Polytope of Type {6,136}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,136}*1632
Also Known As : {6,136|2}. if this polytope has another name.
Group : SmallGroup(1632,325)
Rank : 3
Schlafli Type : {6,136}
Number of vertices, edges, etc : 6, 408, 136
Order of s0s1s2 : 408
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,68}*816a
   3-fold quotients : {2,136}*544
   4-fold quotients : {6,34}*408
   6-fold quotients : {2,68}*272
   12-fold quotients : {2,34}*136
   17-fold quotients : {6,8}*96
   24-fold quotients : {2,17}*68
   34-fold quotients : {6,4}*48a
   51-fold quotients : {2,8}*32
   68-fold quotients : {6,2}*24
   102-fold quotients : {2,4}*16
   136-fold quotients : {3,2}*12
   204-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 := ( 18, 35)( 19, 36)( 20, 37)( 21, 38)( 22, 39)( 23, 40)( 24, 41)( 25, 42)( 26, 43)( 27, 44)( 28, 45)( 29, 46)( 30, 47)( 31, 48)( 32, 49)( 33, 50)( 34, 51)( 69, 86)( 70, 87)( 71, 88)( 72, 89)( 73, 90)( 74, 91)( 75, 92)( 76, 93)( 77, 94)( 78, 95)( 79, 96)( 80, 97)( 81, 98)( 82, 99)( 83,100)( 84,101)( 85,102)(120,137)(121,138)(122,139)(123,140)(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)(133,150)(134,151)(135,152)(136,153)(171,188)(172,189)(173,190)(174,191)(175,192)(176,193)(177,194)(178,195)(179,196)(180,197)(181,198)(182,199)(183,200)(184,201)(185,202)(186,203)(187,204)(222,239)(223,240)(224,241)(225,242)(226,243)(227,244)(228,245)(229,246)(230,247)(231,248)(232,249)(233,250)(234,251)(235,252)(236,253)(237,254)(238,255)(273,290)(274,291)(275,292)(276,293)(277,294)(278,295)(279,296)(280,297)(281,298)(282,299)(283,300)(284,301)(285,302)(286,303)(287,304)(288,305)(289,306)(324,341)(325,342)(326,343)(327,344)(328,345)(329,346)(330,347)(331,348)(332,349)(333,350)(334,351)(335,352)(336,353)(337,354)(338,355)(339,356)(340,357)(375,392)(376,393)(377,394)(378,395)(379,396)(380,397)(381,398)(382,399)(383,400)(384,401)(385,402)(386,403)(387,404)(388,405)(389,406)(390,407)(391,408);;
s1 := (  1, 18)(  2, 34)(  3, 33)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 28)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 43, 44)( 52, 69)( 53, 85)( 54, 84)( 55, 83)( 56, 82)( 57, 81)( 58, 80)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(103,171)(104,187)(105,186)(106,185)(107,184)(108,183)(109,182)(110,181)(111,180)(112,179)(113,178)(114,177)(115,176)(116,175)(117,174)(118,173)(119,172)(120,154)(121,170)(122,169)(123,168)(124,167)(125,166)(126,165)(127,164)(128,163)(129,162)(130,161)(131,160)(132,159)(133,158)(134,157)(135,156)(136,155)(137,188)(138,204)(139,203)(140,202)(141,201)(142,200)(143,199)(144,198)(145,197)(146,196)(147,195)(148,194)(149,193)(150,192)(151,191)(152,190)(153,189)(205,324)(206,340)(207,339)(208,338)(209,337)(210,336)(211,335)(212,334)(213,333)(214,332)(215,331)(216,330)(217,329)(218,328)(219,327)(220,326)(221,325)(222,307)(223,323)(224,322)(225,321)(226,320)(227,319)(228,318)(229,317)(230,316)(231,315)(232,314)(233,313)(234,312)(235,311)(236,310)(237,309)(238,308)(239,341)(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,351)(247,350)(248,349)(249,348)(250,347)(251,346)(252,345)(253,344)(254,343)(255,342)(256,375)(257,391)(258,390)(259,389)(260,388)(261,387)(262,386)(263,385)(264,384)(265,383)(266,382)(267,381)(268,380)(269,379)(270,378)(271,377)(272,376)(273,358)(274,374)(275,373)(276,372)(277,371)(278,370)(279,369)(280,368)(281,367)(282,366)(283,365)(284,364)(285,363)(286,362)(287,361)(288,360)(289,359)(290,392)(291,408)(292,407)(293,406)(294,405)(295,404)(296,403)(297,402)(298,401)(299,400)(300,399)(301,398)(302,397)(303,396)(304,395)(305,394)(306,393);;
s2 := (  1,206)(  2,205)(  3,221)(  4,220)(  5,219)(  6,218)(  7,217)(  8,216)(  9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,210)( 15,209)( 16,208)( 17,207)( 18,223)( 19,222)( 20,238)( 21,237)( 22,236)( 23,235)( 24,234)( 25,233)( 26,232)( 27,231)( 28,230)( 29,229)( 30,228)( 31,227)( 32,226)( 33,225)( 34,224)( 35,240)( 36,239)( 37,255)( 38,254)( 39,253)( 40,252)( 41,251)( 42,250)( 43,249)( 44,248)( 45,247)( 46,246)( 47,245)( 48,244)( 49,243)( 50,242)( 51,241)( 52,257)( 53,256)( 54,272)( 55,271)( 56,270)( 57,269)( 58,268)( 59,267)( 60,266)( 61,265)( 62,264)( 63,263)( 64,262)( 65,261)( 66,260)( 67,259)( 68,258)( 69,274)( 70,273)( 71,289)( 72,288)( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,282)( 79,281)( 80,280)( 81,279)( 82,278)( 83,277)( 84,276)( 85,275)( 86,291)( 87,290)( 88,306)( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,359)(104,358)(105,374)(106,373)(107,372)(108,371)(109,370)(110,369)(111,368)(112,367)(113,366)(114,365)(115,364)(116,363)(117,362)(118,361)(119,360)(120,376)(121,375)(122,391)(123,390)(124,389)(125,388)(126,387)(127,386)(128,385)(129,384)(130,383)(131,382)(132,381)(133,380)(134,379)(135,378)(136,377)(137,393)(138,392)(139,408)(140,407)(141,406)(142,405)(143,404)(144,403)(145,402)(146,401)(147,400)(148,399)(149,398)(150,397)(151,396)(152,395)(153,394)(154,308)(155,307)(156,323)(157,322)(158,321)(159,320)(160,319)(161,318)(162,317)(163,316)(164,315)(165,314)(166,313)(167,312)(168,311)(169,310)(170,309)(171,325)(172,324)(173,340)(174,339)(175,338)(176,337)(177,336)(178,335)(179,334)(180,333)(181,332)(182,331)(183,330)(184,329)(185,328)(186,327)(187,326)(188,342)(189,341)(190,357)(191,356)(192,355)(193,354)(194,353)(195,352)(196,351)(197,350)(198,349)(199,348)(200,347)(201,346)(202,345)(203,344)(204,343);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*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*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(408)!( 18, 35)( 19, 36)( 20, 37)( 21, 38)( 22, 39)( 23, 40)( 24, 41)( 25, 42)( 26, 43)( 27, 44)( 28, 45)( 29, 46)( 30, 47)( 31, 48)( 32, 49)( 33, 50)( 34, 51)( 69, 86)( 70, 87)( 71, 88)( 72, 89)( 73, 90)( 74, 91)( 75, 92)( 76, 93)( 77, 94)( 78, 95)( 79, 96)( 80, 97)( 81, 98)( 82, 99)( 83,100)( 84,101)( 85,102)(120,137)(121,138)(122,139)(123,140)(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)(133,150)(134,151)(135,152)(136,153)(171,188)(172,189)(173,190)(174,191)(175,192)(176,193)(177,194)(178,195)(179,196)(180,197)(181,198)(182,199)(183,200)(184,201)(185,202)(186,203)(187,204)(222,239)(223,240)(224,241)(225,242)(226,243)(227,244)(228,245)(229,246)(230,247)(231,248)(232,249)(233,250)(234,251)(235,252)(236,253)(237,254)(238,255)(273,290)(274,291)(275,292)(276,293)(277,294)(278,295)(279,296)(280,297)(281,298)(282,299)(283,300)(284,301)(285,302)(286,303)(287,304)(288,305)(289,306)(324,341)(325,342)(326,343)(327,344)(328,345)(329,346)(330,347)(331,348)(332,349)(333,350)(334,351)(335,352)(336,353)(337,354)(338,355)(339,356)(340,357)(375,392)(376,393)(377,394)(378,395)(379,396)(380,397)(381,398)(382,399)(383,400)(384,401)(385,402)(386,403)(387,404)(388,405)(389,406)(390,407)(391,408);
s1 := Sym(408)!(  1, 18)(  2, 34)(  3, 33)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 28)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 43, 44)( 52, 69)( 53, 85)( 54, 84)( 55, 83)( 56, 82)( 57, 81)( 58, 80)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(103,171)(104,187)(105,186)(106,185)(107,184)(108,183)(109,182)(110,181)(111,180)(112,179)(113,178)(114,177)(115,176)(116,175)(117,174)(118,173)(119,172)(120,154)(121,170)(122,169)(123,168)(124,167)(125,166)(126,165)(127,164)(128,163)(129,162)(130,161)(131,160)(132,159)(133,158)(134,157)(135,156)(136,155)(137,188)(138,204)(139,203)(140,202)(141,201)(142,200)(143,199)(144,198)(145,197)(146,196)(147,195)(148,194)(149,193)(150,192)(151,191)(152,190)(153,189)(205,324)(206,340)(207,339)(208,338)(209,337)(210,336)(211,335)(212,334)(213,333)(214,332)(215,331)(216,330)(217,329)(218,328)(219,327)(220,326)(221,325)(222,307)(223,323)(224,322)(225,321)(226,320)(227,319)(228,318)(229,317)(230,316)(231,315)(232,314)(233,313)(234,312)(235,311)(236,310)(237,309)(238,308)(239,341)(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,351)(247,350)(248,349)(249,348)(250,347)(251,346)(252,345)(253,344)(254,343)(255,342)(256,375)(257,391)(258,390)(259,389)(260,388)(261,387)(262,386)(263,385)(264,384)(265,383)(266,382)(267,381)(268,380)(269,379)(270,378)(271,377)(272,376)(273,358)(274,374)(275,373)(276,372)(277,371)(278,370)(279,369)(280,368)(281,367)(282,366)(283,365)(284,364)(285,363)(286,362)(287,361)(288,360)(289,359)(290,392)(291,408)(292,407)(293,406)(294,405)(295,404)(296,403)(297,402)(298,401)(299,400)(300,399)(301,398)(302,397)(303,396)(304,395)(305,394)(306,393);
s2 := Sym(408)!(  1,206)(  2,205)(  3,221)(  4,220)(  5,219)(  6,218)(  7,217)(  8,216)(  9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,210)( 15,209)( 16,208)( 17,207)( 18,223)( 19,222)( 20,238)( 21,237)( 22,236)( 23,235)( 24,234)( 25,233)( 26,232)( 27,231)( 28,230)( 29,229)( 30,228)( 31,227)( 32,226)( 33,225)( 34,224)( 35,240)( 36,239)( 37,255)( 38,254)( 39,253)( 40,252)( 41,251)( 42,250)( 43,249)( 44,248)( 45,247)( 46,246)( 47,245)( 48,244)( 49,243)( 50,242)( 51,241)( 52,257)( 53,256)( 54,272)( 55,271)( 56,270)( 57,269)( 58,268)( 59,267)( 60,266)( 61,265)( 62,264)( 63,263)( 64,262)( 65,261)( 66,260)( 67,259)( 68,258)( 69,274)( 70,273)( 71,289)( 72,288)( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,282)( 79,281)( 80,280)( 81,279)( 82,278)( 83,277)( 84,276)( 85,275)( 86,291)( 87,290)( 88,306)( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,359)(104,358)(105,374)(106,373)(107,372)(108,371)(109,370)(110,369)(111,368)(112,367)(113,366)(114,365)(115,364)(116,363)(117,362)(118,361)(119,360)(120,376)(121,375)(122,391)(123,390)(124,389)(125,388)(126,387)(127,386)(128,385)(129,384)(130,383)(131,382)(132,381)(133,380)(134,379)(135,378)(136,377)(137,393)(138,392)(139,408)(140,407)(141,406)(142,405)(143,404)(144,403)(145,402)(146,401)(147,400)(148,399)(149,398)(150,397)(151,396)(152,395)(153,394)(154,308)(155,307)(156,323)(157,322)(158,321)(159,320)(160,319)(161,318)(162,317)(163,316)(164,315)(165,314)(166,313)(167,312)(168,311)(169,310)(170,309)(171,325)(172,324)(173,340)(174,339)(175,338)(176,337)(177,336)(178,335)(179,334)(180,333)(181,332)(182,331)(183,330)(184,329)(185,328)(186,327)(187,326)(188,342)(189,341)(190,357)(191,356)(192,355)(193,354)(194,353)(195,352)(196,351)(197,350)(198,349)(199,348)(200,347)(201,346)(202,345)(203,344)(204,343);
poly := sub<Sym(408)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*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*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

Twisty Puzzle