)(135,414)
(136,413)(137,412)(138,411)(139,410)(140,409)(141,408)(142,407)(143,406)
(144,392)(145,391)(146,403)(147,402)(148,401)(149,400)(150,399)(151,398)
(152,397)(153,396)(154,395)(155,394)(156,393)(157,314)(158,313)(159,325)
(160,324)(161,323)(162,322)(163,321)(164,320)(165,319)(166,318)(167,317)
(168,316)(169,315)(170,327)(171,326)(172,338)(173,337)(174,336)(175,335)
(176,334)(177,333)(178,332)(179,331)(180,330)(181,329)(182,328)(183,353)
(184,352)(185,364)(186,363)(187,362)(188,361)(189,360)(190,359)(191,358)
(192,357)(193,356)(194,355)(195,354)(196,340)(197,339)(198,351)(199,350)
(200,349)(201,348)(202,347)(203,346)(204,345)(205,344)(206,343)(207,342)
(208,341)(417,730)(418,729)(419,741)(420,740)(421,739)(422,738)(423,737)
(424,736)(425,735)(426,734)(427,733)(428,732)(429,731)(430,743)(431,742)
(432,754)(433,753)(434,752)(435,751)(436,750)(437,749)(438,748)(439,747)
(440,746)(441,745)(442,744)(443,769)(444,768)(445,780)(446,779)(447,778)
(448,777)(449,776)(450,775)(451,774)(452,773)(453,772)(454,771)(455,770)
(456,756)(457,755)(458,767)(459,766)(460,765)(461,764)(462,763)(463,762)
(464,761)(465,760)(466,759)(467,758)(468,757)(469,808)(470,807)(471,819)
(472,818)(473,817)(474,816)(475,815)(476,814)(477,813)(478,812)(479,811)
(480,810)(481,809)(482,821)(483,820)(484,832)(485,831)(486,830)(487,829)
(488,828)(489,827)(490,826)(491,825)(492,824)(493,823)(494,822)(495,782)
(496,781)(497,793)(498,792)(499,791)(500,790)(501,789)(502,788)(503,787)
(504,786)(505,785)(506,784)(507,783)(508,795)(509,794)(510,806)(511,805)
(512,804)(513,803)(514,802)(515,801)(516,800)(517,799)(518,798)(519,797)
(520,796)(521,626)(522,625)(523,637)(524,636)(525,635)(526,634)(527,633)
(528,632)(529,631)(530,630)(531,629)(532,628)(533,627)(534,639)(535,638)
(536,650)(537,649)(538,648)(539,647)(540,646)(541,645)(542,644)(543,643)
(544,642)(545,641)(546,640)(547,665)(548,664)(549,676)(550,675)(551,674)
(552,673)(553,672)(554,671)(555,670)(556,669)(557,668)(558,667)(559,666)
(560,652)(561,651)(562,663)(563,662)(564,661)(565,660)(566,659)(567,658)
(568,657)(569,656)(570,655)(571,654)(572,653)(573,704)(574,703)(575,715)
(576,714)(577,713)(578,712)(579,711)(580,710)(581,709)(582,708)(583,707)
(584,706)(585,705)(586,717)(587,716)(588,728)(589,727)(590,726)(591,725)
(592,724)(593,723)(594,722)(595,721)(596,720)(597,719)(598,718)(599,678)
(600,677)(601,689)(602,688)(603,687)(604,686)(605,685)(606,684)(607,683)
(608,682)(609,681)(610,680)(611,679)(612,691)(613,690)(614,702)(615,701)
(616,700)(617,699)(618,698)(619,697)(620,696)(621,695)(622,694)(623,693)
(624,692);
s2 := Sym(832)!( 1,417)( 2,418)( 3,419)( 4,420)( 5,421)( 6,422)( 7,423)
( 8,424)( 9,425)( 10,426)( 11,427)( 12,428)( 13,429)( 14,430)( 15,431)
( 16,432)( 17,433)( 18,434)( 19,435)( 20,436)( 21,437)( 22,438)( 23,439)
( 24,440)( 25,441)( 26,442)( 27,456)( 28,457)( 29,458)( 30,459)( 31,460)
( 32,461)( 33,462)( 34,463)( 35,464)( 36,465)( 37,466)( 38,467)( 39,468)
( 40,443)( 41,444)( 42,445)( 43,446)( 44,447)( 45,448)( 46,449)( 47,450)
( 48,451)( 49,452)( 50,453)( 51,454)( 52,455)( 53,495)( 54,496)( 55,497)
( 56,498)( 57,499)( 58,500)( 59,501)( 60,502)( 61,503)( 62,504)( 63,505)
( 64,506)( 65,507)( 66,508)( 67,509)( 68,510)( 69,511)( 70,512)( 71,513)
( 72,514)( 73,515)( 74,516)( 75,517)( 76,518)( 77,519)( 78,520)( 79,469)
( 80,470)( 81,471)( 82,472)( 83,473)( 84,474)( 85,475)( 86,476)( 87,477)
( 88,478)( 89,479)( 90,480)( 91,481)( 92,482)( 93,483)( 94,484)( 95,485)
( 96,486)( 97,487)( 98,488)( 99,489)(100,490)(101,491)(102,492)(103,493)
(104,494)(105,573)(106,574)(107,575)(108,576)(109,577)(110,578)(111,579)
(112,580)(113,581)(114,582)(115,583)(116,584)(117,585)(118,586)(119,587)
(120,588)(121,589)(122,590)(123,591)(124,592)(125,593)(126,594)(127,595)
(128,596)(129,597)(130,598)(131,612)(132,613)(133,614)(134,615)(135,616)
(136,617)(137,618)(138,619)(139,620)(140,621)(141,622)(142,623)(143,624)
(144,599)(145,600)(146,601)(147,602)(148,603)(149,604)(150,605)(151,606)
(152,607)(153,608)(154,609)(155,610)(156,611)(157,521)(158,522)(159,523)
(160,524)(161,525)(162,526)(163,527)(164,528)(165,529)(166,530)(167,531)
(168,532)(169,533)(170,534)(171,535)(172,536)(173,537)(174,538)(175,539)
(176,540)(177,541)(178,542)(179,543)(180,544)(181,545)(182,546)(183,560)
(184,561)(185,562)(186,563)(187,564)(188,565)(189,566)(190,567)(191,568)
(192,569)(193,570)(194,571)(195,572)(196,547)(197,548)(198,549)(199,550)
(200,551)(201,552)(202,553)(203,554)(204,555)(205,556)(206,557)(207,558)
(208,559)(209,625)(210,626)(211,627)(212,628)(213,629)(214,630)(215,631)
(216,632)(217,633)(218,634)(219,635)(220,636)(221,637)(222,638)(223,639)
(224,640)(225,641)(226,642)(227,643)(228,644)(229,645)(230,646)(231,647)
(232,648)(233,649)(234,650)(235,664)(236,665)(237,666)(238,667)(239,668)
(240,669)(241,670)(242,671)(243,672)(244,673)(245,674)(246,675)(247,676)
(248,651)(249,652)(250,653)(251,654)(252,655)(253,656)(254,657)(255,658)
(256,659)(257,660)(258,661)(259,662)(260,663)(261,703)(262,704)(263,705)
(264,706)(265,707)(266,708)(267,709)(268,710)(269,711)(270,712)(271,713)
(272,714)(273,715)(274,716)(275,717)(276,718)(277,719)(278,720)(279,721)
(280,722)(281,723)(282,724)(283,725)(284,726)(285,727)(286,728)(287,677)
(288,678)(289,679)(290,680)(291,681)(292,682)(293,683)(294,684)(295,685)
(296,686)(297,687)(298,688)(299,689)(300,690)(301,691)(302,692)(303,693)
(304,694)(305,695)(306,696)(307,697)(308,698)(309,699)(310,700)(311,701)
(312,702)(313,781)(314,782)(315,783)(316,784)(317,785)(318,786)(319,787)
(320,788)(321,789)(322,790)(323,791)(324,792)(325,793)(326,794)(327,795)
(328,796)(329,797)(330,798)(331,799)(332,800)(333,801)(334,802)(335,803)
(336,804)(337,805)(338,806)(339,820)(340,821)(341,822)(342,823)(343,824)
(344,825)(345,826)(346,827)(347,828)(348,829)(349,830)(350,831)(351,832)
(352,807)(353,808)(354,809)(355,810)(356,811)(357,812)(358,813)(359,814)
(360,815)(361,816)(362,817)(363,818)(364,819)(365,729)(366,730)(367,731)
(368,732)(369,733)(370,734)(371,735)(372,736)(373,737)(374,738)(375,739)
(376,740)(377,741)(378,742)(379,743)(380,744)(381,745)(382,746)(383,747)
(384,748)(385,749)(386,750)(387,751)(388,752)(389,753)(390,754)(391,768)
(392,769)(393,770)(394,771)(395,772)(396,773)(397,774)(398,775)(399,776)
(400,777)(401,778)(402,779)(403,780)(404,755)(405,756)(406,757)(407,758)
(408,759)(409,760)(410,761)(411,762)(412,763)(413,764)(414,765)(415,766)
(416,767);
poly := sub<Sym(832)|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*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,
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