Polytope of Type {6,114} with group SmallGroup(1368,201)

Overview

Group: SmallGroup(1368,201)
Rank: 3
Schläfli Type: {6,114}
Vertices, edges, …: 6, 342, 114
Order of s₀s₁s₂: 114
Order of s₀s₁s₂s₁: 2
Also known as: {6,114|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

3-fold

6-fold

{2,57}*228

9-fold

{2,38}*152

18-fold

{2,19}*76

19-fold

{6,6}*72a

57-fold

114-fold

171-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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