Part of the Atlas of Small Regular Polytopes

Polytope of Type {14,8}

Atlas Canonical Name {14,8}*1568a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1568,805)
Rank
3
Schläfli Type
{14,8}
Vertices, edges, …
98, 392, 56
Order of s0s1s2
8
Order of s0s1s2s1
14
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

49-fold

98-fold

196-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*s0*s1*s2*(s1*s0)^3*s1*s2> of order 7

8 facets

14 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2> of order 7

8 facets

14 vertex figures

P/N, where N=<(s0*s1)^2> of order 7

32 facets

14 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle