Polytope of Type {114,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {114,6}*1368c
if this polytope has a 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 : 6
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) :
   2-fold quotients : {57,6}*684
   3-fold quotients : {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}*72c
   38-fold quotients : {3,6}*36
   57-fold quotients : {6,2}*24
   114-fold quotients : {3,2}*12
   171-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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)( 58,115)( 59,133)( 60,132)( 61,131)
( 62,130)( 63,129)( 64,128)( 65,127)( 66,126)( 67,125)( 68,124)( 69,123)
( 70,122)( 71,121)( 72,120)( 73,119)( 74,118)( 75,117)( 76,116)( 77,153)
( 78,171)( 79,170)( 80,169)( 81,168)( 82,167)( 83,166)( 84,165)( 85,164)
( 86,163)( 87,162)( 88,161)( 89,160)( 90,159)( 91,158)( 92,157)( 93,156)
( 94,155)( 95,154)( 96,134)( 97,152)( 98,151)( 99,150)(100,149)(101,148)
(102,147)(103,146)(104,145)(105,144)(106,143)(107,142)(108,141)(109,140)
(110,139)(111,138)(112,137)(113,136)(114,135)(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)(229,286)(230,304)(231,303)(232,302)(233,301)(234,300)(235,299)
(236,298)(237,297)(238,296)(239,295)(240,294)(241,293)(242,292)(243,291)
(244,290)(245,289)(246,288)(247,287)(248,324)(249,342)(250,341)(251,340)
(252,339)(253,338)(254,337)(255,336)(256,335)(257,334)(258,333)(259,332)
(260,331)(261,330)(262,329)(263,328)(264,327)(265,326)(266,325)(267,305)
(268,323)(269,322)(270,321)(271,320)(272,319)(273,318)(274,317)(275,316)
(276,315)(277,314)(278,313)(279,312)(280,311)(281,310)(282,309)(283,308)
(284,307)(285,306);;
s1 := (  1,249)(  2,248)(  3,266)(  4,265)(  5,264)(  6,263)(  7,262)(  8,261)
(  9,260)( 10,259)( 11,258)( 12,257)( 13,256)( 14,255)( 15,254)( 16,253)
( 17,252)( 18,251)( 19,250)( 20,230)( 21,229)( 22,247)( 23,246)( 24,245)
( 25,244)( 26,243)( 27,242)( 28,241)( 29,240)( 30,239)( 31,238)( 32,237)
( 33,236)( 34,235)( 35,234)( 36,233)( 37,232)( 38,231)( 39,268)( 40,267)
( 41,285)( 42,284)( 43,283)( 44,282)( 45,281)( 46,280)( 47,279)( 48,278)
( 49,277)( 50,276)( 51,275)( 52,274)( 53,273)( 54,272)( 55,271)( 56,270)
( 57,269)( 58,192)( 59,191)( 60,209)( 61,208)( 62,207)( 63,206)( 64,205)
( 65,204)( 66,203)( 67,202)( 68,201)( 69,200)( 70,199)( 71,198)( 72,197)
( 73,196)( 74,195)( 75,194)( 76,193)( 77,173)( 78,172)( 79,190)( 80,189)
( 81,188)( 82,187)( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)( 88,181)
( 89,180)( 90,179)( 91,178)( 92,177)( 93,176)( 94,175)( 95,174)( 96,211)
( 97,210)( 98,228)( 99,227)(100,226)(101,225)(102,224)(103,223)(104,222)
(105,221)(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)(112,214)
(113,213)(114,212)(115,306)(116,305)(117,323)(118,322)(119,321)(120,320)
(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)(128,312)
(129,311)(130,310)(131,309)(132,308)(133,307)(134,287)(135,286)(136,304)
(137,303)(138,302)(139,301)(140,300)(141,299)(142,298)(143,297)(144,296)
(145,295)(146,294)(147,293)(148,292)(149,291)(150,290)(151,289)(152,288)
(153,325)(154,324)(155,342)(156,341)(157,340)(158,339)(159,338)(160,337)
(161,336)(162,335)(163,334)(164,333)(165,332)(166,331)(167,330)(168,329)
(169,328)(170,327)(171,326);;
s2 := ( 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);;
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*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*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*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)( 58,115)( 59,133)( 60,132)
( 61,131)( 62,130)( 63,129)( 64,128)( 65,127)( 66,126)( 67,125)( 68,124)
( 69,123)( 70,122)( 71,121)( 72,120)( 73,119)( 74,118)( 75,117)( 76,116)
( 77,153)( 78,171)( 79,170)( 80,169)( 81,168)( 82,167)( 83,166)( 84,165)
( 85,164)( 86,163)( 87,162)( 88,161)( 89,160)( 90,159)( 91,158)( 92,157)
( 93,156)( 94,155)( 95,154)( 96,134)( 97,152)( 98,151)( 99,150)(100,149)
(101,148)(102,147)(103,146)(104,145)(105,144)(106,143)(107,142)(108,141)
(109,140)(110,139)(111,138)(112,137)(113,136)(114,135)(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)(229,286)(230,304)(231,303)(232,302)(233,301)(234,300)
(235,299)(236,298)(237,297)(238,296)(239,295)(240,294)(241,293)(242,292)
(243,291)(244,290)(245,289)(246,288)(247,287)(248,324)(249,342)(250,341)
(251,340)(252,339)(253,338)(254,337)(255,336)(256,335)(257,334)(258,333)
(259,332)(260,331)(261,330)(262,329)(263,328)(264,327)(265,326)(266,325)
(267,305)(268,323)(269,322)(270,321)(271,320)(272,319)(273,318)(274,317)
(275,316)(276,315)(277,314)(278,313)(279,312)(280,311)(281,310)(282,309)
(283,308)(284,307)(285,306);
s1 := Sym(342)!(  1,249)(  2,248)(  3,266)(  4,265)(  5,264)(  6,263)(  7,262)
(  8,261)(  9,260)( 10,259)( 11,258)( 12,257)( 13,256)( 14,255)( 15,254)
( 16,253)( 17,252)( 18,251)( 19,250)( 20,230)( 21,229)( 22,247)( 23,246)
( 24,245)( 25,244)( 26,243)( 27,242)( 28,241)( 29,240)( 30,239)( 31,238)
( 32,237)( 33,236)( 34,235)( 35,234)( 36,233)( 37,232)( 38,231)( 39,268)
( 40,267)( 41,285)( 42,284)( 43,283)( 44,282)( 45,281)( 46,280)( 47,279)
( 48,278)( 49,277)( 50,276)( 51,275)( 52,274)( 53,273)( 54,272)( 55,271)
( 56,270)( 57,269)( 58,192)( 59,191)( 60,209)( 61,208)( 62,207)( 63,206)
( 64,205)( 65,204)( 66,203)( 67,202)( 68,201)( 69,200)( 70,199)( 71,198)
( 72,197)( 73,196)( 74,195)( 75,194)( 76,193)( 77,173)( 78,172)( 79,190)
( 80,189)( 81,188)( 82,187)( 83,186)( 84,185)( 85,184)( 86,183)( 87,182)
( 88,181)( 89,180)( 90,179)( 91,178)( 92,177)( 93,176)( 94,175)( 95,174)
( 96,211)( 97,210)( 98,228)( 99,227)(100,226)(101,225)(102,224)(103,223)
(104,222)(105,221)(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)
(112,214)(113,213)(114,212)(115,306)(116,305)(117,323)(118,322)(119,321)
(120,320)(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)
(128,312)(129,311)(130,310)(131,309)(132,308)(133,307)(134,287)(135,286)
(136,304)(137,303)(138,302)(139,301)(140,300)(141,299)(142,298)(143,297)
(144,296)(145,295)(146,294)(147,293)(148,292)(149,291)(150,290)(151,289)
(152,288)(153,325)(154,324)(155,342)(156,341)(157,340)(158,339)(159,338)
(160,337)(161,336)(162,335)(163,334)(164,333)(165,332)(166,331)(167,330)
(168,329)(169,328)(170,327)(171,326);
s2 := 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);
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*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*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*s0*s1*s0*s1 >;

References : None.
to this polytope