Polytope of Type {44,12}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope