Polytope of Type {46,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,12}*1104
Also Known As : {46,12|2}. if this polytope has another name.
Group : SmallGroup(1104,107)
Rank : 3
Schlafli Type : {46,12}
Number of vertices, edges, etc : 46, 276, 12
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 : {46,6}*552
   3-fold quotients : {46,4}*368
   6-fold quotients : {46,2}*184
   12-fold quotients : {23,2}*92
   23-fold quotients : {2,12}*48
   46-fold quotients : {2,6}*24
   69-fold quotients : {2,4}*16
   92-fold quotients : {2,3}*12
   138-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(276)!(  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)
( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)
( 49, 68)( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)
( 57, 60)( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)
( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 94,115)( 95,114)( 96,113)
( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)
(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)
(125,130)(126,129)(127,128)(140,161)(141,160)(142,159)(143,158)(144,157)
(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)
(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)
(173,174)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)
(193,200)(194,199)(195,198)(196,197)(209,230)(210,229)(211,228)(212,227)
(213,226)(214,225)(215,224)(216,223)(217,222)(218,221)(219,220)(232,253)
(233,252)(234,251)(235,250)(236,249)(237,248)(238,247)(239,246)(240,245)
(241,244)(242,243)(255,276)(256,275)(257,274)(258,273)(259,272)(260,271)
(261,270)(262,269)(263,268)(264,267)(265,266);
s1 := 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, 48)( 25, 47)( 26, 69)( 27, 68)
( 28, 67)( 29, 66)( 30, 65)( 31, 64)( 32, 63)( 33, 62)( 34, 61)( 35, 60)
( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)( 41, 54)( 42, 53)( 43, 52)
( 44, 51)( 45, 50)( 46, 49)( 70, 71)( 72, 92)( 73, 91)( 74, 90)( 75, 89)
( 76, 88)( 77, 87)( 78, 86)( 79, 85)( 80, 84)( 81, 83)( 93,117)( 94,116)
( 95,138)( 96,137)( 97,136)( 98,135)( 99,134)(100,133)(101,132)(102,131)
(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)
(111,122)(112,121)(113,120)(114,119)(115,118)(139,209)(140,208)(141,230)
(142,229)(143,228)(144,227)(145,226)(146,225)(147,224)(148,223)(149,222)
(150,221)(151,220)(152,219)(153,218)(154,217)(155,216)(156,215)(157,214)
(158,213)(159,212)(160,211)(161,210)(162,255)(163,254)(164,276)(165,275)
(166,274)(167,273)(168,272)(169,271)(170,270)(171,269)(172,268)(173,267)
(174,266)(175,265)(176,264)(177,263)(178,262)(179,261)(180,260)(181,259)
(182,258)(183,257)(184,256)(185,232)(186,231)(187,253)(188,252)(189,251)
(190,250)(191,249)(192,248)(193,247)(194,246)(195,245)(196,244)(197,243)
(198,242)(199,241)(200,240)(201,239)(202,238)(203,237)(204,236)(205,235)
(206,234)(207,233);
s2 := Sym(276)!(  1,162)(  2,163)(  3,164)(  4,165)(  5,166)(  6,167)(  7,168)
(  8,169)(  9,170)( 10,171)( 11,172)( 12,173)( 13,174)( 14,175)( 15,176)
( 16,177)( 17,178)( 18,179)( 19,180)( 20,181)( 21,182)( 22,183)( 23,184)
( 24,139)( 25,140)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,146)
( 32,147)( 33,148)( 34,149)( 35,150)( 36,151)( 37,152)( 38,153)( 39,154)
( 40,155)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,161)( 47,185)
( 48,186)( 49,187)( 50,188)( 51,189)( 52,190)( 53,191)( 54,192)( 55,193)
( 56,194)( 57,195)( 58,196)( 59,197)( 60,198)( 61,199)( 62,200)( 63,201)
( 64,202)( 65,203)( 66,204)( 67,205)( 68,206)( 69,207)( 70,231)( 71,232)
( 72,233)( 73,234)( 74,235)( 75,236)( 76,237)( 77,238)( 78,239)( 79,240)
( 80,241)( 81,242)( 82,243)( 83,244)( 84,245)( 85,246)( 86,247)( 87,248)
( 88,249)( 89,250)( 90,251)( 91,252)( 92,253)( 93,208)( 94,209)( 95,210)
( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,216)(102,217)(103,218)
(104,219)(105,220)(106,221)(107,222)(108,223)(109,224)(110,225)(111,226)
(112,227)(113,228)(114,229)(115,230)(116,254)(117,255)(118,256)(119,257)
(120,258)(121,259)(122,260)(123,261)(124,262)(125,263)(126,264)(127,265)
(128,266)(129,267)(130,268)(131,269)(132,270)(133,271)(134,272)(135,273)
(136,274)(137,275)(138,276);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;

References : None.
to this polytope