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Polytope of Type {12,46}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,46}*1104
Also Known As : {12,46|2}. if this polytope has another name.
Group : SmallGroup(1104,107)
Rank : 3
Schlafli Type : {12,46}
Number of vertices, edges, etc : 12, 276, 46
Order of s0s1s2 : 276
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 : {6,46}*552
   3-fold quotients : {4,46}*368
   6-fold quotients : {2,46}*184
   12-fold quotients : {2,23}*92
   23-fold quotients : {12,2}*48
   46-fold quotients : {6,2}*24
   69-fold quotients : {4,2}*16
   92-fold quotients : {3,2}*12
   138-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 24, 47)( 25, 48)( 26, 49)( 27, 50)( 28, 51)( 29, 52)( 30, 53)( 31, 54)
( 32, 55)( 33, 56)( 34, 57)( 35, 58)( 36, 59)( 37, 60)( 38, 61)( 39, 62)
( 40, 63)( 41, 64)( 42, 65)( 43, 66)( 44, 67)( 45, 68)( 46, 69)( 93,116)
( 94,117)( 95,118)( 96,119)( 97,120)( 98,121)( 99,122)(100,123)(101,124)
(102,125)(103,126)(104,127)(105,128)(106,129)(107,130)(108,131)(109,132)
(110,133)(111,134)(112,135)(113,136)(114,137)(115,138)(139,208)(140,209)
(141,210)(142,211)(143,212)(144,213)(145,214)(146,215)(147,216)(148,217)
(149,218)(150,219)(151,220)(152,221)(153,222)(154,223)(155,224)(156,225)
(157,226)(158,227)(159,228)(160,229)(161,230)(162,254)(163,255)(164,256)
(165,257)(166,258)(167,259)(168,260)(169,261)(170,262)(171,263)(172,264)
(173,265)(174,266)(175,267)(176,268)(177,269)(178,270)(179,271)(180,272)
(181,273)(182,274)(183,275)(184,276)(185,231)(186,232)(187,233)(188,234)
(189,235)(190,236)(191,237)(192,238)(193,239)(194,240)(195,241)(196,242)
(197,243)(198,244)(199,245)(200,246)(201,247)(202,248)(203,249)(204,250)
(205,251)(206,252)(207,253);;
s1 := (  1,162)(  2,184)(  3,183)(  4,182)(  5,181)(  6,180)(  7,179)(  8,178)
(  9,177)( 10,176)( 11,175)( 12,174)( 13,173)( 14,172)( 15,171)( 16,170)
( 17,169)( 18,168)( 19,167)( 20,166)( 21,165)( 22,164)( 23,163)( 24,139)
( 25,161)( 26,160)( 27,159)( 28,158)( 29,157)( 30,156)( 31,155)( 32,154)
( 33,153)( 34,152)( 35,151)( 36,150)( 37,149)( 38,148)( 39,147)( 40,146)
( 41,145)( 42,144)( 43,143)( 44,142)( 45,141)( 46,140)( 47,185)( 48,207)
( 49,206)( 50,205)( 51,204)( 52,203)( 53,202)( 54,201)( 55,200)( 56,199)
( 57,198)( 58,197)( 59,196)( 60,195)( 61,194)( 62,193)( 63,192)( 64,191)
( 65,190)( 66,189)( 67,188)( 68,187)( 69,186)( 70,231)( 71,253)( 72,252)
( 73,251)( 74,250)( 75,249)( 76,248)( 77,247)( 78,246)( 79,245)( 80,244)
( 81,243)( 82,242)( 83,241)( 84,240)( 85,239)( 86,238)( 87,237)( 88,236)
( 89,235)( 90,234)( 91,233)( 92,232)( 93,208)( 94,230)( 95,229)( 96,228)
( 97,227)( 98,226)( 99,225)(100,224)(101,223)(102,222)(103,221)(104,220)
(105,219)(106,218)(107,217)(108,216)(109,215)(110,214)(111,213)(112,212)
(113,211)(114,210)(115,209)(116,254)(117,276)(118,275)(119,274)(120,273)
(121,272)(122,271)(123,270)(124,269)(125,268)(126,267)(127,266)(128,265)
(129,264)(130,263)(131,262)(132,261)(133,260)(134,259)(135,258)(136,257)
(137,256)(138,255);;
s2 := (  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)
( 10, 16)( 11, 15)( 12, 14)( 24, 25)( 26, 46)( 27, 45)( 28, 44)( 29, 43)
( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 48)( 49, 69)
( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)( 55, 63)( 56, 62)( 57, 61)
( 58, 60)( 70, 71)( 72, 92)( 73, 91)( 74, 90)( 75, 89)( 76, 88)( 77, 87)
( 78, 86)( 79, 85)( 80, 84)( 81, 83)( 93, 94)( 95,115)( 96,114)( 97,113)
( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)(104,106)(116,117)
(118,138)(119,137)(120,136)(121,135)(122,134)(123,133)(124,132)(125,131)
(126,130)(127,129)(139,140)(141,161)(142,160)(143,159)(144,158)(145,157)
(146,156)(147,155)(148,154)(149,153)(150,152)(162,163)(164,184)(165,183)
(166,182)(167,181)(168,180)(169,179)(170,178)(171,177)(172,176)(173,175)
(185,186)(187,207)(188,206)(189,205)(190,204)(191,203)(192,202)(193,201)
(194,200)(195,199)(196,198)(208,209)(210,230)(211,229)(212,228)(213,227)
(214,226)(215,225)(216,224)(217,223)(218,222)(219,221)(231,232)(233,253)
(234,252)(235,251)(236,250)(237,249)(238,248)(239,247)(240,246)(241,245)
(242,244)(254,255)(256,276)(257,275)(258,274)(259,273)(260,272)(261,271)
(262,270)(263,269)(264,268)(265,267);;
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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(276)!( 24, 47)( 25, 48)( 26, 49)( 27, 50)( 28, 51)( 29, 52)( 30, 53)
( 31, 54)( 32, 55)( 33, 56)( 34, 57)( 35, 58)( 36, 59)( 37, 60)( 38, 61)
( 39, 62)( 40, 63)( 41, 64)( 42, 65)( 43, 66)( 44, 67)( 45, 68)( 46, 69)
( 93,116)( 94,117)( 95,118)( 96,119)( 97,120)( 98,121)( 99,122)(100,123)
(101,124)(102,125)(103,126)(104,127)(105,128)(106,129)(107,130)(108,131)
(109,132)(110,133)(111,134)(112,135)(113,136)(114,137)(115,138)(139,208)
(140,209)(141,210)(142,211)(143,212)(144,213)(145,214)(146,215)(147,216)
(148,217)(149,218)(150,219)(151,220)(152,221)(153,222)(154,223)(155,224)
(156,225)(157,226)(158,227)(159,228)(160,229)(161,230)(162,254)(163,255)
(164,256)(165,257)(166,258)(167,259)(168,260)(169,261)(170,262)(171,263)
(172,264)(173,265)(174,266)(175,267)(176,268)(177,269)(178,270)(179,271)
(180,272)(181,273)(182,274)(183,275)(184,276)(185,231)(186,232)(187,233)
(188,234)(189,235)(190,236)(191,237)(192,238)(193,239)(194,240)(195,241)
(196,242)(197,243)(198,244)(199,245)(200,246)(201,247)(202,248)(203,249)
(204,250)(205,251)(206,252)(207,253);
s1 := Sym(276)!(  1,162)(  2,184)(  3,183)(  4,182)(  5,181)(  6,180)(  7,179)
(  8,178)(  9,177)( 10,176)( 11,175)( 12,174)( 13,173)( 14,172)( 15,171)
( 16,170)( 17,169)( 18,168)( 19,167)( 20,166)( 21,165)( 22,164)( 23,163)
( 24,139)( 25,161)( 26,160)( 27,159)( 28,158)( 29,157)( 30,156)( 31,155)
( 32,154)( 33,153)( 34,152)( 35,151)( 36,150)( 37,149)( 38,148)( 39,147)
( 40,146)( 41,145)( 42,144)( 43,143)( 44,142)( 45,141)( 46,140)( 47,185)
( 48,207)( 49,206)( 50,205)( 51,204)( 52,203)( 53,202)( 54,201)( 55,200)
( 56,199)( 57,198)( 58,197)( 59,196)( 60,195)( 61,194)( 62,193)( 63,192)
( 64,191)( 65,190)( 66,189)( 67,188)( 68,187)( 69,186)( 70,231)( 71,253)
( 72,252)( 73,251)( 74,250)( 75,249)( 76,248)( 77,247)( 78,246)( 79,245)
( 80,244)( 81,243)( 82,242)( 83,241)( 84,240)( 85,239)( 86,238)( 87,237)
( 88,236)( 89,235)( 90,234)( 91,233)( 92,232)( 93,208)( 94,230)( 95,229)
( 96,228)( 97,227)( 98,226)( 99,225)(100,224)(101,223)(102,222)(103,221)
(104,220)(105,219)(106,218)(107,217)(108,216)(109,215)(110,214)(111,213)
(112,212)(113,211)(114,210)(115,209)(116,254)(117,276)(118,275)(119,274)
(120,273)(121,272)(122,271)(123,270)(124,269)(125,268)(126,267)(127,266)
(128,265)(129,264)(130,263)(131,262)(132,261)(133,260)(134,259)(135,258)
(136,257)(137,256)(138,255);
s2 := Sym(276)!(  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)
(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 24, 25)( 26, 46)( 27, 45)( 28, 44)
( 29, 43)( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 48)
( 49, 69)( 50, 68)( 51, 67)( 52, 66)( 53, 65)( 54, 64)( 55, 63)( 56, 62)
( 57, 61)( 58, 60)( 70, 71)( 72, 92)( 73, 91)( 74, 90)( 75, 89)( 76, 88)
( 77, 87)( 78, 86)( 79, 85)( 80, 84)( 81, 83)( 93, 94)( 95,115)( 96,114)
( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)(104,106)
(116,117)(118,138)(119,137)(120,136)(121,135)(122,134)(123,133)(124,132)
(125,131)(126,130)(127,129)(139,140)(141,161)(142,160)(143,159)(144,158)
(145,157)(146,156)(147,155)(148,154)(149,153)(150,152)(162,163)(164,184)
(165,183)(166,182)(167,181)(168,180)(169,179)(170,178)(171,177)(172,176)
(173,175)(185,186)(187,207)(188,206)(189,205)(190,204)(191,203)(192,202)
(193,201)(194,200)(195,199)(196,198)(208,209)(210,230)(211,229)(212,228)
(213,227)(214,226)(215,225)(216,224)(217,223)(218,222)(219,221)(231,232)
(233,253)(234,252)(235,251)(236,250)(237,249)(238,248)(239,247)(240,246)
(241,245)(242,244)(254,255)(256,276)(257,275)(258,274)(259,273)(260,272)
(261,271)(262,270)(263,269)(264,268)(265,267);
poly := sub<Sym(276)|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*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 >; 
 
References : None.
to this polytope