Polytope of Type {8,26,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,26,4}*1664
Also Known As : {{8,26|2},{26,4|2}}. if this polytope has another name.
Group : SmallGroup(1664,16180)
Rank : 4
Schlafli Type : {8,26,4}
Number of vertices, edges, etc : 8, 104, 52, 4
Order of s0s1s2s3 : 104
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 : {4,26,4}*832, {8,26,2}*832
4-fold quotients : {2,26,4}*416, {4,26,2}*416
8-fold quotients : {2,26,2}*208
13-fold quotients : {8,2,4}*128
16-fold quotients : {2,13,2}*104
26-fold quotients : {4,2,4}*64, {8,2,2}*64
52-fold quotients : {2,2,4}*32, {4,2,2}*32
104-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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)( 27,443)( 28,444)( 29,445)( 30,446)( 31,447)( 32,448)
( 33,449)( 34,450)( 35,451)( 36,452)( 37,453)( 38,454)( 39,455)( 40,456)
( 41,457)( 42,458)( 43,459)( 44,460)( 45,461)( 46,462)( 47,463)( 48,464)
( 49,465)( 50,466)( 51,467)( 52,468)( 53,482)( 54,483)( 55,484)( 56,485)
( 57,486)( 58,487)( 59,488)( 60,489)( 61,490)( 62,491)( 63,492)( 64,493)
( 65,494)( 66,469)( 67,470)( 68,471)( 69,472)( 70,473)( 71,474)( 72,475)
( 73,476)( 74,477)( 75,478)( 76,479)( 77,480)( 78,481)( 79,508)( 80,509)
( 81,510)( 82,511)( 83,512)( 84,513)( 85,514)( 86,515)( 87,516)( 88,517)
( 89,518)( 90,519)( 91,520)( 92,495)( 93,496)( 94,497)( 95,498)( 96,499)
( 97,500)( 98,501)( 99,502)(100,503)(101,504)(102,505)(103,506)(104,507)
(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)(131,599)(132,600)(133,601)(134,602)(135,603)(136,604)
(137,605)(138,606)(139,607)(140,608)(141,609)(142,610)(143,611)(144,612)
(145,613)(146,614)(147,615)(148,616)(149,617)(150,618)(151,619)(152,620)
(153,621)(154,622)(155,623)(156,624)(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)(183,547)(184,548)
(185,549)(186,550)(187,551)(188,552)(189,553)(190,554)(191,555)(192,556)
(193,557)(194,558)(195,559)(196,560)(197,561)(198,562)(199,563)(200,564)
(201,565)(202,566)(203,567)(204,568)(205,569)(206,570)(207,571)(208,572)
(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)(235,651)(236,652)(237,653)(238,654)(239,655)(240,656)
(241,657)(242,658)(243,659)(244,660)(245,661)(246,662)(247,663)(248,664)
(249,665)(250,666)(251,667)(252,668)(253,669)(254,670)(255,671)(256,672)
(257,673)(258,674)(259,675)(260,676)(261,690)(262,691)(263,692)(264,693)
(265,694)(266,695)(267,696)(268,697)(269,698)(270,699)(271,700)(272,701)
(273,702)(274,677)(275,678)(276,679)(277,680)(278,681)(279,682)(280,683)
(281,684)(282,685)(283,686)(284,687)(285,688)(286,689)(287,716)(288,717)
(289,718)(290,719)(291,720)(292,721)(293,722)(294,723)(295,724)(296,725)
(297,726)(298,727)(299,728)(300,703)(301,704)(302,705)(303,706)(304,707)
(305,708)(306,709)(307,710)(308,711)(309,712)(310,713)(311,714)(312,715)
(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)(339,807)(340,808)(341,809)(342,810)(343,811)(344,812)
(345,813)(346,814)(347,815)(348,816)(349,817)(350,818)(351,819)(352,820)
(353,821)(354,822)(355,823)(356,824)(357,825)(358,826)(359,827)(360,828)
(361,829)(362,830)(363,831)(364,832)(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)(391,755)(392,756)
(393,757)(394,758)(395,759)(396,760)(397,761)(398,762)(399,763)(400,764)
(401,765)(402,766)(403,767)(404,768)(405,769)(406,770)(407,771)(408,772)
(409,773)(410,774)(411,775)(412,776)(413,777)(414,778)(415,779)(416,780);;
s1 := ( 1,105)( 2,117)( 3,116)( 4,115)( 5,114)( 6,113)( 7,112)( 8,111)
( 9,110)( 10,109)( 11,108)( 12,107)( 13,106)( 14,118)( 15,130)( 16,129)
( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)
( 25,120)( 26,119)( 27,131)( 28,143)( 29,142)( 30,141)( 31,140)( 32,139)
( 33,138)( 34,137)( 35,136)( 36,135)( 37,134)( 38,133)( 39,132)( 40,144)
( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)( 48,149)
( 49,148)( 50,147)( 51,146)( 52,145)( 53,170)( 54,182)( 55,181)( 56,180)
( 57,179)( 58,178)( 59,177)( 60,176)( 61,175)( 62,174)( 63,173)( 64,172)
( 65,171)( 66,157)( 67,169)( 68,168)( 69,167)( 70,166)( 71,165)( 72,164)
( 73,163)( 74,162)( 75,161)( 76,160)( 77,159)( 78,158)( 79,196)( 80,208)
( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)( 88,200)
( 89,199)( 90,198)( 91,197)( 92,183)( 93,195)( 94,194)( 95,193)( 96,192)
( 97,191)( 98,190)( 99,189)(100,188)(101,187)(102,186)(103,185)(104,184)
(209,313)(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)(216,319)
(217,318)(218,317)(219,316)(220,315)(221,314)(222,326)(223,338)(224,337)
(225,336)(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)(232,329)
(233,328)(234,327)(235,339)(236,351)(237,350)(238,349)(239,348)(240,347)
(241,346)(242,345)(243,344)(244,343)(245,342)(246,341)(247,340)(248,352)
(249,364)(250,363)(251,362)(252,361)(253,360)(254,359)(255,358)(256,357)
(257,356)(258,355)(259,354)(260,353)(261,378)(262,390)(263,389)(264,388)
(265,387)(266,386)(267,385)(268,384)(269,383)(270,382)(271,381)(272,380)
(273,379)(274,365)(275,377)(276,376)(277,375)(278,374)(279,373)(280,372)
(281,371)(282,370)(283,369)(284,368)(285,367)(286,366)(287,404)(288,416)
(289,415)(290,414)(291,413)(292,412)(293,411)(294,410)(295,409)(296,408)
(297,407)(298,406)(299,405)(300,391)(301,403)(302,402)(303,401)(304,400)
(305,399)(306,398)(307,397)(308,396)(309,395)(310,394)(311,393)(312,392)
(417,521)(418,533)(419,532)(420,531)(421,530)(422,529)(423,528)(424,527)
(425,526)(426,525)(427,524)(428,523)(429,522)(430,534)(431,546)(432,545)
(433,544)(434,543)(435,542)(436,541)(437,540)(438,539)(439,538)(440,537)
(441,536)(442,535)(443,547)(444,559)(445,558)(446,557)(447,556)(448,555)
(449,554)(450,553)(451,552)(452,551)(453,550)(454,549)(455,548)(456,560)
(457,572)(458,571)(459,570)(460,569)(461,568)(462,567)(463,566)(464,565)
(465,564)(466,563)(467,562)(468,561)(469,586)(470,598)(471,597)(472,596)
(473,595)(474,594)(475,593)(476,592)(477,591)(478,590)(479,589)(480,588)
(481,587)(482,573)(483,585)(484,584)(485,583)(486,582)(487,581)(488,580)
(489,579)(490,578)(491,577)(492,576)(493,575)(494,574)(495,612)(496,624)
(497,623)(498,622)(499,621)(500,620)(501,619)(502,618)(503,617)(504,616)
(505,615)(506,614)(507,613)(508,599)(509,611)(510,610)(511,609)(512,608)
(513,607)(514,606)(515,605)(516,604)(517,603)(518,602)(519,601)(520,600)
(625,729)(626,741)(627,740)(628,739)(629,738)(630,737)(631,736)(632,735)
(633,734)(634,733)(635,732)(636,731)(637,730)(638,742)(639,754)(640,753)
(641,752)(642,751)(643,750)(644,749)(645,748)(646,747)(647,746)(648,745)
(649,744)(650,743)(651,755)(652,767)(653,766)(654,765)(655,764)(656,763)
(657,762)(658,761)(659,760)(660,759)(661,758)(662,757)(663,756)(664,768)
(665,780)(666,779)(667,778)(668,777)(669,776)(670,775)(671,774)(672,773)
(673,772)(674,771)(675,770)(676,769)(677,794)(678,806)(679,805)(680,804)
(681,803)(682,802)(683,801)(684,800)(685,799)(686,798)(687,797)(688,796)
(689,795)(690,781)(691,793)(692,792)(693,791)(694,790)(695,789)(696,788)
(697,787)(698,786)(699,785)(700,784)(701,783)(702,782)(703,820)(704,832)
(705,831)(706,830)(707,829)(708,828)(709,827)(710,826)(711,825)(712,824)
(713,823)(714,822)(715,821)(716,807)(717,819)(718,818)(719,817)(720,816)
(721,815)(722,814)(723,813)(724,812)(725,811)(726,810)(727,809)(728,808);;
s2 := ( 1,158)( 2,157)( 3,169)( 4,168)( 5,167)( 6,166)( 7,165)( 8,164)
( 9,163)( 10,162)( 11,161)( 12,160)( 13,159)( 14,171)( 15,170)( 16,182)
( 17,181)( 18,180)( 19,179)( 20,178)( 21,177)( 22,176)( 23,175)( 24,174)
( 25,173)( 26,172)( 27,184)( 28,183)( 29,195)( 30,194)( 31,193)( 32,192)
( 33,191)( 34,190)( 35,189)( 36,188)( 37,187)( 38,186)( 39,185)( 40,197)
( 41,196)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)( 48,202)
( 49,201)( 50,200)( 51,199)( 52,198)( 53,119)( 54,118)( 55,130)( 56,129)
( 57,128)( 58,127)( 59,126)( 60,125)( 61,124)( 62,123)( 63,122)( 64,121)
( 65,120)( 66,106)( 67,105)( 68,117)( 69,116)( 70,115)( 71,114)( 72,113)
( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,107)( 79,145)( 80,144)
( 81,156)( 82,155)( 83,154)( 84,153)( 85,152)( 86,151)( 87,150)( 88,149)
( 89,148)( 90,147)( 91,146)( 92,132)( 93,131)( 94,143)( 95,142)( 96,141)
( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)
(209,392)(210,391)(211,403)(212,402)(213,401)(214,400)(215,399)(216,398)
(217,397)(218,396)(219,395)(220,394)(221,393)(222,405)(223,404)(224,416)
(225,415)(226,414)(227,413)(228,412)(229,411)(230,410)(231,409)(232,408)
(233,407)(234,406)(235,366)(236,365)(237,377)(238,376)(239,375)(240,374)
(241,373)(242,372)(243,371)(244,370)(245,369)(246,368)(247,367)(248,379)
(249,378)(250,390)(251,389)(252,388)(253,387)(254,386)(255,385)(256,384)
(257,383)(258,382)(259,381)(260,380)(261,353)(262,352)(263,364)(264,363)
(265,362)(266,361)(267,360)(268,359)(269,358)(270,357)(271,356)(272,355)
(273,354)(274,340)(275,339)(276,351)(277,350)(278,349)(279,348)(280,347)
(281,346)(282,345)(283,344)(284,343)(285,342)(286,341)(287,327)(288,326)
(289,338)(290,337)(291,336)(292,335)(293,334)(294,333)(295,332)(296,331)
(297,330)(298,329)(299,328)(300,314)(301,313)(302,325)(303,324)(304,323)
(305,322)(306,321)(307,320)(308,319)(309,318)(310,317)(311,316)(312,315)
(417,522)(418,521)(419,533)(420,532)(421,531)(422,530)(423,529)(424,528)
(425,527)(426,526)(427,525)(428,524)(429,523)(430,535)(431,534)(432,546)
(433,545)(434,544)(435,543)(436,542)(437,541)(438,540)(439,539)(440,538)
(441,537)(442,536)(443,548)(444,547)(445,559)(446,558)(447,557)(448,556)
(449,555)(450,554)(451,553)(452,552)(453,551)(454,550)(455,549)(456,561)
(457,560)(458,572)(459,571)(460,570)(461,569)(462,568)(463,567)(464,566)
(465,565)(466,564)(467,563)(468,562)(469,574)(470,573)(471,585)(472,584)
(473,583)(474,582)(475,581)(476,580)(477,579)(478,578)(479,577)(480,576)
(481,575)(482,587)(483,586)(484,598)(485,597)(486,596)(487,595)(488,594)
(489,593)(490,592)(491,591)(492,590)(493,589)(494,588)(495,600)(496,599)
(497,611)(498,610)(499,609)(500,608)(501,607)(502,606)(503,605)(504,604)
(505,603)(506,602)(507,601)(508,613)(509,612)(510,624)(511,623)(512,622)
(513,621)(514,620)(515,619)(516,618)(517,617)(518,616)(519,615)(520,614)
(625,756)(626,755)(627,767)(628,766)(629,765)(630,764)(631,763)(632,762)
(633,761)(634,760)(635,759)(636,758)(637,757)(638,769)(639,768)(640,780)
(641,779)(642,778)(643,777)(644,776)(645,775)(646,774)(647,773)(648,772)
(649,771)(650,770)(651,730)(652,729)(653,741)(654,740)(655,739)(656,738)
(657,737)(658,736)(659,735)(660,734)(661,733)(662,732)(663,731)(664,743)
(665,742)(666,754)(667,753)(668,752)(669,751)(670,750)(671,749)(672,748)
(673,747)(674,746)(675,745)(676,744)(677,808)(678,807)(679,819)(680,818)
(681,817)(682,816)(683,815)(684,814)(685,813)(686,812)(687,811)(688,810)
(689,809)(690,821)(691,820)(692,832)(693,831)(694,830)(695,829)(696,828)
(697,827)(698,826)(699,825)(700,824)(701,823)(702,822)(703,782)(704,781)
(705,793)(706,792)(707,791)(708,790)(709,789)(710,788)(711,787)(712,786)
(713,785)(714,784)(715,783)(716,795)(717,794)(718,806)(719,805)(720,804)
(721,803)(722,802)(723,801)(724,800)(725,799)(726,798)(727,797)(728,796);;
s3 := ( 1,209)( 2,210)( 3,211)( 4,212)( 5,213)( 6,214)( 7,215)( 8,216)
( 9,217)( 10,218)( 11,219)( 12,220)( 13,221)( 14,222)( 15,223)( 16,224)
( 17,225)( 18,226)( 19,227)( 20,228)( 21,229)( 22,230)( 23,231)( 24,232)
( 25,233)( 26,234)( 27,235)( 28,236)( 29,237)( 30,238)( 31,239)( 32,240)
( 33,241)( 34,242)( 35,243)( 36,244)( 37,245)( 38,246)( 39,247)( 40,248)
( 41,249)( 42,250)( 43,251)( 44,252)( 45,253)( 46,254)( 47,255)( 48,256)
( 49,257)( 50,258)( 51,259)( 52,260)( 53,261)( 54,262)( 55,263)( 56,264)
( 57,265)( 58,266)( 59,267)( 60,268)( 61,269)( 62,270)( 63,271)( 64,272)
( 65,273)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)( 72,280)
( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,287)( 80,288)
( 81,289)( 82,290)( 83,291)( 84,292)( 85,293)( 86,294)( 87,295)( 88,296)
( 89,297)( 90,298)( 91,299)( 92,300)( 93,301)( 94,302)( 95,303)( 96,304)
( 97,305)( 98,306)( 99,307)(100,308)(101,309)(102,310)(103,311)(104,312)
(105,313)(106,314)(107,315)(108,316)(109,317)(110,318)(111,319)(112,320)
(113,321)(114,322)(115,323)(116,324)(117,325)(118,326)(119,327)(120,328)
(121,329)(122,330)(123,331)(124,332)(125,333)(126,334)(127,335)(128,336)
(129,337)(130,338)(131,339)(132,340)(133,341)(134,342)(135,343)(136,344)
(137,345)(138,346)(139,347)(140,348)(141,349)(142,350)(143,351)(144,352)
(145,353)(146,354)(147,355)(148,356)(149,357)(150,358)(151,359)(152,360)
(153,361)(154,362)(155,363)(156,364)(157,365)(158,366)(159,367)(160,368)
(161,369)(162,370)(163,371)(164,372)(165,373)(166,374)(167,375)(168,376)
(169,377)(170,378)(171,379)(172,380)(173,381)(174,382)(175,383)(176,384)
(177,385)(178,386)(179,387)(180,388)(181,389)(182,390)(183,391)(184,392)
(185,393)(186,394)(187,395)(188,396)(189,397)(190,398)(191,399)(192,400)
(193,401)(194,402)(195,403)(196,404)(197,405)(198,406)(199,407)(200,408)
(201,409)(202,410)(203,411)(204,412)(205,413)(206,414)(207,415)(208,416)
(417,625)(418,626)(419,627)(420,628)(421,629)(422,630)(423,631)(424,632)
(425,633)(426,634)(427,635)(428,636)(429,637)(430,638)(431,639)(432,640)
(433,641)(434,642)(435,643)(436,644)(437,645)(438,646)(439,647)(440,648)
(441,649)(442,650)(443,651)(444,652)(445,653)(446,654)(447,655)(448,656)
(449,657)(450,658)(451,659)(452,660)(453,661)(454,662)(455,663)(456,664)
(457,665)(458,666)(459,667)(460,668)(461,669)(462,670)(463,671)(464,672)
(465,673)(466,674)(467,675)(468,676)(469,677)(470,678)(471,679)(472,680)
(473,681)(474,682)(475,683)(476,684)(477,685)(478,686)(479,687)(480,688)
(481,689)(482,690)(483,691)(484,692)(485,693)(486,694)(487,695)(488,696)
(489,697)(490,698)(491,699)(492,700)(493,701)(494,702)(495,703)(496,704)
(497,705)(498,706)(499,707)(500,708)(501,709)(502,710)(503,711)(504,712)
(505,713)(506,714)(507,715)(508,716)(509,717)(510,718)(511,719)(512,720)
(513,721)(514,722)(515,723)(516,724)(517,725)(518,726)(519,727)(520,728)
(521,729)(522,730)(523,731)(524,732)(525,733)(526,734)(527,735)(528,736)
(529,737)(530,738)(531,739)(532,740)(533,741)(534,742)(535,743)(536,744)
(537,745)(538,746)(539,747)(540,748)(541,749)(542,750)(543,751)(544,752)
(545,753)(546,754)(547,755)(548,756)(549,757)(550,758)(551,759)(552,760)
(553,761)(554,762)(555,763)(556,764)(557,765)(558,766)(559,767)(560,768)
(561,769)(562,770)(563,771)(564,772)(565,773)(566,774)(567,775)(568,776)
(569,777)(570,778)(571,779)(572,780)(573,781)(574,782)(575,783)(576,784)
(577,785)(578,786)(579,787)(580,788)(581,789)(582,790)(583,791)(584,792)
(585,793)(586,794)(587,795)(588,796)(589,797)(590,798)(591,799)(592,800)
(593,801)(594,802)(595,803)(596,804)(597,805)(598,806)(599,807)(600,808)
(601,809)(602,810)(603,811)(604,812)(605,813)(606,814)(607,815)(608,816)
(609,817)(610,818)(611,819)(612,820)(613,821)(614,822)(615,823)(616,824)
(617,825)(618,826)(619,827)(620,828)(621,829)(622,830)(623,831)(624,832);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 27,443)( 28,444)( 29,445)( 30,446)( 31,447)
( 32,448)( 33,449)( 34,450)( 35,451)( 36,452)( 37,453)( 38,454)( 39,455)
( 40,456)( 41,457)( 42,458)( 43,459)( 44,460)( 45,461)( 46,462)( 47,463)
( 48,464)( 49,465)( 50,466)( 51,467)( 52,468)( 53,482)( 54,483)( 55,484)
( 56,485)( 57,486)( 58,487)( 59,488)( 60,489)( 61,490)( 62,491)( 63,492)
( 64,493)( 65,494)( 66,469)( 67,470)( 68,471)( 69,472)( 70,473)( 71,474)
( 72,475)( 73,476)( 74,477)( 75,478)( 76,479)( 77,480)( 78,481)( 79,508)
( 80,509)( 81,510)( 82,511)( 83,512)( 84,513)( 85,514)( 86,515)( 87,516)
( 88,517)( 89,518)( 90,519)( 91,520)( 92,495)( 93,496)( 94,497)( 95,498)
( 96,499)( 97,500)( 98,501)( 99,502)(100,503)(101,504)(102,505)(103,506)
(104,507)(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)(131,599)(132,600)(133,601)(134,602)(135,603)
(136,604)(137,605)(138,606)(139,607)(140,608)(141,609)(142,610)(143,611)
(144,612)(145,613)(146,614)(147,615)(148,616)(149,617)(150,618)(151,619)
(152,620)(153,621)(154,622)(155,623)(156,624)(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)(183,547)
(184,548)(185,549)(186,550)(187,551)(188,552)(189,553)(190,554)(191,555)
(192,556)(193,557)(194,558)(195,559)(196,560)(197,561)(198,562)(199,563)
(200,564)(201,565)(202,566)(203,567)(204,568)(205,569)(206,570)(207,571)
(208,572)(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)(235,651)(236,652)(237,653)(238,654)(239,655)
(240,656)(241,657)(242,658)(243,659)(244,660)(245,661)(246,662)(247,663)
(248,664)(249,665)(250,666)(251,667)(252,668)(253,669)(254,670)(255,671)
(256,672)(257,673)(258,674)(259,675)(260,676)(261,690)(262,691)(263,692)
(264,693)(265,694)(266,695)(267,696)(268,697)(269,698)(270,699)(271,700)
(272,701)(273,702)(274,677)(275,678)(276,679)(277,680)(278,681)(279,682)
(280,683)(281,684)(282,685)(283,686)(284,687)(285,688)(286,689)(287,716)
(288,717)(289,718)(290,719)(291,720)(292,721)(293,722)(294,723)(295,724)
(296,725)(297,726)(298,727)(299,728)(300,703)(301,704)(302,705)(303,706)
(304,707)(305,708)(306,709)(307,710)(308,711)(309,712)(310,713)(311,714)
(312,715)(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)(339,807)(340,808)(341,809)(342,810)(343,811)
(344,812)(345,813)(346,814)(347,815)(348,816)(349,817)(350,818)(351,819)
(352,820)(353,821)(354,822)(355,823)(356,824)(357,825)(358,826)(359,827)
(360,828)(361,829)(362,830)(363,831)(364,832)(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)(391,755)
(392,756)(393,757)(394,758)(395,759)(396,760)(397,761)(398,762)(399,763)
(400,764)(401,765)(402,766)(403,767)(404,768)(405,769)(406,770)(407,771)
(408,772)(409,773)(410,774)(411,775)(412,776)(413,777)(414,778)(415,779)
(416,780);
s1 := Sym(832)!( 1,105)( 2,117)( 3,116)( 4,115)( 5,114)( 6,113)( 7,112)
( 8,111)( 9,110)( 10,109)( 11,108)( 12,107)( 13,106)( 14,118)( 15,130)
( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)
( 24,121)( 25,120)( 26,119)( 27,131)( 28,143)( 29,142)( 30,141)( 31,140)
( 32,139)( 33,138)( 34,137)( 35,136)( 36,135)( 37,134)( 38,133)( 39,132)
( 40,144)( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)
( 48,149)( 49,148)( 50,147)( 51,146)( 52,145)( 53,170)( 54,182)( 55,181)
( 56,180)( 57,179)( 58,178)( 59,177)( 60,176)( 61,175)( 62,174)( 63,173)
( 64,172)( 65,171)( 66,157)( 67,169)( 68,168)( 69,167)( 70,166)( 71,165)
( 72,164)( 73,163)( 74,162)( 75,161)( 76,160)( 77,159)( 78,158)( 79,196)
( 80,208)( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)
( 88,200)( 89,199)( 90,198)( 91,197)( 92,183)( 93,195)( 94,194)( 95,193)
( 96,192)( 97,191)( 98,190)( 99,189)(100,188)(101,187)(102,186)(103,185)
(104,184)(209,313)(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)
(216,319)(217,318)(218,317)(219,316)(220,315)(221,314)(222,326)(223,338)
(224,337)(225,336)(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)
(232,329)(233,328)(234,327)(235,339)(236,351)(237,350)(238,349)(239,348)
(240,347)(241,346)(242,345)(243,344)(244,343)(245,342)(246,341)(247,340)
(248,352)(249,364)(250,363)(251,362)(252,361)(253,360)(254,359)(255,358)
(256,357)(257,356)(258,355)(259,354)(260,353)(261,378)(262,390)(263,389)
(264,388)(265,387)(266,386)(267,385)(268,384)(269,383)(270,382)(271,381)
(272,380)(273,379)(274,365)(275,377)(276,376)(277,375)(278,374)(279,373)
(280,372)(281,371)(282,370)(283,369)(284,368)(285,367)(286,366)(287,404)
(288,416)(289,415)(290,414)(291,413)(292,412)(293,411)(294,410)(295,409)
(296,408)(297,407)(298,406)(299,405)(300,391)(301,403)(302,402)(303,401)
(304,400)(305,399)(306,398)(307,397)(308,396)(309,395)(310,394)(311,393)
(312,392)(417,521)(418,533)(419,532)(420,531)(421,530)(422,529)(423,528)
(424,527)(425,526)(426,525)(427,524)(428,523)(429,522)(430,534)(431,546)
(432,545)(433,544)(434,543)(435,542)(436,541)(437,540)(438,539)(439,538)
(440,537)(441,536)(442,535)(443,547)(444,559)(445,558)(446,557)(447,556)
(448,555)(449,554)(450,553)(451,552)(452,551)(453,550)(454,549)(455,548)
(456,560)(457,572)(458,571)(459,570)(460,569)(461,568)(462,567)(463,566)
(464,565)(465,564)(466,563)(467,562)(468,561)(469,586)(470,598)(471,597)
(472,596)(473,595)(474,594)(475,593)(476,592)(477,591)(478,590)(479,589)
(480,588)(481,587)(482,573)(483,585)(484,584)(485,583)(486,582)(487,581)
(488,580)(489,579)(490,578)(491,577)(492,576)(493,575)(494,574)(495,612)
(496,624)(497,623)(498,622)(499,621)(500,620)(501,619)(502,618)(503,617)
(504,616)(505,615)(506,614)(507,613)(508,599)(509,611)(510,610)(511,609)
(512,608)(513,607)(514,606)(515,605)(516,604)(517,603)(518,602)(519,601)
(520,600)(625,729)(626,741)(627,740)(628,739)(629,738)(630,737)(631,736)
(632,735)(633,734)(634,733)(635,732)(636,731)(637,730)(638,742)(639,754)
(640,753)(641,752)(642,751)(643,750)(644,749)(645,748)(646,747)(647,746)
(648,745)(649,744)(650,743)(651,755)(652,767)(653,766)(654,765)(655,764)
(656,763)(657,762)(658,761)(659,760)(660,759)(661,758)(662,757)(663,756)
(664,768)(665,780)(666,779)(667,778)(668,777)(669,776)(670,775)(671,774)
(672,773)(673,772)(674,771)(675,770)(676,769)(677,794)(678,806)(679,805)
(680,804)(681,803)(682,802)(683,801)(684,800)(685,799)(686,798)(687,797)
(688,796)(689,795)(690,781)(691,793)(692,792)(693,791)(694,790)(695,789)
(696,788)(697,787)(698,786)(699,785)(700,784)(701,783)(702,782)(703,820)
(704,832)(705,831)(706,830)(707,829)(708,828)(709,827)(710,826)(711,825)
(712,824)(713,823)(714,822)(715,821)(716,807)(717,819)(718,818)(719,817)
(720,816)(721,815)(722,814)(723,813)(724,812)(725,811)(726,810)(727,809)
(728,808);
s2 := Sym(832)!( 1,158)( 2,157)( 3,169)( 4,168)( 5,167)( 6,166)( 7,165)
( 8,164)( 9,163)( 10,162)( 11,161)( 12,160)( 13,159)( 14,171)( 15,170)
( 16,182)( 17,181)( 18,180)( 19,179)( 20,178)( 21,177)( 22,176)( 23,175)
( 24,174)( 25,173)( 26,172)( 27,184)( 28,183)( 29,195)( 30,194)( 31,193)
( 32,192)( 33,191)( 34,190)( 35,189)( 36,188)( 37,187)( 38,186)( 39,185)
( 40,197)( 41,196)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)
( 48,202)( 49,201)( 50,200)( 51,199)( 52,198)( 53,119)( 54,118)( 55,130)
( 56,129)( 57,128)( 58,127)( 59,126)( 60,125)( 61,124)( 62,123)( 63,122)
( 64,121)( 65,120)( 66,106)( 67,105)( 68,117)( 69,116)( 70,115)( 71,114)
( 72,113)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,107)( 79,145)
( 80,144)( 81,156)( 82,155)( 83,154)( 84,153)( 85,152)( 86,151)( 87,150)
( 88,149)( 89,148)( 90,147)( 91,146)( 92,132)( 93,131)( 94,143)( 95,142)
( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)
(104,133)(209,392)(210,391)(211,403)(212,402)(213,401)(214,400)(215,399)
(216,398)(217,397)(218,396)(219,395)(220,394)(221,393)(222,405)(223,404)
(224,416)(225,415)(226,414)(227,413)(228,412)(229,411)(230,410)(231,409)
(232,408)(233,407)(234,406)(235,366)(236,365)(237,377)(238,376)(239,375)
(240,374)(241,373)(242,372)(243,371)(244,370)(245,369)(246,368)(247,367)
(248,379)(249,378)(250,390)(251,389)(252,388)(253,387)(254,386)(255,385)
(256,384)(257,383)(258,382)(259,381)(260,380)(261,353)(262,352)(263,364)
(264,363)(265,362)(266,361)(267,360)(268,359)(269,358)(270,357)(271,356)
(272,355)(273,354)(274,340)(275,339)(276,351)(277,350)(278,349)(279,348)
(280,347)(281,346)(282,345)(283,344)(284,343)(285,342)(286,341)(287,327)
(288,326)(289,338)(290,337)(291,336)(292,335)(293,334)(294,333)(295,332)
(296,331)(297,330)(298,329)(299,328)(300,314)(301,313)(302,325)(303,324)
(304,323)(305,322)(306,321)(307,320)(308,319)(309,318)(310,317)(311,316)
(312,315)(417,522)(418,521)(419,533)(420,532)(421,531)(422,530)(423,529)
(424,528)(425,527)(426,526)(427,525)(428,524)(429,523)(430,535)(431,534)
(432,546)(433,545)(434,544)(435,543)(436,542)(437,541)(438,540)(439,539)
(440,538)(441,537)(442,536)(443,548)(444,547)(445,559)(446,558)(447,557)
(448,556)(449,555)(450,554)(451,553)(452,552)(453,551)(454,550)(455,549)
(456,561)(457,560)(458,572)(459,571)(460,570)(461,569)(462,568)(463,567)
(464,566)(465,565)(466,564)(467,563)(468,562)(469,574)(470,573)(471,585)
(472,584)(473,583)(474,582)(475,581)(476,580)(477,579)(478,578)(479,577)
(480,576)(481,575)(482,587)(483,586)(484,598)(485,597)(486,596)(487,595)
(488,594)(489,593)(490,592)(491,591)(492,590)(493,589)(494,588)(495,600)
(496,599)(497,611)(498,610)(499,609)(500,608)(501,607)(502,606)(503,605)
(504,604)(505,603)(506,602)(507,601)(508,613)(509,612)(510,624)(511,623)
(512,622)(513,621)(514,620)(515,619)(516,618)(517,617)(518,616)(519,615)
(520,614)(625,756)(626,755)(627,767)(628,766)(629,765)(630,764)(631,763)
(632,762)(633,761)(634,760)(635,759)(636,758)(637,757)(638,769)(639,768)
(640,780)(641,779)(642,778)(643,777)(644,776)(645,775)(646,774)(647,773)
(648,772)(649,771)(650,770)(651,730)(652,729)(653,741)(654,740)(655,739)
(656,738)(657,737)(658,736)(659,735)(660,734)(661,733)(662,732)(663,731)
(664,743)(665,742)(666,754)(667,753)(668,752)(669,751)(670,750)(671,749)
(672,748)(673,747)(674,746)(675,745)(676,744)(677,808)(678,807)(679,819)
(680,818)(681,817)(682,816)(683,815)(684,814)(685,813)(686,812)(687,811)
(688,810)(689,809)(690,821)(691,820)(692,832)(693,831)(694,830)(695,829)
(696,828)(697,827)(698,826)(699,825)(700,824)(701,823)(702,822)(703,782)
(704,781)(705,793)(706,792)(707,791)(708,790)(709,789)(710,788)(711,787)
(712,786)(713,785)(714,784)(715,783)(716,795)(717,794)(718,806)(719,805)
(720,804)(721,803)(722,802)(723,801)(724,800)(725,799)(726,798)(727,797)
(728,796);
s3 := Sym(832)!( 1,209)( 2,210)( 3,211)( 4,212)( 5,213)( 6,214)( 7,215)
( 8,216)( 9,217)( 10,218)( 11,219)( 12,220)( 13,221)( 14,222)( 15,223)
( 16,224)( 17,225)( 18,226)( 19,227)( 20,228)( 21,229)( 22,230)( 23,231)
( 24,232)( 25,233)( 26,234)( 27,235)( 28,236)( 29,237)( 30,238)( 31,239)
( 32,240)( 33,241)( 34,242)( 35,243)( 36,244)( 37,245)( 38,246)( 39,247)
( 40,248)( 41,249)( 42,250)( 43,251)( 44,252)( 45,253)( 46,254)( 47,255)
( 48,256)( 49,257)( 50,258)( 51,259)( 52,260)( 53,261)( 54,262)( 55,263)
( 56,264)( 57,265)( 58,266)( 59,267)( 60,268)( 61,269)( 62,270)( 63,271)
( 64,272)( 65,273)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)
( 72,280)( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,287)
( 80,288)( 81,289)( 82,290)( 83,291)( 84,292)( 85,293)( 86,294)( 87,295)
( 88,296)( 89,297)( 90,298)( 91,299)( 92,300)( 93,301)( 94,302)( 95,303)
( 96,304)( 97,305)( 98,306)( 99,307)(100,308)(101,309)(102,310)(103,311)
(104,312)(105,313)(106,314)(107,315)(108,316)(109,317)(110,318)(111,319)
(112,320)(113,321)(114,322)(115,323)(116,324)(117,325)(118,326)(119,327)
(120,328)(121,329)(122,330)(123,331)(124,332)(125,333)(126,334)(127,335)
(128,336)(129,337)(130,338)(131,339)(132,340)(133,341)(134,342)(135,343)
(136,344)(137,345)(138,346)(139,347)(140,348)(141,349)(142,350)(143,351)
(144,352)(145,353)(146,354)(147,355)(148,356)(149,357)(150,358)(151,359)
(152,360)(153,361)(154,362)(155,363)(156,364)(157,365)(158,366)(159,367)
(160,368)(161,369)(162,370)(163,371)(164,372)(165,373)(166,374)(167,375)
(168,376)(169,377)(170,378)(171,379)(172,380)(173,381)(174,382)(175,383)
(176,384)(177,385)(178,386)(179,387)(180,388)(181,389)(182,390)(183,391)
(184,392)(185,393)(186,394)(187,395)(188,396)(189,397)(190,398)(191,399)
(192,400)(193,401)(194,402)(195,403)(196,404)(197,405)(198,406)(199,407)
(200,408)(201,409)(202,410)(203,411)(204,412)(205,413)(206,414)(207,415)
(208,416)(417,625)(418,626)(419,627)(420,628)(421,629)(422,630)(423,631)
(424,632)(425,633)(426,634)(427,635)(428,636)(429,637)(430,638)(431,639)
(432,640)(433,641)(434,642)(435,643)(436,644)(437,645)(438,646)(439,647)
(440,648)(441,649)(442,650)(443,651)(444,652)(445,653)(446,654)(447,655)
(448,656)(449,657)(450,658)(451,659)(452,660)(453,661)(454,662)(455,663)
(456,664)(457,665)(458,666)(459,667)(460,668)(461,669)(462,670)(463,671)
(464,672)(465,673)(466,674)(467,675)(468,676)(469,677)(470,678)(471,679)
(472,680)(473,681)(474,682)(475,683)(476,684)(477,685)(478,686)(479,687)
(480,688)(481,689)(482,690)(483,691)(484,692)(485,693)(486,694)(487,695)
(488,696)(489,697)(490,698)(491,699)(492,700)(493,701)(494,702)(495,703)
(496,704)(497,705)(498,706)(499,707)(500,708)(501,709)(502,710)(503,711)
(504,712)(505,713)(506,714)(507,715)(508,716)(509,717)(510,718)(511,719)
(512,720)(513,721)(514,722)(515,723)(516,724)(517,725)(518,726)(519,727)
(520,728)(521,729)(522,730)(523,731)(524,732)(525,733)(526,734)(527,735)
(528,736)(529,737)(530,738)(531,739)(532,740)(533,741)(534,742)(535,743)
(536,744)(537,745)(538,746)(539,747)(540,748)(541,749)(542,750)(543,751)
(544,752)(545,753)(546,754)(547,755)(548,756)(549,757)(550,758)(551,759)
(552,760)(553,761)(554,762)(555,763)(556,764)(557,765)(558,766)(559,767)
(560,768)(561,769)(562,770)(563,771)(564,772)(565,773)(566,774)(567,775)
(568,776)(569,777)(570,778)(571,779)(572,780)(573,781)(574,782)(575,783)
(576,784)(577,785)(578,786)(579,787)(580,788)(581,789)(582,790)(583,791)
(584,792)(585,793)(586,794)(587,795)(588,796)(589,797)(590,798)(591,799)
(592,800)(593,801)(594,802)(595,803)(596,804)(597,805)(598,806)(599,807)
(600,808)(601,809)(602,810)(603,811)(604,812)(605,813)(606,814)(607,815)
(608,816)(609,817)(610,818)(611,819)(612,820)(613,821)(614,822)(615,823)
(616,824)(617,825)(618,826)(619,827)(620,828)(621,829)(622,830)(623,831)
(624,832);
poly := sub<Sym(832)|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*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, 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 >;
References : None.
to this polytope