Polytope of Type {6,114}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,114}*1368b
Also Known As : {6,114|2}. if this polytope has another 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 : 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) :
3-fold quotients : {6,38}*456, {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}*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 := ( 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)( 58,249)( 59,248)( 60,266)( 61,265)( 62,264)( 63,263)( 64,262)
( 65,261)( 66,260)( 67,259)( 68,258)( 69,257)( 70,256)( 71,255)( 72,254)
( 73,253)( 74,252)( 75,251)( 76,250)( 77,230)( 78,229)( 79,247)( 80,246)
( 81,245)( 82,244)( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)( 88,238)
( 89,237)( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)( 96,268)
( 97,267)( 98,285)( 99,284)(100,283)(101,282)(102,281)(103,280)(104,279)
(105,278)(106,277)(107,276)(108,275)(109,274)(110,273)(111,272)(112,271)
(113,270)(114,269)(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);;
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 ];;
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)( 58,249)( 59,248)( 60,266)( 61,265)( 62,264)( 63,263)
( 64,262)( 65,261)( 66,260)( 67,259)( 68,258)( 69,257)( 70,256)( 71,255)
( 72,254)( 73,253)( 74,252)( 75,251)( 76,250)( 77,230)( 78,229)( 79,247)
( 80,246)( 81,245)( 82,244)( 83,243)( 84,242)( 85,241)( 86,240)( 87,239)
( 88,238)( 89,237)( 90,236)( 91,235)( 92,234)( 93,233)( 94,232)( 95,231)
( 96,268)( 97,267)( 98,285)( 99,284)(100,283)(101,282)(102,281)(103,280)
(104,279)(105,278)(106,277)(107,276)(108,275)(109,274)(110,273)(111,272)
(112,271)(113,270)(114,269)(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);
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,
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