Polytope of Type {4,132}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,132}*1056a
Also Known As : {4,132|2}. if this polytope has another name.
Group : SmallGroup(1056,759)
Rank : 3
Schlafli Type : {4,132}
Number of vertices, edges, etc : 4, 264, 132
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 : {2,132}*528, {4,66}*528a
   3-fold quotients : {4,44}*352
   4-fold quotients : {2,66}*264
   6-fold quotients : {2,44}*176, {4,22}*176
   8-fold quotients : {2,33}*132
   11-fold quotients : {4,12}*96a
   12-fold quotients : {2,22}*88
   22-fold quotients : {2,12}*48, {4,6}*48a
   24-fold quotients : {2,11}*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 := (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);;
s1 := (  1,133)(  2,143)(  3,142)(  4,141)(  5,140)(  6,139)(  7,138)(  8,137)
(  9,136)( 10,135)( 11,134)( 12,155)( 13,165)( 14,164)( 15,163)( 16,162)
( 17,161)( 18,160)( 19,159)( 20,158)( 21,157)( 22,156)( 23,144)( 24,154)
( 25,153)( 26,152)( 27,151)( 28,150)( 29,149)( 30,148)( 31,147)( 32,146)
( 33,145)( 34,166)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)( 40,171)
( 41,170)( 42,169)( 43,168)( 44,167)( 45,188)( 46,198)( 47,197)( 48,196)
( 49,195)( 50,194)( 51,193)( 52,192)( 53,191)( 54,190)( 55,189)( 56,177)
( 57,187)( 58,186)( 59,185)( 60,184)( 61,183)( 62,182)( 63,181)( 64,180)
( 65,179)( 66,178)( 67,199)( 68,209)( 69,208)( 70,207)( 71,206)( 72,205)
( 73,204)( 74,203)( 75,202)( 76,201)( 77,200)( 78,221)( 79,231)( 80,230)
( 81,229)( 82,228)( 83,227)( 84,226)( 85,225)( 86,224)( 87,223)( 88,222)
( 89,210)( 90,220)( 91,219)( 92,218)( 93,217)( 94,216)( 95,215)( 96,214)
( 97,213)( 98,212)( 99,211)(100,232)(101,242)(102,241)(103,240)(104,239)
(105,238)(106,237)(107,236)(108,235)(109,234)(110,233)(111,254)(112,264)
(113,263)(114,262)(115,261)(116,260)(117,259)(118,258)(119,257)(120,256)
(121,255)(122,243)(123,253)(124,252)(125,251)(126,250)(127,249)(128,248)
(129,247)(130,246)(131,245)(132,244);;
s2 := (  1, 13)(  2, 12)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 34, 46)( 35, 45)( 36, 55)( 37, 54)( 38, 53)( 39, 52)( 40, 51)( 41, 50)
( 42, 49)( 43, 48)( 44, 47)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)
( 67, 79)( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)
( 75, 82)( 76, 81)( 77, 80)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)
(100,112)(101,111)(102,121)(103,120)(104,119)(105,118)(106,117)(107,116)
(108,115)(109,114)(110,113)(122,123)(124,132)(125,131)(126,130)(127,129)
(133,178)(134,177)(135,187)(136,186)(137,185)(138,184)(139,183)(140,182)
(141,181)(142,180)(143,179)(144,167)(145,166)(146,176)(147,175)(148,174)
(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,189)(156,188)
(157,198)(158,197)(159,196)(160,195)(161,194)(162,193)(163,192)(164,191)
(165,190)(199,244)(200,243)(201,253)(202,252)(203,251)(204,250)(205,249)
(206,248)(207,247)(208,246)(209,245)(210,233)(211,232)(212,242)(213,241)
(214,240)(215,239)(216,238)(217,237)(218,236)(219,235)(220,234)(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*s0*s1*s0*s1*s0*s1, 
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*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*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*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)!(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);
s1 := Sym(264)!(  1,133)(  2,143)(  3,142)(  4,141)(  5,140)(  6,139)(  7,138)
(  8,137)(  9,136)( 10,135)( 11,134)( 12,155)( 13,165)( 14,164)( 15,163)
( 16,162)( 17,161)( 18,160)( 19,159)( 20,158)( 21,157)( 22,156)( 23,144)
( 24,154)( 25,153)( 26,152)( 27,151)( 28,150)( 29,149)( 30,148)( 31,147)
( 32,146)( 33,145)( 34,166)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)
( 40,171)( 41,170)( 42,169)( 43,168)( 44,167)( 45,188)( 46,198)( 47,197)
( 48,196)( 49,195)( 50,194)( 51,193)( 52,192)( 53,191)( 54,190)( 55,189)
( 56,177)( 57,187)( 58,186)( 59,185)( 60,184)( 61,183)( 62,182)( 63,181)
( 64,180)( 65,179)( 66,178)( 67,199)( 68,209)( 69,208)( 70,207)( 71,206)
( 72,205)( 73,204)( 74,203)( 75,202)( 76,201)( 77,200)( 78,221)( 79,231)
( 80,230)( 81,229)( 82,228)( 83,227)( 84,226)( 85,225)( 86,224)( 87,223)
( 88,222)( 89,210)( 90,220)( 91,219)( 92,218)( 93,217)( 94,216)( 95,215)
( 96,214)( 97,213)( 98,212)( 99,211)(100,232)(101,242)(102,241)(103,240)
(104,239)(105,238)(106,237)(107,236)(108,235)(109,234)(110,233)(111,254)
(112,264)(113,263)(114,262)(115,261)(116,260)(117,259)(118,258)(119,257)
(120,256)(121,255)(122,243)(123,253)(124,252)(125,251)(126,250)(127,249)
(128,248)(129,247)(130,246)(131,245)(132,244);
s2 := Sym(264)!(  1, 13)(  2, 12)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)
(  8, 17)(  9, 16)( 10, 15)( 11, 14)( 23, 24)( 25, 33)( 26, 32)( 27, 31)
( 28, 30)( 34, 46)( 35, 45)( 36, 55)( 37, 54)( 38, 53)( 39, 52)( 40, 51)
( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 56, 57)( 58, 66)( 59, 65)( 60, 64)
( 61, 63)( 67, 79)( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)
( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 89, 90)( 91, 99)( 92, 98)( 93, 97)
( 94, 96)(100,112)(101,111)(102,121)(103,120)(104,119)(105,118)(106,117)
(107,116)(108,115)(109,114)(110,113)(122,123)(124,132)(125,131)(126,130)
(127,129)(133,178)(134,177)(135,187)(136,186)(137,185)(138,184)(139,183)
(140,182)(141,181)(142,180)(143,179)(144,167)(145,166)(146,176)(147,175)
(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,189)
(156,188)(157,198)(158,197)(159,196)(160,195)(161,194)(162,193)(163,192)
(164,191)(165,190)(199,244)(200,243)(201,253)(202,252)(203,251)(204,250)
(205,249)(206,248)(207,247)(208,246)(209,245)(210,233)(211,232)(212,242)
(213,241)(214,240)(215,239)(216,238)(217,237)(218,236)(219,235)(220,234)
(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*s0*s1*s0*s1*s0*s1, 
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*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*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*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