Polytope of Type {114,6}

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.
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