Polytope of Type {12,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,44}*1056
Also Known As : {12,44|2}. if this polytope has another name.
Group : SmallGroup(1056,463)
Rank : 3
Schlafli Type : {12,44}
Number of vertices, edges, etc : 12, 264, 44
Order of s₀s₁s₂ : 132
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 : {12,22}*528, {6,44}*528a
   3-fold quotients : {4,44}*352
   4-fold quotients : {6,22}*264
   6-fold quotients : {2,44}*176, {4,22}*176
   11-fold quotients : {12,4}*96a
   12-fold quotients : {2,22}*88
   22-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {2,11}*44
   33-fold quotients : {4,4}*32
   44-fold quotients : {6,2}*24
   66-fold quotients : {2,4}*16, {4,2}*16
   88-fold quotients : {3,2}*12
   132-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope