Polytope of Type {40,16}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,16}*1280e
if this polytope has a name.
Group : SmallGroup(1280,83049)
Rank : 3
Schlafli Type : {40,16}
Number of vertices, edges, etc : 40, 320, 16
Order of s0s1s2 : 80
Order of s0s1s2s1 : 4
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 : {40,8}*640d, {20,16}*640b
   4-fold quotients : {40,4}*320b, {20,8}*320a
   5-fold quotients : {8,16}*256e
   8-fold quotients : {20,4}*160, {10,8}*160
   10-fold quotients : {8,8}*128a, {4,16}*128b
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {4,8}*64a, {8,4}*64b
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32, {2,8}*32
   64-fold quotients : {5,2}*20
   80-fold quotients : {2,4}*16, {4,2}*16
   160-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 := (  1,161)(  2,165)(  3,164)(  4,163)(  5,162)(  6,166)(  7,170)(  8,169)(  9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)( 16,176)( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)( 24,183)( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)( 32,195)( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)( 40,197)( 41,216)( 42,220)( 43,219)( 44,218)( 45,217)( 46,211)( 47,215)( 48,214)( 49,213)( 50,212)( 51,206)( 52,210)( 53,209)( 54,208)( 55,207)( 56,201)( 57,205)( 58,204)( 59,203)( 60,202)( 61,236)( 62,240)( 63,239)( 64,238)( 65,237)( 66,231)( 67,235)( 68,234)( 69,233)( 70,232)( 71,226)( 72,230)( 73,229)( 74,228)( 75,227)( 76,221)( 77,225)( 78,224)( 79,223)( 80,222)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,256)( 87,260)( 88,259)( 89,258)( 90,257)( 91,241)( 92,245)( 93,244)( 94,243)( 95,242)( 96,246)( 97,250)( 98,249)( 99,248)(100,247)(101,271)(102,275)(103,274)(104,273)(105,272)(106,276)(107,280)(108,279)(109,278)(110,277)(111,261)(112,265)(113,264)(114,263)(115,262)(116,266)(117,270)(118,269)(119,268)(120,267)(121,286)(122,290)(123,289)(124,288)(125,287)(126,281)(127,285)(128,284)(129,283)(130,282)(131,296)(132,300)(133,299)(134,298)(135,297)(136,291)(137,295)(138,294)(139,293)(140,292)(141,306)(142,310)(143,309)(144,308)(145,307)(146,301)(147,305)(148,304)(149,303)(150,302)(151,316)(152,320)(153,319)(154,318)(155,317)(156,311)(157,315)(158,314)(159,313)(160,312)(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)(328,489)(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)(336,496)(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)(344,503)(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)(352,515)(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)(360,517)(361,536)(362,540)(363,539)(364,538)(365,537)(366,531)(367,535)(368,534)(369,533)(370,532)(371,526)(372,530)(373,529)(374,528)(375,527)(376,521)(377,525)(378,524)(379,523)(380,522)(381,556)(382,560)(383,559)(384,558)(385,557)(386,551)(387,555)(388,554)(389,553)(390,552)(391,546)(392,550)(393,549)(394,548)(395,547)(396,541)(397,545)(398,544)(399,543)(400,542)(401,571)(402,575)(403,574)(404,573)(405,572)(406,576)(407,580)(408,579)(409,578)(410,577)(411,561)(412,565)(413,564)(414,563)(415,562)(416,566)(417,570)(418,569)(419,568)(420,567)(421,591)(422,595)(423,594)(424,593)(425,592)(426,596)(427,600)(428,599)(429,598)(430,597)(431,581)(432,585)(433,584)(434,583)(435,582)(436,586)(437,590)(438,589)(439,588)(440,587)(441,606)(442,610)(443,609)(444,608)(445,607)(446,601)(447,605)(448,604)(449,603)(450,602)(451,616)(452,620)(453,619)(454,618)(455,617)(456,611)(457,615)(458,614)(459,613)(460,612)(461,626)(462,630)(463,629)(464,628)(465,627)(466,621)(467,625)(468,624)(469,623)(470,622)(471,636)(472,640)(473,639)(474,638)(475,637)(476,631)(477,635)(478,634)(479,633)(480,632);;
s1 := (  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 38)( 32, 37)( 33, 36)( 34, 40)( 35, 39)( 41, 58)( 42, 57)( 43, 56)( 44, 60)( 45, 59)( 46, 53)( 47, 52)( 48, 51)( 49, 55)( 50, 54)( 61, 73)( 62, 72)( 63, 71)( 64, 75)( 65, 74)( 66, 78)( 67, 77)( 68, 76)( 69, 80)( 70, 79)( 81,103)( 82,102)( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,113)( 92,112)( 93,111)( 94,115)( 95,114)( 96,118)( 97,117)( 98,116)( 99,120)(100,119)(121,158)(122,157)(123,156)(124,160)(125,159)(126,153)(127,152)(128,151)(129,155)(130,154)(131,148)(132,147)(133,146)(134,150)(135,149)(136,143)(137,142)(138,141)(139,145)(140,144)(161,203)(162,202)(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,213)(172,212)(173,211)(174,215)(175,214)(176,218)(177,217)(178,216)(179,220)(180,219)(181,228)(182,227)(183,226)(184,230)(185,229)(186,223)(187,222)(188,221)(189,225)(190,224)(191,238)(192,237)(193,236)(194,240)(195,239)(196,233)(197,232)(198,231)(199,235)(200,234)(241,303)(242,302)(243,301)(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)(260,319)(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)(268,286)(269,290)(270,289)(271,293)(272,292)(273,291)(274,295)(275,294)(276,298)(277,297)(278,296)(279,300)(280,299)(321,403)(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)(331,413)(332,412)(333,411)(334,415)(335,414)(336,418)(337,417)(338,416)(339,420)(340,419)(341,428)(342,427)(343,426)(344,430)(345,429)(346,423)(347,422)(348,421)(349,425)(350,424)(351,438)(352,437)(353,436)(354,440)(355,439)(356,433)(357,432)(358,431)(359,435)(360,434)(361,458)(362,457)(363,456)(364,460)(365,459)(366,453)(367,452)(368,451)(369,455)(370,454)(371,448)(372,447)(373,446)(374,450)(375,449)(376,443)(377,442)(378,441)(379,445)(380,444)(381,473)(382,472)(383,471)(384,475)(385,474)(386,478)(387,477)(388,476)(389,480)(390,479)(391,463)(392,462)(393,461)(394,465)(395,464)(396,468)(397,467)(398,466)(399,470)(400,469)(481,613)(482,612)(483,611)(484,615)(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,603)(492,602)(493,601)(494,605)(495,604)(496,608)(497,607)(498,606)(499,610)(500,609)(501,638)(502,637)(503,636)(504,640)(505,639)(506,633)(507,632)(508,631)(509,635)(510,634)(511,628)(512,627)(513,626)(514,630)(515,629)(516,623)(517,622)(518,621)(519,625)(520,624)(521,573)(522,572)(523,571)(524,575)(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,563)(532,562)(533,561)(534,565)(535,564)(536,568)(537,567)(538,566)(539,570)(540,569)(541,598)(542,597)(543,596)(544,600)(545,599)(546,593)(547,592)(548,591)(549,595)(550,594)(551,588)(552,587)(553,586)(554,590)(555,589)(556,583)(557,582)(558,581)(559,585)(560,584);;
s2 := (  1,321)(  2,322)(  3,323)(  4,324)(  5,325)(  6,326)(  7,327)(  8,328)(  9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)( 16,336)( 17,337)( 18,338)( 19,339)( 20,340)( 21,346)( 22,347)( 23,348)( 24,349)( 25,350)( 26,341)( 27,342)( 28,343)( 29,344)( 30,345)( 31,356)( 32,357)( 33,358)( 34,359)( 35,360)( 36,351)( 37,352)( 38,353)( 39,354)( 40,355)( 41,371)( 42,372)( 43,373)( 44,374)( 45,375)( 46,376)( 47,377)( 48,378)( 49,379)( 50,380)( 51,361)( 52,362)( 53,363)( 54,364)( 55,365)( 56,366)( 57,367)( 58,368)( 59,369)( 60,370)( 61,396)( 62,397)( 63,398)( 64,399)( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)( 72,387)( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)( 80,385)( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,426)( 87,427)( 88,428)( 89,429)( 90,430)( 91,431)( 92,432)( 93,433)( 94,434)( 95,435)( 96,436)( 97,437)( 98,438)( 99,439)(100,440)(101,401)(102,402)(103,403)(104,404)(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,411)(112,412)(113,413)(114,414)(115,415)(116,416)(117,417)(118,418)(119,419)(120,420)(121,471)(122,472)(123,473)(124,474)(125,475)(126,476)(127,477)(128,478)(129,479)(130,480)(131,461)(132,462)(133,463)(134,464)(135,465)(136,466)(137,467)(138,468)(139,469)(140,470)(141,451)(142,452)(143,453)(144,454)(145,455)(146,456)(147,457)(148,458)(149,459)(150,460)(151,441)(152,442)(153,443)(154,444)(155,445)(156,446)(157,447)(158,448)(159,449)(160,450)(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)(169,489)(170,490)(171,491)(172,492)(173,493)(174,494)(175,495)(176,496)(177,497)(178,498)(179,499)(180,500)(181,506)(182,507)(183,508)(184,509)(185,510)(186,501)(187,502)(188,503)(189,504)(190,505)(191,516)(192,517)(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)(200,515)(201,531)(202,532)(203,533)(204,534)(205,535)(206,536)(207,537)(208,538)(209,539)(210,540)(211,521)(212,522)(213,523)(214,524)(215,525)(216,526)(217,527)(218,528)(219,529)(220,530)(221,556)(222,557)(223,558)(224,559)(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)(232,547)(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)(240,545)(241,581)(242,582)(243,583)(244,584)(245,585)(246,586)(247,587)(248,588)(249,589)(250,590)(251,591)(252,592)(253,593)(254,594)(255,595)(256,596)(257,597)(258,598)(259,599)(260,600)(261,561)(262,562)(263,563)(264,564)(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,571)(272,572)(273,573)(274,574)(275,575)(276,576)(277,577)(278,578)(279,579)(280,580)(281,631)(282,632)(283,633)(284,634)(285,635)(286,636)(287,637)(288,638)(289,639)(290,640)(291,621)(292,622)(293,623)(294,624)(295,625)(296,626)(297,627)(298,628)(299,629)(300,630)(301,611)(302,612)(303,613)(304,614)(305,615)(306,616)(307,617)(308,618)(309,619)(310,620)(311,601)(312,602)(313,603)(314,604)(315,605)(316,606)(317,607)(318,608)(319,609)(320,610);;
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*s0*s1*s0*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(640)!(  1,161)(  2,165)(  3,164)(  4,163)(  5,162)(  6,166)(  7,170)(  8,169)(  9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)( 16,176)( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)( 24,183)( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)( 32,195)( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)( 40,197)( 41,216)( 42,220)( 43,219)( 44,218)( 45,217)( 46,211)( 47,215)( 48,214)( 49,213)( 50,212)( 51,206)( 52,210)( 53,209)( 54,208)( 55,207)( 56,201)( 57,205)( 58,204)( 59,203)( 60,202)( 61,236)( 62,240)( 63,239)( 64,238)( 65,237)( 66,231)( 67,235)( 68,234)( 69,233)( 70,232)( 71,226)( 72,230)( 73,229)( 74,228)( 75,227)( 76,221)( 77,225)( 78,224)( 79,223)( 80,222)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,256)( 87,260)( 88,259)( 89,258)( 90,257)( 91,241)( 92,245)( 93,244)( 94,243)( 95,242)( 96,246)( 97,250)( 98,249)( 99,248)(100,247)(101,271)(102,275)(103,274)(104,273)(105,272)(106,276)(107,280)(108,279)(109,278)(110,277)(111,261)(112,265)(113,264)(114,263)(115,262)(116,266)(117,270)(118,269)(119,268)(120,267)(121,286)(122,290)(123,289)(124,288)(125,287)(126,281)(127,285)(128,284)(129,283)(130,282)(131,296)(132,300)(133,299)(134,298)(135,297)(136,291)(137,295)(138,294)(139,293)(140,292)(141,306)(142,310)(143,309)(144,308)(145,307)(146,301)(147,305)(148,304)(149,303)(150,302)(151,316)(152,320)(153,319)(154,318)(155,317)(156,311)(157,315)(158,314)(159,313)(160,312)(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)(328,489)(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)(336,496)(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)(344,503)(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)(352,515)(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)(360,517)(361,536)(362,540)(363,539)(364,538)(365,537)(366,531)(367,535)(368,534)(369,533)(370,532)(371,526)(372,530)(373,529)(374,528)(375,527)(376,521)(377,525)(378,524)(379,523)(380,522)(381,556)(382,560)(383,559)(384,558)(385,557)(386,551)(387,555)(388,554)(389,553)(390,552)(391,546)(392,550)(393,549)(394,548)(395,547)(396,541)(397,545)(398,544)(399,543)(400,542)(401,571)(402,575)(403,574)(404,573)(405,572)(406,576)(407,580)(408,579)(409,578)(410,577)(411,561)(412,565)(413,564)(414,563)(415,562)(416,566)(417,570)(418,569)(419,568)(420,567)(421,591)(422,595)(423,594)(424,593)(425,592)(426,596)(427,600)(428,599)(429,598)(430,597)(431,581)(432,585)(433,584)(434,583)(435,582)(436,586)(437,590)(438,589)(439,588)(440,587)(441,606)(442,610)(443,609)(444,608)(445,607)(446,601)(447,605)(448,604)(449,603)(450,602)(451,616)(452,620)(453,619)(454,618)(455,617)(456,611)(457,615)(458,614)(459,613)(460,612)(461,626)(462,630)(463,629)(464,628)(465,627)(466,621)(467,625)(468,624)(469,623)(470,622)(471,636)(472,640)(473,639)(474,638)(475,637)(476,631)(477,635)(478,634)(479,633)(480,632);
s1 := Sym(640)!(  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 38)( 32, 37)( 33, 36)( 34, 40)( 35, 39)( 41, 58)( 42, 57)( 43, 56)( 44, 60)( 45, 59)( 46, 53)( 47, 52)( 48, 51)( 49, 55)( 50, 54)( 61, 73)( 62, 72)( 63, 71)( 64, 75)( 65, 74)( 66, 78)( 67, 77)( 68, 76)( 69, 80)( 70, 79)( 81,103)( 82,102)( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,113)( 92,112)( 93,111)( 94,115)( 95,114)( 96,118)( 97,117)( 98,116)( 99,120)(100,119)(121,158)(122,157)(123,156)(124,160)(125,159)(126,153)(127,152)(128,151)(129,155)(130,154)(131,148)(132,147)(133,146)(134,150)(135,149)(136,143)(137,142)(138,141)(139,145)(140,144)(161,203)(162,202)(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,213)(172,212)(173,211)(174,215)(175,214)(176,218)(177,217)(178,216)(179,220)(180,219)(181,228)(182,227)(183,226)(184,230)(185,229)(186,223)(187,222)(188,221)(189,225)(190,224)(191,238)(192,237)(193,236)(194,240)(195,239)(196,233)(197,232)(198,231)(199,235)(200,234)(241,303)(242,302)(243,301)(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)(260,319)(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)(268,286)(269,290)(270,289)(271,293)(272,292)(273,291)(274,295)(275,294)(276,298)(277,297)(278,296)(279,300)(280,299)(321,403)(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)(331,413)(332,412)(333,411)(334,415)(335,414)(336,418)(337,417)(338,416)(339,420)(340,419)(341,428)(342,427)(343,426)(344,430)(345,429)(346,423)(347,422)(348,421)(349,425)(350,424)(351,438)(352,437)(353,436)(354,440)(355,439)(356,433)(357,432)(358,431)(359,435)(360,434)(361,458)(362,457)(363,456)(364,460)(365,459)(366,453)(367,452)(368,451)(369,455)(370,454)(371,448)(372,447)(373,446)(374,450)(375,449)(376,443)(377,442)(378,441)(379,445)(380,444)(381,473)(382,472)(383,471)(384,475)(385,474)(386,478)(387,477)(388,476)(389,480)(390,479)(391,463)(392,462)(393,461)(394,465)(395,464)(396,468)(397,467)(398,466)(399,470)(400,469)(481,613)(482,612)(483,611)(484,615)(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,603)(492,602)(493,601)(494,605)(495,604)(496,608)(497,607)(498,606)(499,610)(500,609)(501,638)(502,637)(503,636)(504,640)(505,639)(506,633)(507,632)(508,631)(509,635)(510,634)(511,628)(512,627)(513,626)(514,630)(515,629)(516,623)(517,622)(518,621)(519,625)(520,624)(521,573)(522,572)(523,571)(524,575)(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,563)(532,562)(533,561)(534,565)(535,564)(536,568)(537,567)(538,566)(539,570)(540,569)(541,598)(542,597)(543,596)(544,600)(545,599)(546,593)(547,592)(548,591)(549,595)(550,594)(551,588)(552,587)(553,586)(554,590)(555,589)(556,583)(557,582)(558,581)(559,585)(560,584);
s2 := Sym(640)!(  1,321)(  2,322)(  3,323)(  4,324)(  5,325)(  6,326)(  7,327)(  8,328)(  9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)( 16,336)( 17,337)( 18,338)( 19,339)( 20,340)( 21,346)( 22,347)( 23,348)( 24,349)( 25,350)( 26,341)( 27,342)( 28,343)( 29,344)( 30,345)( 31,356)( 32,357)( 33,358)( 34,359)( 35,360)( 36,351)( 37,352)( 38,353)( 39,354)( 40,355)( 41,371)( 42,372)( 43,373)( 44,374)( 45,375)( 46,376)( 47,377)( 48,378)( 49,379)( 50,380)( 51,361)( 52,362)( 53,363)( 54,364)( 55,365)( 56,366)( 57,367)( 58,368)( 59,369)( 60,370)( 61,396)( 62,397)( 63,398)( 64,399)( 65,400)( 66,391)( 67,392)( 68,393)( 69,394)( 70,395)( 71,386)( 72,387)( 73,388)( 74,389)( 75,390)( 76,381)( 77,382)( 78,383)( 79,384)( 80,385)( 81,421)( 82,422)( 83,423)( 84,424)( 85,425)( 86,426)( 87,427)( 88,428)( 89,429)( 90,430)( 91,431)( 92,432)( 93,433)( 94,434)( 95,435)( 96,436)( 97,437)( 98,438)( 99,439)(100,440)(101,401)(102,402)(103,403)(104,404)(105,405)(106,406)(107,407)(108,408)(109,409)(110,410)(111,411)(112,412)(113,413)(114,414)(115,415)(116,416)(117,417)(118,418)(119,419)(120,420)(121,471)(122,472)(123,473)(124,474)(125,475)(126,476)(127,477)(128,478)(129,479)(130,480)(131,461)(132,462)(133,463)(134,464)(135,465)(136,466)(137,467)(138,468)(139,469)(140,470)(141,451)(142,452)(143,453)(144,454)(145,455)(146,456)(147,457)(148,458)(149,459)(150,460)(151,441)(152,442)(153,443)(154,444)(155,445)(156,446)(157,447)(158,448)(159,449)(160,450)(161,481)(162,482)(163,483)(164,484)(165,485)(166,486)(167,487)(168,488)(169,489)(170,490)(171,491)(172,492)(173,493)(174,494)(175,495)(176,496)(177,497)(178,498)(179,499)(180,500)(181,506)(182,507)(183,508)(184,509)(185,510)(186,501)(187,502)(188,503)(189,504)(190,505)(191,516)(192,517)(193,518)(194,519)(195,520)(196,511)(197,512)(198,513)(199,514)(200,515)(201,531)(202,532)(203,533)(204,534)(205,535)(206,536)(207,537)(208,538)(209,539)(210,540)(211,521)(212,522)(213,523)(214,524)(215,525)(216,526)(217,527)(218,528)(219,529)(220,530)(221,556)(222,557)(223,558)(224,559)(225,560)(226,551)(227,552)(228,553)(229,554)(230,555)(231,546)(232,547)(233,548)(234,549)(235,550)(236,541)(237,542)(238,543)(239,544)(240,545)(241,581)(242,582)(243,583)(244,584)(245,585)(246,586)(247,587)(248,588)(249,589)(250,590)(251,591)(252,592)(253,593)(254,594)(255,595)(256,596)(257,597)(258,598)(259,599)(260,600)(261,561)(262,562)(263,563)(264,564)(265,565)(266,566)(267,567)(268,568)(269,569)(270,570)(271,571)(272,572)(273,573)(274,574)(275,575)(276,576)(277,577)(278,578)(279,579)(280,580)(281,631)(282,632)(283,633)(284,634)(285,635)(286,636)(287,637)(288,638)(289,639)(290,640)(291,621)(292,622)(293,623)(294,624)(295,625)(296,626)(297,627)(298,628)(299,629)(300,630)(301,611)(302,612)(303,613)(304,614)(305,615)(306,616)(307,617)(308,618)(309,619)(310,620)(311,601)(312,602)(313,603)(314,604)(315,605)(316,606)(317,607)(318,608)(319,609)(320,610);
poly := sub<Sym(640)|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*s0*s1*s0*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 >;
References : None.
to this polytope

Twisty Puzzle