Polytope of Type {118,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {118,6}*1416
Also Known As : {118,6|2}. if this polytope has another name.
Group : SmallGroup(1416,34)
Rank : 3
Schlafli Type : {118,6}
Number of vertices, edges, etc : 118, 354, 6
Order of s₀s₁s₂ : 354
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 : {118,2}*472
   6-fold quotients : {59,2}*236
   59-fold quotients : {2,6}*24
   118-fold quotients : {2,3}*12
   177-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 59)(  3, 58)(  4, 57)(  5, 56)(  6, 55)(  7, 54)(  8, 53)(  9, 52)
( 10, 51)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 46)( 16, 45)( 17, 44)
( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 38)( 24, 37)( 25, 36)
( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 61,118)( 62,117)( 63,116)
( 64,115)( 65,114)( 66,113)( 67,112)( 68,111)( 69,110)( 70,109)( 71,108)
( 72,107)( 73,106)( 74,105)( 75,104)( 76,103)( 77,102)( 78,101)( 79,100)
( 80, 99)( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)
( 88, 91)( 89, 90)(120,177)(121,176)(122,175)(123,174)(124,173)(125,172)
(126,171)(127,170)(128,169)(129,168)(130,167)(131,166)(132,165)(133,164)
(134,163)(135,162)(136,161)(137,160)(138,159)(139,158)(140,157)(141,156)
(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(179,236)
(180,235)(181,234)(182,233)(183,232)(184,231)(185,230)(186,229)(187,228)
(188,227)(189,226)(190,225)(191,224)(192,223)(193,222)(194,221)(195,220)
(196,219)(197,218)(198,217)(199,216)(200,215)(201,214)(202,213)(203,212)
(204,211)(205,210)(206,209)(207,208)(238,295)(239,294)(240,293)(241,292)
(242,291)(243,290)(244,289)(245,288)(246,287)(247,286)(248,285)(249,284)
(250,283)(251,282)(252,281)(253,280)(254,279)(255,278)(256,277)(257,276)
(258,275)(259,274)(260,273)(261,272)(262,271)(263,270)(264,269)(265,268)
(266,267)(297,354)(298,353)(299,352)(300,351)(301,350)(302,349)(303,348)
(304,347)(305,346)(306,345)(307,344)(308,343)(309,342)(310,341)(311,340)
(312,339)(313,338)(314,337)(315,336)(316,335)(317,334)(318,333)(319,332)
(320,331)(321,330)(322,329)(323,328)(324,327)(325,326);;
s1 := (  1,  2)(  3, 59)(  4, 58)(  5, 57)(  6, 56)(  7, 55)(  8, 54)(  9, 53)
( 10, 52)( 11, 51)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 46)( 17, 45)
( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)( 23, 39)( 24, 38)( 25, 37)
( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 60,120)( 61,119)( 62,177)
( 63,176)( 64,175)( 65,174)( 66,173)( 67,172)( 68,171)( 69,170)( 70,169)
( 71,168)( 72,167)( 73,166)( 74,165)( 75,164)( 76,163)( 77,162)( 78,161)
( 79,160)( 80,159)( 81,158)( 82,157)( 83,156)( 84,155)( 85,154)( 86,153)
( 87,152)( 88,151)( 89,150)( 90,149)( 91,148)( 92,147)( 93,146)( 94,145)
( 95,144)( 96,143)( 97,142)( 98,141)( 99,140)(100,139)(101,138)(102,137)
(103,136)(104,135)(105,134)(106,133)(107,132)(108,131)(109,130)(110,129)
(111,128)(112,127)(113,126)(114,125)(115,124)(116,123)(117,122)(118,121)
(178,179)(180,236)(181,235)(182,234)(183,233)(184,232)(185,231)(186,230)
(187,229)(188,228)(189,227)(190,226)(191,225)(192,224)(193,223)(194,222)
(195,221)(196,220)(197,219)(198,218)(199,217)(200,216)(201,215)(202,214)
(203,213)(204,212)(205,211)(206,210)(207,209)(237,297)(238,296)(239,354)
(240,353)(241,352)(242,351)(243,350)(244,349)(245,348)(246,347)(247,346)
(248,345)(249,344)(250,343)(251,342)(252,341)(253,340)(254,339)(255,338)
(256,337)(257,336)(258,335)(259,334)(260,333)(261,332)(262,331)(263,330)
(264,329)(265,328)(266,327)(267,326)(268,325)(269,324)(270,323)(271,322)
(272,321)(273,320)(274,319)(275,318)(276,317)(277,316)(278,315)(279,314)
(280,313)(281,312)(282,311)(283,310)(284,309)(285,308)(286,307)(287,306)
(288,305)(289,304)(290,303)(291,302)(292,301)(293,300)(294,299)(295,298);;
s2 := (  1,237)(  2,238)(  3,239)(  4,240)(  5,241)(  6,242)(  7,243)(  8,244)
(  9,245)( 10,246)( 11,247)( 12,248)( 13,249)( 14,250)( 15,251)( 16,252)
( 17,253)( 18,254)( 19,255)( 20,256)( 21,257)( 22,258)( 23,259)( 24,260)
( 25,261)( 26,262)( 27,263)( 28,264)( 29,265)( 30,266)( 31,267)( 32,268)
( 33,269)( 34,270)( 35,271)( 36,272)( 37,273)( 38,274)( 39,275)( 40,276)
( 41,277)( 42,278)( 43,279)( 44,280)( 45,281)( 46,282)( 47,283)( 48,284)
( 49,285)( 50,286)( 51,287)( 52,288)( 53,289)( 54,290)( 55,291)( 56,292)
( 57,293)( 58,294)( 59,295)( 60,178)( 61,179)( 62,180)( 63,181)( 64,182)
( 65,183)( 66,184)( 67,185)( 68,186)( 69,187)( 70,188)( 71,189)( 72,190)
( 73,191)( 74,192)( 75,193)( 76,194)( 77,195)( 78,196)( 79,197)( 80,198)
( 81,199)( 82,200)( 83,201)( 84,202)( 85,203)( 86,204)( 87,205)( 88,206)
( 89,207)( 90,208)( 91,209)( 92,210)( 93,211)( 94,212)( 95,213)( 96,214)
( 97,215)( 98,216)( 99,217)(100,218)(101,219)(102,220)(103,221)(104,222)
(105,223)(106,224)(107,225)(108,226)(109,227)(110,228)(111,229)(112,230)
(113,231)(114,232)(115,233)(116,234)(117,235)(118,236)(119,296)(120,297)
(121,298)(122,299)(123,300)(124,301)(125,302)(126,303)(127,304)(128,305)
(129,306)(130,307)(131,308)(132,309)(133,310)(134,311)(135,312)(136,313)
(137,314)(138,315)(139,316)(140,317)(141,318)(142,319)(143,320)(144,321)
(145,322)(146,323)(147,324)(148,325)(149,326)(150,327)(151,328)(152,329)
(153,330)(154,331)(155,332)(156,333)(157,334)(158,335)(159,336)(160,337)
(161,338)(162,339)(163,340)(164,341)(165,342)(166,343)(167,344)(168,345)
(169,346)(170,347)(171,348)(172,349)(173,350)(174,351)(175,352)(176,353)
(177,354);;
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(354)!(  2, 59)(  3, 58)(  4, 57)(  5, 56)(  6, 55)(  7, 54)(  8, 53)
(  9, 52)( 10, 51)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 46)( 16, 45)
( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 38)( 24, 37)
( 25, 36)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 61,118)( 62,117)
( 63,116)( 64,115)( 65,114)( 66,113)( 67,112)( 68,111)( 69,110)( 70,109)
( 71,108)( 72,107)( 73,106)( 74,105)( 75,104)( 76,103)( 77,102)( 78,101)
( 79,100)( 80, 99)( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)
( 87, 92)( 88, 91)( 89, 90)(120,177)(121,176)(122,175)(123,174)(124,173)
(125,172)(126,171)(127,170)(128,169)(129,168)(130,167)(131,166)(132,165)
(133,164)(134,163)(135,162)(136,161)(137,160)(138,159)(139,158)(140,157)
(141,156)(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)
(179,236)(180,235)(181,234)(182,233)(183,232)(184,231)(185,230)(186,229)
(187,228)(188,227)(189,226)(190,225)(191,224)(192,223)(193,222)(194,221)
(195,220)(196,219)(197,218)(198,217)(199,216)(200,215)(201,214)(202,213)
(203,212)(204,211)(205,210)(206,209)(207,208)(238,295)(239,294)(240,293)
(241,292)(242,291)(243,290)(244,289)(245,288)(246,287)(247,286)(248,285)
(249,284)(250,283)(251,282)(252,281)(253,280)(254,279)(255,278)(256,277)
(257,276)(258,275)(259,274)(260,273)(261,272)(262,271)(263,270)(264,269)
(265,268)(266,267)(297,354)(298,353)(299,352)(300,351)(301,350)(302,349)
(303,348)(304,347)(305,346)(306,345)(307,344)(308,343)(309,342)(310,341)
(311,340)(312,339)(313,338)(314,337)(315,336)(316,335)(317,334)(318,333)
(319,332)(320,331)(321,330)(322,329)(323,328)(324,327)(325,326);
s1 := Sym(354)!(  1,  2)(  3, 59)(  4, 58)(  5, 57)(  6, 56)(  7, 55)(  8, 54)
(  9, 53)( 10, 52)( 11, 51)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 46)
( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)( 23, 39)( 24, 38)
( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 60,120)( 61,119)
( 62,177)( 63,176)( 64,175)( 65,174)( 66,173)( 67,172)( 68,171)( 69,170)
( 70,169)( 71,168)( 72,167)( 73,166)( 74,165)( 75,164)( 76,163)( 77,162)
( 78,161)( 79,160)( 80,159)( 81,158)( 82,157)( 83,156)( 84,155)( 85,154)
( 86,153)( 87,152)( 88,151)( 89,150)( 90,149)( 91,148)( 92,147)( 93,146)
( 94,145)( 95,144)( 96,143)( 97,142)( 98,141)( 99,140)(100,139)(101,138)
(102,137)(103,136)(104,135)(105,134)(106,133)(107,132)(108,131)(109,130)
(110,129)(111,128)(112,127)(113,126)(114,125)(115,124)(116,123)(117,122)
(118,121)(178,179)(180,236)(181,235)(182,234)(183,233)(184,232)(185,231)
(186,230)(187,229)(188,228)(189,227)(190,226)(191,225)(192,224)(193,223)
(194,222)(195,221)(196,220)(197,219)(198,218)(199,217)(200,216)(201,215)
(202,214)(203,213)(204,212)(205,211)(206,210)(207,209)(237,297)(238,296)
(239,354)(240,353)(241,352)(242,351)(243,350)(244,349)(245,348)(246,347)
(247,346)(248,345)(249,344)(250,343)(251,342)(252,341)(253,340)(254,339)
(255,338)(256,337)(257,336)(258,335)(259,334)(260,333)(261,332)(262,331)
(263,330)(264,329)(265,328)(266,327)(267,326)(268,325)(269,324)(270,323)
(271,322)(272,321)(273,320)(274,319)(275,318)(276,317)(277,316)(278,315)
(279,314)(280,313)(281,312)(282,311)(283,310)(284,309)(285,308)(286,307)
(287,306)(288,305)(289,304)(290,303)(291,302)(292,301)(293,300)(294,299)
(295,298);
s2 := Sym(354)!(  1,237)(  2,238)(  3,239)(  4,240)(  5,241)(  6,242)(  7,243)
(  8,244)(  9,245)( 10,246)( 11,247)( 12,248)( 13,249)( 14,250)( 15,251)
( 16,252)( 17,253)( 18,254)( 19,255)( 20,256)( 21,257)( 22,258)( 23,259)
( 24,260)( 25,261)( 26,262)( 27,263)( 28,264)( 29,265)( 30,266)( 31,267)
( 32,268)( 33,269)( 34,270)( 35,271)( 36,272)( 37,273)( 38,274)( 39,275)
( 40,276)( 41,277)( 42,278)( 43,279)( 44,280)( 45,281)( 46,282)( 47,283)
( 48,284)( 49,285)( 50,286)( 51,287)( 52,288)( 53,289)( 54,290)( 55,291)
( 56,292)( 57,293)( 58,294)( 59,295)( 60,178)( 61,179)( 62,180)( 63,181)
( 64,182)( 65,183)( 66,184)( 67,185)( 68,186)( 69,187)( 70,188)( 71,189)
( 72,190)( 73,191)( 74,192)( 75,193)( 76,194)( 77,195)( 78,196)( 79,197)
( 80,198)( 81,199)( 82,200)( 83,201)( 84,202)( 85,203)( 86,204)( 87,205)
( 88,206)( 89,207)( 90,208)( 91,209)( 92,210)( 93,211)( 94,212)( 95,213)
( 96,214)( 97,215)( 98,216)( 99,217)(100,218)(101,219)(102,220)(103,221)
(104,222)(105,223)(106,224)(107,225)(108,226)(109,227)(110,228)(111,229)
(112,230)(113,231)(114,232)(115,233)(116,234)(117,235)(118,236)(119,296)
(120,297)(121,298)(122,299)(123,300)(124,301)(125,302)(126,303)(127,304)
(128,305)(129,306)(130,307)(131,308)(132,309)(133,310)(134,311)(135,312)
(136,313)(137,314)(138,315)(139,316)(140,317)(141,318)(142,319)(143,320)
(144,321)(145,322)(146,323)(147,324)(148,325)(149,326)(150,327)(151,328)
(152,329)(153,330)(154,331)(155,332)(156,333)(157,334)(158,335)(159,336)
(160,337)(161,338)(162,339)(163,340)(164,341)(165,342)(166,343)(167,344)
(168,345)(169,346)(170,347)(171,348)(172,349)(173,350)(174,351)(175,352)
(176,353)(177,354);
poly := sub<Sym(354)|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*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope