Polytope of Type {132,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {132,4}*1056a
Also Known As : {132,4|2}. if this polytope has another name.
Group : SmallGroup(1056,759)
Rank : 3
Schlafli Type : {132,4}
Number of vertices, edges, etc : 132, 264, 4
Order of s₀s₁s₂ : 132
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {132,2}*528, {66,4}*528a
   3-fold quotients : {44,4}*352
   4-fold quotients : {66,2}*264
   6-fold quotients : {44,2}*176, {22,4}*176
   8-fold quotients : {33,2}*132
   11-fold quotients : {12,4}*96a
   12-fold quotients : {22,2}*88
   22-fold quotients : {12,2}*48, {6,4}*48a
   24-fold quotients : {11,2}*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 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 12, 23)( 13, 33)( 14, 32)
( 15, 31)( 16, 30)( 17, 29)( 18, 28)( 19, 27)( 20, 26)( 21, 25)( 22, 24)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)
( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 78, 89)( 79, 99)( 80, 98)
( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)
(101,110)(102,109)(103,108)(104,107)(105,106)(111,122)(112,132)(113,131)
(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)(121,123)
(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)(140,170)
(141,169)(142,168)(143,167)(144,188)(145,198)(146,197)(147,196)(148,195)
(149,194)(150,193)(151,192)(152,191)(153,190)(154,189)(155,177)(156,187)
(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)
(165,178)(199,232)(200,242)(201,241)(202,240)(203,239)(204,238)(205,237)
(206,236)(207,235)(208,234)(209,233)(210,254)(211,264)(212,263)(213,262)
(214,261)(215,260)(216,259)(217,258)(218,257)(219,256)(220,255)(221,243)
(222,253)(223,252)(224,251)(225,250)(226,249)(227,248)(228,247)(229,246)
(230,245)(231,244);;
s1 := (  1,145)(  2,144)(  3,154)(  4,153)(  5,152)(  6,151)(  7,150)(  8,149)
(  9,148)( 10,147)( 11,146)( 12,134)( 13,133)( 14,143)( 15,142)( 16,141)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,135)( 23,156)( 24,155)
( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)( 32,158)
( 33,157)( 34,178)( 35,177)( 36,187)( 37,186)( 38,185)( 39,184)( 40,183)
( 41,182)( 42,181)( 43,180)( 44,179)( 45,167)( 46,166)( 47,176)( 48,175)
( 49,174)( 50,173)( 51,172)( 52,171)( 53,170)( 54,169)( 55,168)( 56,189)
( 57,188)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)( 64,192)
( 65,191)( 66,190)( 67,211)( 68,210)( 69,220)( 70,219)( 71,218)( 72,217)
( 73,216)( 74,215)( 75,214)( 76,213)( 77,212)( 78,200)( 79,199)( 80,209)
( 81,208)( 82,207)( 83,206)( 84,205)( 85,204)( 86,203)( 87,202)( 88,201)
( 89,222)( 90,221)( 91,231)( 92,230)( 93,229)( 94,228)( 95,227)( 96,226)
( 97,225)( 98,224)( 99,223)(100,244)(101,243)(102,253)(103,252)(104,251)
(105,250)(106,249)(107,248)(108,247)(109,246)(110,245)(111,233)(112,232)
(113,242)(114,241)(115,240)(116,239)(117,238)(118,237)(119,236)(120,235)
(121,234)(122,255)(123,254)(124,264)(125,263)(126,262)(127,261)(128,260)
(129,259)(130,258)(131,257)(132,256);;
s2 := (133,199)(134,200)(135,201)(136,202)(137,203)(138,204)(139,205)(140,206)
(141,207)(142,208)(143,209)(144,210)(145,211)(146,212)(147,213)(148,214)
(149,215)(150,216)(151,217)(152,218)(153,219)(154,220)(155,221)(156,222)
(157,223)(158,224)(159,225)(160,226)(161,227)(162,228)(163,229)(164,230)
(165,231)(166,232)(167,233)(168,234)(169,235)(170,236)(171,237)(172,238)
(173,239)(174,240)(175,241)(176,242)(177,243)(178,244)(179,245)(180,246)
(181,247)(182,248)(183,249)(184,250)(185,251)(186,252)(187,253)(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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 12, 23)( 13, 33)
( 14, 32)( 15, 31)( 16, 30)( 17, 29)( 18, 28)( 19, 27)( 20, 26)( 21, 25)
( 22, 24)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)
( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)
( 55, 57)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 78, 89)( 79, 99)
( 80, 98)( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)
( 88, 90)(101,110)(102,109)(103,108)(104,107)(105,106)(111,122)(112,132)
(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)
(121,123)(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)
(140,170)(141,169)(142,168)(143,167)(144,188)(145,198)(146,197)(147,196)
(148,195)(149,194)(150,193)(151,192)(152,191)(153,190)(154,189)(155,177)
(156,187)(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)
(164,179)(165,178)(199,232)(200,242)(201,241)(202,240)(203,239)(204,238)
(205,237)(206,236)(207,235)(208,234)(209,233)(210,254)(211,264)(212,263)
(213,262)(214,261)(215,260)(216,259)(217,258)(218,257)(219,256)(220,255)
(221,243)(222,253)(223,252)(224,251)(225,250)(226,249)(227,248)(228,247)
(229,246)(230,245)(231,244);
s1 := Sym(264)!(  1,145)(  2,144)(  3,154)(  4,153)(  5,152)(  6,151)(  7,150)
(  8,149)(  9,148)( 10,147)( 11,146)( 12,134)( 13,133)( 14,143)( 15,142)
( 16,141)( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,135)( 23,156)
( 24,155)( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)
( 32,158)( 33,157)( 34,178)( 35,177)( 36,187)( 37,186)( 38,185)( 39,184)
( 40,183)( 41,182)( 42,181)( 43,180)( 44,179)( 45,167)( 46,166)( 47,176)
( 48,175)( 49,174)( 50,173)( 51,172)( 52,171)( 53,170)( 54,169)( 55,168)
( 56,189)( 57,188)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)
( 64,192)( 65,191)( 66,190)( 67,211)( 68,210)( 69,220)( 70,219)( 71,218)
( 72,217)( 73,216)( 74,215)( 75,214)( 76,213)( 77,212)( 78,200)( 79,199)
( 80,209)( 81,208)( 82,207)( 83,206)( 84,205)( 85,204)( 86,203)( 87,202)
( 88,201)( 89,222)( 90,221)( 91,231)( 92,230)( 93,229)( 94,228)( 95,227)
( 96,226)( 97,225)( 98,224)( 99,223)(100,244)(101,243)(102,253)(103,252)
(104,251)(105,250)(106,249)(107,248)(108,247)(109,246)(110,245)(111,233)
(112,232)(113,242)(114,241)(115,240)(116,239)(117,238)(118,237)(119,236)
(120,235)(121,234)(122,255)(123,254)(124,264)(125,263)(126,262)(127,261)
(128,260)(129,259)(130,258)(131,257)(132,256);
s2 := Sym(264)!(133,199)(134,200)(135,201)(136,202)(137,203)(138,204)(139,205)
(140,206)(141,207)(142,208)(143,209)(144,210)(145,211)(146,212)(147,213)
(148,214)(149,215)(150,216)(151,217)(152,218)(153,219)(154,220)(155,221)
(156,222)(157,223)(158,224)(159,225)(160,226)(161,227)(162,228)(163,229)
(164,230)(165,231)(166,232)(167,233)(168,234)(169,235)(170,236)(171,237)
(172,238)(173,239)(174,240)(175,241)(176,242)(177,243)(178,244)(179,245)
(180,246)(181,247)(182,248)(183,249)(184,250)(185,251)(186,252)(187,253)
(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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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