Polytope of Type {6,116}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,116}*1392a
Also Known As : {6,116|2}. if this polytope has another name.
Group : SmallGroup(1392,131)
Rank : 3
Schlafli Type : {6,116}
Number of vertices, edges, etc : 6, 348, 116
Order of s₀s₁s₂ : 348
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) :
   2-fold quotients : {6,58}*696
   3-fold quotients : {2,116}*464
   6-fold quotients : {2,58}*232
   12-fold quotients : {2,29}*116
   29-fold quotients : {6,4}*48a
   58-fold quotients : {6,2}*24
   87-fold quotients : {2,4}*16
   116-fold quotients : {3,2}*12
   174-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 30, 59)( 31, 60)( 32, 61)( 33, 62)( 34, 63)( 35, 64)( 36, 65)( 37, 66)
( 38, 67)( 39, 68)( 40, 69)( 41, 70)( 42, 71)( 43, 72)( 44, 73)( 45, 74)
( 46, 75)( 47, 76)( 48, 77)( 49, 78)( 50, 79)( 51, 80)( 52, 81)( 53, 82)
( 54, 83)( 55, 84)( 56, 85)( 57, 86)( 58, 87)(117,146)(118,147)(119,148)
(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)
(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)
(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)(142,171)(143,172)
(144,173)(145,174)(204,233)(205,234)(206,235)(207,236)(208,237)(209,238)
(210,239)(211,240)(212,241)(213,242)(214,243)(215,244)(216,245)(217,246)
(218,247)(219,248)(220,249)(221,250)(222,251)(223,252)(224,253)(225,254)
(226,255)(227,256)(228,257)(229,258)(230,259)(231,260)(232,261)(291,320)
(292,321)(293,322)(294,323)(295,324)(296,325)(297,326)(298,327)(299,328)
(300,329)(301,330)(302,331)(303,332)(304,333)(305,334)(306,335)(307,336)
(308,337)(309,338)(310,339)(311,340)(312,341)(313,342)(314,343)(315,344)
(316,345)(317,346)(318,347)(319,348);;
s1 := (  1, 30)(  2, 58)(  3, 57)(  4, 56)(  5, 55)(  6, 54)(  7, 53)(  8, 52)
(  9, 51)( 10, 50)( 11, 49)( 12, 48)( 13, 47)( 14, 46)( 15, 45)( 16, 44)
( 17, 43)( 18, 42)( 19, 41)( 20, 40)( 21, 39)( 22, 38)( 23, 37)( 24, 36)
( 25, 35)( 26, 34)( 27, 33)( 28, 32)( 29, 31)( 60, 87)( 61, 86)( 62, 85)
( 63, 84)( 64, 83)( 65, 82)( 66, 81)( 67, 80)( 68, 79)( 69, 78)( 70, 77)
( 71, 76)( 72, 75)( 73, 74)( 88,117)( 89,145)( 90,144)( 91,143)( 92,142)
( 93,141)( 94,140)( 95,139)( 96,138)( 97,137)( 98,136)( 99,135)(100,134)
(101,133)(102,132)(103,131)(104,130)(105,129)(106,128)(107,127)(108,126)
(109,125)(110,124)(111,123)(112,122)(113,121)(114,120)(115,119)(116,118)
(147,174)(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)
(155,166)(156,165)(157,164)(158,163)(159,162)(160,161)(175,291)(176,319)
(177,318)(178,317)(179,316)(180,315)(181,314)(182,313)(183,312)(184,311)
(185,310)(186,309)(187,308)(188,307)(189,306)(190,305)(191,304)(192,303)
(193,302)(194,301)(195,300)(196,299)(197,298)(198,297)(199,296)(200,295)
(201,294)(202,293)(203,292)(204,262)(205,290)(206,289)(207,288)(208,287)
(209,286)(210,285)(211,284)(212,283)(213,282)(214,281)(215,280)(216,279)
(217,278)(218,277)(219,276)(220,275)(221,274)(222,273)(223,272)(224,271)
(225,270)(226,269)(227,268)(228,267)(229,266)(230,265)(231,264)(232,263)
(233,320)(234,348)(235,347)(236,346)(237,345)(238,344)(239,343)(240,342)
(241,341)(242,340)(243,339)(244,338)(245,337)(246,336)(247,335)(248,334)
(249,333)(250,332)(251,331)(252,330)(253,329)(254,328)(255,327)(256,326)
(257,325)(258,324)(259,323)(260,322)(261,321);;
s2 := (  1,176)(  2,175)(  3,203)(  4,202)(  5,201)(  6,200)(  7,199)(  8,198)
(  9,197)( 10,196)( 11,195)( 12,194)( 13,193)( 14,192)( 15,191)( 16,190)
( 17,189)( 18,188)( 19,187)( 20,186)( 21,185)( 22,184)( 23,183)( 24,182)
( 25,181)( 26,180)( 27,179)( 28,178)( 29,177)( 30,205)( 31,204)( 32,232)
( 33,231)( 34,230)( 35,229)( 36,228)( 37,227)( 38,226)( 39,225)( 40,224)
( 41,223)( 42,222)( 43,221)( 44,220)( 45,219)( 46,218)( 47,217)( 48,216)
( 49,215)( 50,214)( 51,213)( 52,212)( 53,211)( 54,210)( 55,209)( 56,208)
( 57,207)( 58,206)( 59,234)( 60,233)( 61,261)( 62,260)( 63,259)( 64,258)
( 65,257)( 66,256)( 67,255)( 68,254)( 69,253)( 70,252)( 71,251)( 72,250)
( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,244)( 79,243)( 80,242)
( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)( 88,263)
( 89,262)( 90,290)( 91,289)( 92,288)( 93,287)( 94,286)( 95,285)( 96,284)
( 97,283)( 98,282)( 99,281)(100,280)(101,279)(102,278)(103,277)(104,276)
(105,275)(106,274)(107,273)(108,272)(109,271)(110,270)(111,269)(112,268)
(113,267)(114,266)(115,265)(116,264)(117,292)(118,291)(119,319)(120,318)
(121,317)(122,316)(123,315)(124,314)(125,313)(126,312)(127,311)(128,310)
(129,309)(130,308)(131,307)(132,306)(133,305)(134,304)(135,303)(136,302)
(137,301)(138,300)(139,299)(140,298)(141,297)(142,296)(143,295)(144,294)
(145,293)(146,321)(147,320)(148,348)(149,347)(150,346)(151,345)(152,344)
(153,343)(154,342)(155,341)(156,340)(157,339)(158,338)(159,337)(160,336)
(161,335)(162,334)(163,333)(164,332)(165,331)(166,330)(167,329)(168,328)
(169,327)(170,326)(171,325)(172,324)(173,323)(174,322);;
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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(348)!( 30, 59)( 31, 60)( 32, 61)( 33, 62)( 34, 63)( 35, 64)( 36, 65)
( 37, 66)( 38, 67)( 39, 68)( 40, 69)( 41, 70)( 42, 71)( 43, 72)( 44, 73)
( 45, 74)( 46, 75)( 47, 76)( 48, 77)( 49, 78)( 50, 79)( 51, 80)( 52, 81)
( 53, 82)( 54, 83)( 55, 84)( 56, 85)( 57, 86)( 58, 87)(117,146)(118,147)
(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)
(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)
(135,164)(136,165)(137,166)(138,167)(139,168)(140,169)(141,170)(142,171)
(143,172)(144,173)(145,174)(204,233)(205,234)(206,235)(207,236)(208,237)
(209,238)(210,239)(211,240)(212,241)(213,242)(214,243)(215,244)(216,245)
(217,246)(218,247)(219,248)(220,249)(221,250)(222,251)(223,252)(224,253)
(225,254)(226,255)(227,256)(228,257)(229,258)(230,259)(231,260)(232,261)
(291,320)(292,321)(293,322)(294,323)(295,324)(296,325)(297,326)(298,327)
(299,328)(300,329)(301,330)(302,331)(303,332)(304,333)(305,334)(306,335)
(307,336)(308,337)(309,338)(310,339)(311,340)(312,341)(313,342)(314,343)
(315,344)(316,345)(317,346)(318,347)(319,348);
s1 := Sym(348)!(  1, 30)(  2, 58)(  3, 57)(  4, 56)(  5, 55)(  6, 54)(  7, 53)
(  8, 52)(  9, 51)( 10, 50)( 11, 49)( 12, 48)( 13, 47)( 14, 46)( 15, 45)
( 16, 44)( 17, 43)( 18, 42)( 19, 41)( 20, 40)( 21, 39)( 22, 38)( 23, 37)
( 24, 36)( 25, 35)( 26, 34)( 27, 33)( 28, 32)( 29, 31)( 60, 87)( 61, 86)
( 62, 85)( 63, 84)( 64, 83)( 65, 82)( 66, 81)( 67, 80)( 68, 79)( 69, 78)
( 70, 77)( 71, 76)( 72, 75)( 73, 74)( 88,117)( 89,145)( 90,144)( 91,143)
( 92,142)( 93,141)( 94,140)( 95,139)( 96,138)( 97,137)( 98,136)( 99,135)
(100,134)(101,133)(102,132)(103,131)(104,130)(105,129)(106,128)(107,127)
(108,126)(109,125)(110,124)(111,123)(112,122)(113,121)(114,120)(115,119)
(116,118)(147,174)(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)
(154,167)(155,166)(156,165)(157,164)(158,163)(159,162)(160,161)(175,291)
(176,319)(177,318)(178,317)(179,316)(180,315)(181,314)(182,313)(183,312)
(184,311)(185,310)(186,309)(187,308)(188,307)(189,306)(190,305)(191,304)
(192,303)(193,302)(194,301)(195,300)(196,299)(197,298)(198,297)(199,296)
(200,295)(201,294)(202,293)(203,292)(204,262)(205,290)(206,289)(207,288)
(208,287)(209,286)(210,285)(211,284)(212,283)(213,282)(214,281)(215,280)
(216,279)(217,278)(218,277)(219,276)(220,275)(221,274)(222,273)(223,272)
(224,271)(225,270)(226,269)(227,268)(228,267)(229,266)(230,265)(231,264)
(232,263)(233,320)(234,348)(235,347)(236,346)(237,345)(238,344)(239,343)
(240,342)(241,341)(242,340)(243,339)(244,338)(245,337)(246,336)(247,335)
(248,334)(249,333)(250,332)(251,331)(252,330)(253,329)(254,328)(255,327)
(256,326)(257,325)(258,324)(259,323)(260,322)(261,321);
s2 := Sym(348)!(  1,176)(  2,175)(  3,203)(  4,202)(  5,201)(  6,200)(  7,199)
(  8,198)(  9,197)( 10,196)( 11,195)( 12,194)( 13,193)( 14,192)( 15,191)
( 16,190)( 17,189)( 18,188)( 19,187)( 20,186)( 21,185)( 22,184)( 23,183)
( 24,182)( 25,181)( 26,180)( 27,179)( 28,178)( 29,177)( 30,205)( 31,204)
( 32,232)( 33,231)( 34,230)( 35,229)( 36,228)( 37,227)( 38,226)( 39,225)
( 40,224)( 41,223)( 42,222)( 43,221)( 44,220)( 45,219)( 46,218)( 47,217)
( 48,216)( 49,215)( 50,214)( 51,213)( 52,212)( 53,211)( 54,210)( 55,209)
( 56,208)( 57,207)( 58,206)( 59,234)( 60,233)( 61,261)( 62,260)( 63,259)
( 64,258)( 65,257)( 66,256)( 67,255)( 68,254)( 69,253)( 70,252)( 71,251)
( 72,250)( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,244)( 79,243)
( 80,242)( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)
( 88,263)( 89,262)( 90,290)( 91,289)( 92,288)( 93,287)( 94,286)( 95,285)
( 96,284)( 97,283)( 98,282)( 99,281)(100,280)(101,279)(102,278)(103,277)
(104,276)(105,275)(106,274)(107,273)(108,272)(109,271)(110,270)(111,269)
(112,268)(113,267)(114,266)(115,265)(116,264)(117,292)(118,291)(119,319)
(120,318)(121,317)(122,316)(123,315)(124,314)(125,313)(126,312)(127,311)
(128,310)(129,309)(130,308)(131,307)(132,306)(133,305)(134,304)(135,303)
(136,302)(137,301)(138,300)(139,299)(140,298)(141,297)(142,296)(143,295)
(144,294)(145,293)(146,321)(147,320)(148,348)(149,347)(150,346)(151,345)
(152,344)(153,343)(154,342)(155,341)(156,340)(157,339)(158,338)(159,337)
(160,336)(161,335)(162,334)(163,333)(164,332)(165,331)(166,330)(167,329)
(168,328)(169,327)(170,326)(171,325)(172,324)(173,323)(174,322);
poly := sub<Sym(348)|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*s1*s2*s1*s2 >;

References : None.
to this polytope