Polytope of Type {266,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {266,2}*1064
if this polytope has a name.
Group : SmallGroup(1064,34)
Rank : 3
Schlafli Type : {266,2}
Number of vertices, edges, etc : 266, 266, 2
Order of s₀s₁s₂ : 266
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {133,2}*532
   7-fold quotients : {38,2}*152
   14-fold quotients : {19,2}*76
   19-fold quotients : {14,2}*56
   38-fold quotients : {7,2}*28
   133-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 20,115)( 21,133)( 22,132)( 23,131)( 24,130)( 25,129)( 26,128)
( 27,127)( 28,126)( 29,125)( 30,124)( 31,123)( 32,122)( 33,121)( 34,120)
( 35,119)( 36,118)( 37,117)( 38,116)( 39, 96)( 40,114)( 41,113)( 42,112)
( 43,111)( 44,110)( 45,109)( 46,108)( 47,107)( 48,106)( 49,105)( 50,104)
( 51,103)( 52,102)( 53,101)( 54,100)( 55, 99)( 56, 98)( 57, 97)( 58, 77)
( 59, 95)( 60, 94)( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)
( 67, 87)( 68, 86)( 69, 85)( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)
( 75, 79)( 76, 78)(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)
(141,146)(142,145)(143,144)(153,248)(154,266)(155,265)(156,264)(157,263)
(158,262)(159,261)(160,260)(161,259)(162,258)(163,257)(164,256)(165,255)
(166,254)(167,253)(168,252)(169,251)(170,250)(171,249)(172,229)(173,247)
(174,246)(175,245)(176,244)(177,243)(178,242)(179,241)(180,240)(181,239)
(182,238)(183,237)(184,236)(185,235)(186,234)(187,233)(188,232)(189,231)
(190,230)(191,210)(192,228)(193,227)(194,226)(195,225)(196,224)(197,223)
(198,222)(199,221)(200,220)(201,219)(202,218)(203,217)(204,216)(205,215)
(206,214)(207,213)(208,212)(209,211);;
s1 := (  1,154)(  2,153)(  3,171)(  4,170)(  5,169)(  6,168)(  7,167)(  8,166)
(  9,165)( 10,164)( 11,163)( 12,162)( 13,161)( 14,160)( 15,159)( 16,158)
( 17,157)( 18,156)( 19,155)( 20,135)( 21,134)( 22,152)( 23,151)( 24,150)
( 25,149)( 26,148)( 27,147)( 28,146)( 29,145)( 30,144)( 31,143)( 32,142)
( 33,141)( 34,140)( 35,139)( 36,138)( 37,137)( 38,136)( 39,249)( 40,248)
( 41,266)( 42,265)( 43,264)( 44,263)( 45,262)( 46,261)( 47,260)( 48,259)
( 49,258)( 50,257)( 51,256)( 52,255)( 53,254)( 54,253)( 55,252)( 56,251)
( 57,250)( 58,230)( 59,229)( 60,247)( 61,246)( 62,245)( 63,244)( 64,243)
( 65,242)( 66,241)( 67,240)( 68,239)( 69,238)( 70,237)( 71,236)( 72,235)
( 73,234)( 74,233)( 75,232)( 76,231)( 77,211)( 78,210)( 79,228)( 80,227)
( 81,226)( 82,225)( 83,224)( 84,223)( 85,222)( 86,221)( 87,220)( 88,219)
( 89,218)( 90,217)( 91,216)( 92,215)( 93,214)( 94,213)( 95,212)( 96,192)
( 97,191)( 98,209)( 99,208)(100,207)(101,206)(102,205)(103,204)(104,203)
(105,202)(106,201)(107,200)(108,199)(109,198)(110,197)(111,196)(112,195)
(113,194)(114,193)(115,173)(116,172)(117,190)(118,189)(119,188)(120,187)
(121,186)(122,185)(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)
(129,178)(130,177)(131,176)(132,175)(133,174);;
s2 := (267,268);;
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, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(268)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 20,115)( 21,133)( 22,132)( 23,131)( 24,130)( 25,129)
( 26,128)( 27,127)( 28,126)( 29,125)( 30,124)( 31,123)( 32,122)( 33,121)
( 34,120)( 35,119)( 36,118)( 37,117)( 38,116)( 39, 96)( 40,114)( 41,113)
( 42,112)( 43,111)( 44,110)( 45,109)( 46,108)( 47,107)( 48,106)( 49,105)
( 50,104)( 51,103)( 52,102)( 53,101)( 54,100)( 55, 99)( 56, 98)( 57, 97)
( 58, 77)( 59, 95)( 60, 94)( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)
( 66, 88)( 67, 87)( 68, 86)( 69, 85)( 70, 84)( 71, 83)( 72, 82)( 73, 81)
( 74, 80)( 75, 79)( 76, 78)(135,152)(136,151)(137,150)(138,149)(139,148)
(140,147)(141,146)(142,145)(143,144)(153,248)(154,266)(155,265)(156,264)
(157,263)(158,262)(159,261)(160,260)(161,259)(162,258)(163,257)(164,256)
(165,255)(166,254)(167,253)(168,252)(169,251)(170,250)(171,249)(172,229)
(173,247)(174,246)(175,245)(176,244)(177,243)(178,242)(179,241)(180,240)
(181,239)(182,238)(183,237)(184,236)(185,235)(186,234)(187,233)(188,232)
(189,231)(190,230)(191,210)(192,228)(193,227)(194,226)(195,225)(196,224)
(197,223)(198,222)(199,221)(200,220)(201,219)(202,218)(203,217)(204,216)
(205,215)(206,214)(207,213)(208,212)(209,211);
s1 := Sym(268)!(  1,154)(  2,153)(  3,171)(  4,170)(  5,169)(  6,168)(  7,167)
(  8,166)(  9,165)( 10,164)( 11,163)( 12,162)( 13,161)( 14,160)( 15,159)
( 16,158)( 17,157)( 18,156)( 19,155)( 20,135)( 21,134)( 22,152)( 23,151)
( 24,150)( 25,149)( 26,148)( 27,147)( 28,146)( 29,145)( 30,144)( 31,143)
( 32,142)( 33,141)( 34,140)( 35,139)( 36,138)( 37,137)( 38,136)( 39,249)
( 40,248)( 41,266)( 42,265)( 43,264)( 44,263)( 45,262)( 46,261)( 47,260)
( 48,259)( 49,258)( 50,257)( 51,256)( 52,255)( 53,254)( 54,253)( 55,252)
( 56,251)( 57,250)( 58,230)( 59,229)( 60,247)( 61,246)( 62,245)( 63,244)
( 64,243)( 65,242)( 66,241)( 67,240)( 68,239)( 69,238)( 70,237)( 71,236)
( 72,235)( 73,234)( 74,233)( 75,232)( 76,231)( 77,211)( 78,210)( 79,228)
( 80,227)( 81,226)( 82,225)( 83,224)( 84,223)( 85,222)( 86,221)( 87,220)
( 88,219)( 89,218)( 90,217)( 91,216)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,192)( 97,191)( 98,209)( 99,208)(100,207)(101,206)(102,205)(103,204)
(104,203)(105,202)(106,201)(107,200)(108,199)(109,198)(110,197)(111,196)
(112,195)(113,194)(114,193)(115,173)(116,172)(117,190)(118,189)(119,188)
(120,187)(121,186)(122,185)(123,184)(124,183)(125,182)(126,181)(127,180)
(128,179)(129,178)(130,177)(131,176)(132,175)(133,174);
s2 := Sym(268)!(267,268);
poly := sub<Sym(268)|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, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope