Polytope of Type {6,114}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,114}*1368c
if this polytope has a name.
Group : SmallGroup(1368,201)
Rank : 3
Schlafli Type : {6,114}
Number of vertices, edges, etc : 6, 342, 114
Order of s₀s₁s₂ : 114
Order of s₀s₁s₂s₁ : 6
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 : {6,57}*684
   3-fold quotients : {2,114}*456
   6-fold quotients : {2,57}*228
   9-fold quotients : {2,38}*152
   18-fold quotients : {2,19}*76
   19-fold quotients : {6,6}*72b
   38-fold quotients : {6,3}*36
   57-fold quotients : {2,6}*24
   114-fold quotients : {2,3}*12
   171-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 58,115)( 59,116)( 60,117)( 61,118)( 62,119)( 63,120)( 64,121)( 65,122)
( 66,123)( 67,124)( 68,125)( 69,126)( 70,127)( 71,128)( 72,129)( 73,130)
( 74,131)( 75,132)( 76,133)( 77,134)( 78,135)( 79,136)( 80,137)( 81,138)
( 82,139)( 83,140)( 84,141)( 85,142)( 86,143)( 87,144)( 88,145)( 89,146)
( 90,147)( 91,148)( 92,149)( 93,150)( 94,151)( 95,152)( 96,153)( 97,154)
( 98,155)( 99,156)(100,157)(101,158)(102,159)(103,160)(104,161)(105,162)
(106,163)(107,164)(108,165)(109,166)(110,167)(111,168)(112,169)(113,170)
(114,171)(229,286)(230,287)(231,288)(232,289)(233,290)(234,291)(235,292)
(236,293)(237,294)(238,295)(239,296)(240,297)(241,298)(242,299)(243,300)
(244,301)(245,302)(246,303)(247,304)(248,305)(249,306)(250,307)(251,308)
(252,309)(253,310)(254,311)(255,312)(256,313)(257,314)(258,315)(259,316)
(260,317)(261,318)(262,319)(263,320)(264,321)(265,322)(266,323)(267,324)
(268,325)(269,326)(270,327)(271,328)(272,329)(273,330)(274,331)(275,332)
(276,333)(277,334)(278,335)(279,336)(280,337)(281,338)(282,339)(283,340)
(284,341)(285,342);;
s1 := (  1, 58)(  2, 76)(  3, 75)(  4, 74)(  5, 73)(  6, 72)(  7, 71)(  8, 70)
(  9, 69)( 10, 68)( 11, 67)( 12, 66)( 13, 65)( 14, 64)( 15, 63)( 16, 62)
( 17, 61)( 18, 60)( 19, 59)( 20, 96)( 21,114)( 22,113)( 23,112)( 24,111)
( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)( 31,104)( 32,103)
( 33,102)( 34,101)( 35,100)( 36, 99)( 37, 98)( 38, 97)( 39, 77)( 40, 95)
( 41, 94)( 42, 93)( 43, 92)( 44, 91)( 45, 90)( 46, 89)( 47, 88)( 48, 87)
( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 79)
( 57, 78)(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)(172,229)(173,247)(174,246)
(175,245)(176,244)(177,243)(178,242)(179,241)(180,240)(181,239)(182,238)
(183,237)(184,236)(185,235)(186,234)(187,233)(188,232)(189,231)(190,230)
(191,267)(192,285)(193,284)(194,283)(195,282)(196,281)(197,280)(198,279)
(199,278)(200,277)(201,276)(202,275)(203,274)(204,273)(205,272)(206,271)
(207,270)(208,269)(209,268)(210,248)(211,266)(212,265)(213,264)(214,263)
(215,262)(216,261)(217,260)(218,259)(219,258)(220,257)(221,256)(222,255)
(223,254)(224,253)(225,252)(226,251)(227,250)(228,249)(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);;
s2 := (  1,192)(  2,191)(  3,209)(  4,208)(  5,207)(  6,206)(  7,205)(  8,204)
(  9,203)( 10,202)( 11,201)( 12,200)( 13,199)( 14,198)( 15,197)( 16,196)
( 17,195)( 18,194)( 19,193)( 20,173)( 21,172)( 22,190)( 23,189)( 24,188)
( 25,187)( 26,186)( 27,185)( 28,184)( 29,183)( 30,182)( 31,181)( 32,180)
( 33,179)( 34,178)( 35,177)( 36,176)( 37,175)( 38,174)( 39,211)( 40,210)
( 41,228)( 42,227)( 43,226)( 44,225)( 45,224)( 46,223)( 47,222)( 48,221)
( 49,220)( 50,219)( 51,218)( 52,217)( 53,216)( 54,215)( 55,214)( 56,213)
( 57,212)( 58,306)( 59,305)( 60,323)( 61,322)( 62,321)( 63,320)( 64,319)
( 65,318)( 66,317)( 67,316)( 68,315)( 69,314)( 70,313)( 71,312)( 72,311)
( 73,310)( 74,309)( 75,308)( 76,307)( 77,287)( 78,286)( 79,304)( 80,303)
( 81,302)( 82,301)( 83,300)( 84,299)( 85,298)( 86,297)( 87,296)( 88,295)
( 89,294)( 90,293)( 91,292)( 92,291)( 93,290)( 94,289)( 95,288)( 96,325)
( 97,324)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)(104,336)
(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)(112,328)
(113,327)(114,326)(115,249)(116,248)(117,266)(118,265)(119,264)(120,263)
(121,262)(122,261)(123,260)(124,259)(125,258)(126,257)(127,256)(128,255)
(129,254)(130,253)(131,252)(132,251)(133,250)(134,230)(135,229)(136,247)
(137,246)(138,245)(139,244)(140,243)(141,242)(142,241)(143,240)(144,239)
(145,238)(146,237)(147,236)(148,235)(149,234)(150,233)(151,232)(152,231)
(153,268)(154,267)(155,285)(156,284)(157,283)(158,282)(159,281)(160,280)
(161,279)(162,278)(163,277)(164,276)(165,275)(166,274)(167,273)(168,272)
(169,271)(170,270)(171,269);;
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, s2*s0*s1*s0*s1*s2*s0*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(342)!( 58,115)( 59,116)( 60,117)( 61,118)( 62,119)( 63,120)( 64,121)
( 65,122)( 66,123)( 67,124)( 68,125)( 69,126)( 70,127)( 71,128)( 72,129)
( 73,130)( 74,131)( 75,132)( 76,133)( 77,134)( 78,135)( 79,136)( 80,137)
( 81,138)( 82,139)( 83,140)( 84,141)( 85,142)( 86,143)( 87,144)( 88,145)
( 89,146)( 90,147)( 91,148)( 92,149)( 93,150)( 94,151)( 95,152)( 96,153)
( 97,154)( 98,155)( 99,156)(100,157)(101,158)(102,159)(103,160)(104,161)
(105,162)(106,163)(107,164)(108,165)(109,166)(110,167)(111,168)(112,169)
(113,170)(114,171)(229,286)(230,287)(231,288)(232,289)(233,290)(234,291)
(235,292)(236,293)(237,294)(238,295)(239,296)(240,297)(241,298)(242,299)
(243,300)(244,301)(245,302)(246,303)(247,304)(248,305)(249,306)(250,307)
(251,308)(252,309)(253,310)(254,311)(255,312)(256,313)(257,314)(258,315)
(259,316)(260,317)(261,318)(262,319)(263,320)(264,321)(265,322)(266,323)
(267,324)(268,325)(269,326)(270,327)(271,328)(272,329)(273,330)(274,331)
(275,332)(276,333)(277,334)(278,335)(279,336)(280,337)(281,338)(282,339)
(283,340)(284,341)(285,342);
s1 := Sym(342)!(  1, 58)(  2, 76)(  3, 75)(  4, 74)(  5, 73)(  6, 72)(  7, 71)
(  8, 70)(  9, 69)( 10, 68)( 11, 67)( 12, 66)( 13, 65)( 14, 64)( 15, 63)
( 16, 62)( 17, 61)( 18, 60)( 19, 59)( 20, 96)( 21,114)( 22,113)( 23,112)
( 24,111)( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)( 31,104)
( 32,103)( 33,102)( 34,101)( 35,100)( 36, 99)( 37, 98)( 38, 97)( 39, 77)
( 40, 95)( 41, 94)( 42, 93)( 43, 92)( 44, 91)( 45, 90)( 46, 89)( 47, 88)
( 48, 87)( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)
( 56, 79)( 57, 78)(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)(172,229)(173,247)
(174,246)(175,245)(176,244)(177,243)(178,242)(179,241)(180,240)(181,239)
(182,238)(183,237)(184,236)(185,235)(186,234)(187,233)(188,232)(189,231)
(190,230)(191,267)(192,285)(193,284)(194,283)(195,282)(196,281)(197,280)
(198,279)(199,278)(200,277)(201,276)(202,275)(203,274)(204,273)(205,272)
(206,271)(207,270)(208,269)(209,268)(210,248)(211,266)(212,265)(213,264)
(214,263)(215,262)(216,261)(217,260)(218,259)(219,258)(220,257)(221,256)
(222,255)(223,254)(224,253)(225,252)(226,251)(227,250)(228,249)(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);
s2 := Sym(342)!(  1,192)(  2,191)(  3,209)(  4,208)(  5,207)(  6,206)(  7,205)
(  8,204)(  9,203)( 10,202)( 11,201)( 12,200)( 13,199)( 14,198)( 15,197)
( 16,196)( 17,195)( 18,194)( 19,193)( 20,173)( 21,172)( 22,190)( 23,189)
( 24,188)( 25,187)( 26,186)( 27,185)( 28,184)( 29,183)( 30,182)( 31,181)
( 32,180)( 33,179)( 34,178)( 35,177)( 36,176)( 37,175)( 38,174)( 39,211)
( 40,210)( 41,228)( 42,227)( 43,226)( 44,225)( 45,224)( 46,223)( 47,222)
( 48,221)( 49,220)( 50,219)( 51,218)( 52,217)( 53,216)( 54,215)( 55,214)
( 56,213)( 57,212)( 58,306)( 59,305)( 60,323)( 61,322)( 62,321)( 63,320)
( 64,319)( 65,318)( 66,317)( 67,316)( 68,315)( 69,314)( 70,313)( 71,312)
( 72,311)( 73,310)( 74,309)( 75,308)( 76,307)( 77,287)( 78,286)( 79,304)
( 80,303)( 81,302)( 82,301)( 83,300)( 84,299)( 85,298)( 86,297)( 87,296)
( 88,295)( 89,294)( 90,293)( 91,292)( 92,291)( 93,290)( 94,289)( 95,288)
( 96,325)( 97,324)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)
(104,336)(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)
(112,328)(113,327)(114,326)(115,249)(116,248)(117,266)(118,265)(119,264)
(120,263)(121,262)(122,261)(123,260)(124,259)(125,258)(126,257)(127,256)
(128,255)(129,254)(130,253)(131,252)(132,251)(133,250)(134,230)(135,229)
(136,247)(137,246)(138,245)(139,244)(140,243)(141,242)(142,241)(143,240)
(144,239)(145,238)(146,237)(147,236)(148,235)(149,234)(150,233)(151,232)
(152,231)(153,268)(154,267)(155,285)(156,284)(157,283)(158,282)(159,281)
(160,280)(161,279)(162,278)(163,277)(164,276)(165,275)(166,274)(167,273)
(168,272)(169,271)(170,270)(171,269);
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, s2*s0*s1*s0*s1*s2*s0*s1*s0*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 >;

References : None.
to this polytope