Polytope of Type {8,42}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,42}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11408)
Rank : 3
Schlafli Type : {8,42}
Number of vertices, edges, etc : 16, 336, 84
Order of s₀s₁s₂ : 84
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {8,21}*672, {4,42}*672
   4-fold quotients : {4,21}*336, {4,42}*336b, {4,42}*336c
   7-fold quotients : {8,6}*192b
   8-fold quotients : {4,21}*168, {2,42}*168
   14-fold quotients : {8,3}*96, {4,6}*96
   16-fold quotients : {2,21}*84
   24-fold quotients : {2,14}*56
   28-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {2,7}*28
   56-fold quotients : {4,3}*24, {2,6}*24
   112-fold quotients : {2,3}*12
   168-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Polytope of Type {8,42}

Twisty Puzzle