Polytope of Type {2,33,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,33,4}*1056
if this polytope has a name.
Group : SmallGroup(1056,1017)
Rank : 4
Schlafli Type : {2,33,4}
Number of vertices, edges, etc : 2, 66, 132, 8
Order of s₀s₁s₂s₃ : 66
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,33,4}*528
   4-fold quotients : {2,33,2}*264
   11-fold quotients : {2,3,4}*96
   12-fold quotients : {2,11,2}*88
   22-fold quotients : {2,3,4}*48
   44-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  7, 43)(  8, 45)(  9, 44)( 10, 46)( 11, 39)( 12, 41)( 13, 40)
( 14, 42)( 15, 35)( 16, 37)( 17, 36)( 18, 38)( 19, 31)( 20, 33)( 21, 32)
( 22, 34)( 23, 27)( 24, 29)( 25, 28)( 26, 30)( 47, 91)( 48, 93)( 49, 92)
( 50, 94)( 51,131)( 52,133)( 53,132)( 54,134)( 55,127)( 56,129)( 57,128)
( 58,130)( 59,123)( 60,125)( 61,124)( 62,126)( 63,119)( 64,121)( 65,120)
( 66,122)( 67,115)( 68,117)( 69,116)( 70,118)( 71,111)( 72,113)( 73,112)
( 74,114)( 75,107)( 76,109)( 77,108)( 78,110)( 79,103)( 80,105)( 81,104)
( 82,106)( 83, 99)( 84,101)( 85,100)( 86,102)( 87, 95)( 88, 97)( 89, 96)
( 90, 98)(136,137)(139,175)(140,177)(141,176)(142,178)(143,171)(144,173)
(145,172)(146,174)(147,167)(148,169)(149,168)(150,170)(151,163)(152,165)
(153,164)(154,166)(155,159)(156,161)(157,160)(158,162)(179,223)(180,225)
(181,224)(182,226)(183,263)(184,265)(185,264)(186,266)(187,259)(188,261)
(189,260)(190,262)(191,255)(192,257)(193,256)(194,258)(195,251)(196,253)
(197,252)(198,254)(199,247)(200,249)(201,248)(202,250)(203,243)(204,245)
(205,244)(206,246)(207,239)(208,241)(209,240)(210,242)(211,235)(212,237)
(213,236)(214,238)(215,231)(216,233)(217,232)(218,234)(219,227)(220,229)
(221,228)(222,230);;
s2 := (  3, 51)(  4, 52)(  5, 54)(  6, 53)(  7, 47)(  8, 48)(  9, 50)( 10, 49)
( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15, 83)( 16, 84)( 17, 86)( 18, 85)
( 19, 79)( 20, 80)( 21, 82)( 22, 81)( 23, 75)( 24, 76)( 25, 78)( 26, 77)
( 27, 71)( 28, 72)( 29, 74)( 30, 73)( 31, 67)( 32, 68)( 33, 70)( 34, 69)
( 35, 63)( 36, 64)( 37, 66)( 38, 65)( 39, 59)( 40, 60)( 41, 62)( 42, 61)
( 43, 55)( 44, 56)( 45, 58)( 46, 57)( 91, 95)( 92, 96)( 93, 98)( 94, 97)
( 99,131)(100,132)(101,134)(102,133)(103,127)(104,128)(105,130)(106,129)
(107,123)(108,124)(109,126)(110,125)(111,119)(112,120)(113,122)(114,121)
(117,118)(135,183)(136,184)(137,186)(138,185)(139,179)(140,180)(141,182)
(142,181)(143,219)(144,220)(145,222)(146,221)(147,215)(148,216)(149,218)
(150,217)(151,211)(152,212)(153,214)(154,213)(155,207)(156,208)(157,210)
(158,209)(159,203)(160,204)(161,206)(162,205)(163,199)(164,200)(165,202)
(166,201)(167,195)(168,196)(169,198)(170,197)(171,191)(172,192)(173,194)
(174,193)(175,187)(176,188)(177,190)(178,189)(223,227)(224,228)(225,230)
(226,229)(231,263)(232,264)(233,266)(234,265)(235,259)(236,260)(237,262)
(238,261)(239,255)(240,256)(241,258)(242,257)(243,251)(244,252)(245,254)
(246,253)(249,250);;
s3 := (  3,138)(  4,137)(  5,136)(  6,135)(  7,142)(  8,141)(  9,140)( 10,139)
( 11,146)( 12,145)( 13,144)( 14,143)( 15,150)( 16,149)( 17,148)( 18,147)
( 19,154)( 20,153)( 21,152)( 22,151)( 23,158)( 24,157)( 25,156)( 26,155)
( 27,162)( 28,161)( 29,160)( 30,159)( 31,166)( 32,165)( 33,164)( 34,163)
( 35,170)( 36,169)( 37,168)( 38,167)( 39,174)( 40,173)( 41,172)( 42,171)
( 43,178)( 44,177)( 45,176)( 46,175)( 47,182)( 48,181)( 49,180)( 50,179)
( 51,186)( 52,185)( 53,184)( 54,183)( 55,190)( 56,189)( 57,188)( 58,187)
( 59,194)( 60,193)( 61,192)( 62,191)( 63,198)( 64,197)( 65,196)( 66,195)
( 67,202)( 68,201)( 69,200)( 70,199)( 71,206)( 72,205)( 73,204)( 74,203)
( 75,210)( 76,209)( 77,208)( 78,207)( 79,214)( 80,213)( 81,212)( 82,211)
( 83,218)( 84,217)( 85,216)( 86,215)( 87,222)( 88,221)( 89,220)( 90,219)
( 91,226)( 92,225)( 93,224)( 94,223)( 95,230)( 96,229)( 97,228)( 98,227)
( 99,234)(100,233)(101,232)(102,231)(103,238)(104,237)(105,236)(106,235)
(107,242)(108,241)(109,240)(110,239)(111,246)(112,245)(113,244)(114,243)
(115,250)(116,249)(117,248)(118,247)(119,254)(120,253)(121,252)(122,251)
(123,258)(124,257)(125,256)(126,255)(127,262)(128,261)(129,260)(130,259)
(131,266)(132,265)(133,264)(134,263);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(266)!(1,2);
s1 := Sym(266)!(  4,  5)(  7, 43)(  8, 45)(  9, 44)( 10, 46)( 11, 39)( 12, 41)
( 13, 40)( 14, 42)( 15, 35)( 16, 37)( 17, 36)( 18, 38)( 19, 31)( 20, 33)
( 21, 32)( 22, 34)( 23, 27)( 24, 29)( 25, 28)( 26, 30)( 47, 91)( 48, 93)
( 49, 92)( 50, 94)( 51,131)( 52,133)( 53,132)( 54,134)( 55,127)( 56,129)
( 57,128)( 58,130)( 59,123)( 60,125)( 61,124)( 62,126)( 63,119)( 64,121)
( 65,120)( 66,122)( 67,115)( 68,117)( 69,116)( 70,118)( 71,111)( 72,113)
( 73,112)( 74,114)( 75,107)( 76,109)( 77,108)( 78,110)( 79,103)( 80,105)
( 81,104)( 82,106)( 83, 99)( 84,101)( 85,100)( 86,102)( 87, 95)( 88, 97)
( 89, 96)( 90, 98)(136,137)(139,175)(140,177)(141,176)(142,178)(143,171)
(144,173)(145,172)(146,174)(147,167)(148,169)(149,168)(150,170)(151,163)
(152,165)(153,164)(154,166)(155,159)(156,161)(157,160)(158,162)(179,223)
(180,225)(181,224)(182,226)(183,263)(184,265)(185,264)(186,266)(187,259)
(188,261)(189,260)(190,262)(191,255)(192,257)(193,256)(194,258)(195,251)
(196,253)(197,252)(198,254)(199,247)(200,249)(201,248)(202,250)(203,243)
(204,245)(205,244)(206,246)(207,239)(208,241)(209,240)(210,242)(211,235)
(212,237)(213,236)(214,238)(215,231)(216,233)(217,232)(218,234)(219,227)
(220,229)(221,228)(222,230);
s2 := Sym(266)!(  3, 51)(  4, 52)(  5, 54)(  6, 53)(  7, 47)(  8, 48)(  9, 50)
( 10, 49)( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15, 83)( 16, 84)( 17, 86)
( 18, 85)( 19, 79)( 20, 80)( 21, 82)( 22, 81)( 23, 75)( 24, 76)( 25, 78)
( 26, 77)( 27, 71)( 28, 72)( 29, 74)( 30, 73)( 31, 67)( 32, 68)( 33, 70)
( 34, 69)( 35, 63)( 36, 64)( 37, 66)( 38, 65)( 39, 59)( 40, 60)( 41, 62)
( 42, 61)( 43, 55)( 44, 56)( 45, 58)( 46, 57)( 91, 95)( 92, 96)( 93, 98)
( 94, 97)( 99,131)(100,132)(101,134)(102,133)(103,127)(104,128)(105,130)
(106,129)(107,123)(108,124)(109,126)(110,125)(111,119)(112,120)(113,122)
(114,121)(117,118)(135,183)(136,184)(137,186)(138,185)(139,179)(140,180)
(141,182)(142,181)(143,219)(144,220)(145,222)(146,221)(147,215)(148,216)
(149,218)(150,217)(151,211)(152,212)(153,214)(154,213)(155,207)(156,208)
(157,210)(158,209)(159,203)(160,204)(161,206)(162,205)(163,199)(164,200)
(165,202)(166,201)(167,195)(168,196)(169,198)(170,197)(171,191)(172,192)
(173,194)(174,193)(175,187)(176,188)(177,190)(178,189)(223,227)(224,228)
(225,230)(226,229)(231,263)(232,264)(233,266)(234,265)(235,259)(236,260)
(237,262)(238,261)(239,255)(240,256)(241,258)(242,257)(243,251)(244,252)
(245,254)(246,253)(249,250);
s3 := Sym(266)!(  3,138)(  4,137)(  5,136)(  6,135)(  7,142)(  8,141)(  9,140)
( 10,139)( 11,146)( 12,145)( 13,144)( 14,143)( 15,150)( 16,149)( 17,148)
( 18,147)( 19,154)( 20,153)( 21,152)( 22,151)( 23,158)( 24,157)( 25,156)
( 26,155)( 27,162)( 28,161)( 29,160)( 30,159)( 31,166)( 32,165)( 33,164)
( 34,163)( 35,170)( 36,169)( 37,168)( 38,167)( 39,174)( 40,173)( 41,172)
( 42,171)( 43,178)( 44,177)( 45,176)( 46,175)( 47,182)( 48,181)( 49,180)
( 50,179)( 51,186)( 52,185)( 53,184)( 54,183)( 55,190)( 56,189)( 57,188)
( 58,187)( 59,194)( 60,193)( 61,192)( 62,191)( 63,198)( 64,197)( 65,196)
( 66,195)( 67,202)( 68,201)( 69,200)( 70,199)( 71,206)( 72,205)( 73,204)
( 74,203)( 75,210)( 76,209)( 77,208)( 78,207)( 79,214)( 80,213)( 81,212)
( 82,211)( 83,218)( 84,217)( 85,216)( 86,215)( 87,222)( 88,221)( 89,220)
( 90,219)( 91,226)( 92,225)( 93,224)( 94,223)( 95,230)( 96,229)( 97,228)
( 98,227)( 99,234)(100,233)(101,232)(102,231)(103,238)(104,237)(105,236)
(106,235)(107,242)(108,241)(109,240)(110,239)(111,246)(112,245)(113,244)
(114,243)(115,250)(116,249)(117,248)(118,247)(119,254)(120,253)(121,252)
(122,251)(123,258)(124,257)(125,256)(126,255)(127,262)(128,261)(129,260)
(130,259)(131,266)(132,265)(133,264)(134,263);
poly := sub<Sym(266)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope