Polytope of Type {114,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {114,6}*1368b
Also Known As : {114,6|2}. if this polytope has another name.
Group : SmallGroup(1368,201)
Rank : 3
Schlafli Type : {114,6}
Number of vertices, edges, etc : 114, 342, 6
Order of s0s1s2 : 114
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {38,6}*456, {114,2}*456
   6-fold quotients : {57,2}*228
   9-fold quotients : {38,2}*152
   18-fold quotients : {19,2}*76
   19-fold quotients : {6,6}*72a
   57-fold quotients : {2,6}*24, {6,2}*24
   114-fold quotients : {2,3}*12, {3,2}*12
   171-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 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)( 10, 11)( 20, 39)( 21, 57)( 22, 56)( 23, 55)( 24, 54)( 25, 53)( 26, 52)( 27, 51)( 28, 50)( 29, 49)( 30, 48)( 31, 47)( 32, 46)( 33, 45)( 34, 44)( 35, 43)( 36, 42)( 37, 41)( 38, 40)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)(116,133)(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(134,153)(135,171)(136,170)(137,169)(138,168)(139,167)(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(151,155)(152,154)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)(180,183)(181,182)(191,210)(192,228)(193,227)(194,226)(195,225)(196,224)(197,223)(198,222)(199,221)(200,220)(201,219)(202,218)(203,217)(204,216)(205,215)(206,214)(207,213)(208,212)(209,211)(230,247)(231,246)(232,245)(233,244)(234,243)(235,242)(236,241)(237,240)(238,239)(248,267)(249,285)(250,284)(251,283)(252,282)(253,281)(254,280)(255,279)(256,278)(257,277)(258,276)(259,275)(260,274)(261,273)(262,272)(263,271)(264,270)(265,269)(266,268)(287,304)(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(305,324)(306,342)(307,341)(308,340)(309,339)(310,338)(311,337)(312,336)(313,335)(314,334)(315,333)(316,332)(317,331)(318,330)(319,329)(320,328)(321,327)(322,326)(323,325);;
s1 := (  1, 21)(  2, 20)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58,135)( 59,134)( 60,152)( 61,151)( 62,150)( 63,149)( 64,148)( 65,147)( 66,146)( 67,145)( 68,144)( 69,143)( 70,142)( 71,141)( 72,140)( 73,139)( 74,138)( 75,137)( 76,136)( 77,116)( 78,115)( 79,133)( 80,132)( 81,131)( 82,130)( 83,129)( 84,128)( 85,127)( 86,126)( 87,125)( 88,124)( 89,123)( 90,122)( 91,121)( 92,120)( 93,119)( 94,118)( 95,117)( 96,154)( 97,153)( 98,171)( 99,170)(100,169)(101,168)(102,167)(103,166)(104,165)(105,164)(106,163)(107,162)(108,161)(109,160)(110,159)(111,158)(112,157)(113,156)(114,155)(172,192)(173,191)(174,209)(175,208)(176,207)(177,206)(178,205)(179,204)(180,203)(181,202)(182,201)(183,200)(184,199)(185,198)(186,197)(187,196)(188,195)(189,194)(190,193)(210,211)(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)(218,222)(219,221)(229,306)(230,305)(231,323)(232,322)(233,321)(234,320)(235,319)(236,318)(237,317)(238,316)(239,315)(240,314)(241,313)(242,312)(243,311)(244,310)(245,309)(246,308)(247,307)(248,287)(249,286)(250,304)(251,303)(252,302)(253,301)(254,300)(255,299)(256,298)(257,297)(258,296)(259,295)(260,294)(261,293)(262,292)(263,291)(264,290)(265,289)(266,288)(267,325)(268,324)(269,342)(270,341)(271,340)(272,339)(273,338)(274,337)(275,336)(276,335)(277,334)(278,333)(279,332)(280,331)(281,330)(282,329)(283,328)(284,327)(285,326);;
s2 := (  1,229)(  2,230)(  3,231)(  4,232)(  5,233)(  6,234)(  7,235)(  8,236)(  9,237)( 10,238)( 11,239)( 12,240)( 13,241)( 14,242)( 15,243)( 16,244)( 17,245)( 18,246)( 19,247)( 20,248)( 21,249)( 22,250)( 23,251)( 24,252)( 25,253)( 26,254)( 27,255)( 28,256)( 29,257)( 30,258)( 31,259)( 32,260)( 33,261)( 34,262)( 35,263)( 36,264)( 37,265)( 38,266)( 39,267)( 40,268)( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)( 48,276)( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)( 56,284)( 57,285)( 58,172)( 59,173)( 60,174)( 61,175)( 62,176)( 63,177)( 64,178)( 65,179)( 66,180)( 67,181)( 68,182)( 69,183)( 70,184)( 71,185)( 72,186)( 73,187)( 74,188)( 75,189)( 76,190)( 77,191)( 78,192)( 79,193)( 80,194)( 81,195)( 82,196)( 83,197)( 84,198)( 85,199)( 86,200)( 87,201)( 88,202)( 89,203)( 90,204)( 91,205)( 92,206)( 93,207)( 94,208)( 95,209)( 96,210)( 97,211)( 98,212)( 99,213)(100,214)(101,215)(102,216)(103,217)(104,218)(105,219)(106,220)(107,221)(108,222)(109,223)(110,224)(111,225)(112,226)(113,227)(114,228)(115,286)(116,287)(117,288)(118,289)(119,290)(120,291)(121,292)(122,293)(123,294)(124,295)(125,296)(126,297)(127,298)(128,299)(129,300)(130,301)(131,302)(132,303)(133,304)(134,305)(135,306)(136,307)(137,308)(138,309)(139,310)(140,311)(141,312)(142,313)(143,314)(144,315)(145,316)(146,317)(147,318)(148,319)(149,320)(150,321)(151,322)(152,323)(153,324)(154,325)(155,326)(156,327)(157,328)(158,329)(159,330)(160,331)(161,332)(162,333)(163,334)(164,335)(165,336)(166,337)(167,338)(168,339)(169,340)(170,341)(171,342);;
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, 
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*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*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*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*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*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*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*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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(342)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)( 10, 11)( 20, 39)( 21, 57)( 22, 56)( 23, 55)( 24, 54)( 25, 53)( 26, 52)( 27, 51)( 28, 50)( 29, 49)( 30, 48)( 31, 47)( 32, 46)( 33, 45)( 34, 44)( 35, 43)( 36, 42)( 37, 41)( 38, 40)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)(116,133)(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(134,153)(135,171)(136,170)(137,169)(138,168)(139,167)(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(151,155)(152,154)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)(180,183)(181,182)(191,210)(192,228)(193,227)(194,226)(195,225)(196,224)(197,223)(198,222)(199,221)(200,220)(201,219)(202,218)(203,217)(204,216)(205,215)(206,214)(207,213)(208,212)(209,211)(230,247)(231,246)(232,245)(233,244)(234,243)(235,242)(236,241)(237,240)(238,239)(248,267)(249,285)(250,284)(251,283)(252,282)(253,281)(254,280)(255,279)(256,278)(257,277)(258,276)(259,275)(260,274)(261,273)(262,272)(263,271)(264,270)(265,269)(266,268)(287,304)(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(305,324)(306,342)(307,341)(308,340)(309,339)(310,338)(311,337)(312,336)(313,335)(314,334)(315,333)(316,332)(317,331)(318,330)(319,329)(320,328)(321,327)(322,326)(323,325);
s1 := Sym(342)!(  1, 21)(  2, 20)(  3, 38)(  4, 37)(  5, 36)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58,135)( 59,134)( 60,152)( 61,151)( 62,150)( 63,149)( 64,148)( 65,147)( 66,146)( 67,145)( 68,144)( 69,143)( 70,142)( 71,141)( 72,140)( 73,139)( 74,138)( 75,137)( 76,136)( 77,116)( 78,115)( 79,133)( 80,132)( 81,131)( 82,130)( 83,129)( 84,128)( 85,127)( 86,126)( 87,125)( 88,124)( 89,123)( 90,122)( 91,121)( 92,120)( 93,119)( 94,118)( 95,117)( 96,154)( 97,153)( 98,171)( 99,170)(100,169)(101,168)(102,167)(103,166)(104,165)(105,164)(106,163)(107,162)(108,161)(109,160)(110,159)(111,158)(112,157)(113,156)(114,155)(172,192)(173,191)(174,209)(175,208)(176,207)(177,206)(178,205)(179,204)(180,203)(181,202)(182,201)(183,200)(184,199)(185,198)(186,197)(187,196)(188,195)(189,194)(190,193)(210,211)(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)(218,222)(219,221)(229,306)(230,305)(231,323)(232,322)(233,321)(234,320)(235,319)(236,318)(237,317)(238,316)(239,315)(240,314)(241,313)(242,312)(243,311)(244,310)(245,309)(246,308)(247,307)(248,287)(249,286)(250,304)(251,303)(252,302)(253,301)(254,300)(255,299)(256,298)(257,297)(258,296)(259,295)(260,294)(261,293)(262,292)(263,291)(264,290)(265,289)(266,288)(267,325)(268,324)(269,342)(270,341)(271,340)(272,339)(273,338)(274,337)(275,336)(276,335)(277,334)(278,333)(279,332)(280,331)(281,330)(282,329)(283,328)(284,327)(285,326);
s2 := Sym(342)!(  1,229)(  2,230)(  3,231)(  4,232)(  5,233)(  6,234)(  7,235)(  8,236)(  9,237)( 10,238)( 11,239)( 12,240)( 13,241)( 14,242)( 15,243)( 16,244)( 17,245)( 18,246)( 19,247)( 20,248)( 21,249)( 22,250)( 23,251)( 24,252)( 25,253)( 26,254)( 27,255)( 28,256)( 29,257)( 30,258)( 31,259)( 32,260)( 33,261)( 34,262)( 35,263)( 36,264)( 37,265)( 38,266)( 39,267)( 40,268)( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)( 48,276)( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)( 56,284)( 57,285)( 58,172)( 59,173)( 60,174)( 61,175)( 62,176)( 63,177)( 64,178)( 65,179)( 66,180)( 67,181)( 68,182)( 69,183)( 70,184)( 71,185)( 72,186)( 73,187)( 74,188)( 75,189)( 76,190)( 77,191)( 78,192)( 79,193)( 80,194)( 81,195)( 82,196)( 83,197)( 84,198)( 85,199)( 86,200)( 87,201)( 88,202)( 89,203)( 90,204)( 91,205)( 92,206)( 93,207)( 94,208)( 95,209)( 96,210)( 97,211)( 98,212)( 99,213)(100,214)(101,215)(102,216)(103,217)(104,218)(105,219)(106,220)(107,221)(108,222)(109,223)(110,224)(111,225)(112,226)(113,227)(114,228)(115,286)(116,287)(117,288)(118,289)(119,290)(120,291)(121,292)(122,293)(123,294)(124,295)(125,296)(126,297)(127,298)(128,299)(129,300)(130,301)(131,302)(132,303)(133,304)(134,305)(135,306)(136,307)(137,308)(138,309)(139,310)(140,311)(141,312)(142,313)(143,314)(144,315)(145,316)(146,317)(147,318)(148,319)(149,320)(150,321)(151,322)(152,323)(153,324)(154,325)(155,326)(156,327)(157,328)(158,329)(159,330)(160,331)(161,332)(162,333)(163,334)(164,335)(165,336)(166,337)(167,338)(168,339)(169,340)(170,341)(171,342);
poly := sub<Sym(342)|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, 
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*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*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*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*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*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*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*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*s0*s1*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle