Polytope of Type {276,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {276,2}*1104
if this polytope has a name.
Group : SmallGroup(1104,148)
Rank : 3
Schlafli Type : {276,2}
Number of vertices, edges, etc : 276, 276, 2
Order of s₀s₁s₂ : 276
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 : {138,2}*552
   3-fold quotients : {92,2}*368
   4-fold quotients : {69,2}*276
   6-fold quotients : {46,2}*184
   12-fold quotients : {23,2}*92
   23-fold quotients : {12,2}*48
   46-fold quotients : {6,2}*24
   69-fold quotients : {4,2}*16
   92-fold quotients : {3,2}*12
   138-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)
( 10, 15)( 11, 14)( 12, 13)( 24, 47)( 25, 69)( 26, 68)( 27, 67)( 28, 66)
( 29, 65)( 30, 64)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)
( 37, 57)( 38, 56)( 39, 55)( 40, 54)( 41, 53)( 42, 52)( 43, 51)( 44, 50)
( 45, 49)( 46, 48)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)
( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 93,116)( 94,138)( 95,137)
( 96,136)( 97,135)( 98,134)( 99,133)(100,132)(101,131)(102,130)(103,129)
(104,128)(105,127)(106,126)(107,125)(108,124)(109,123)(110,122)(111,121)
(112,120)(113,119)(114,118)(115,117)(139,208)(140,230)(141,229)(142,228)
(143,227)(144,226)(145,225)(146,224)(147,223)(148,222)(149,221)(150,220)
(151,219)(152,218)(153,217)(154,216)(155,215)(156,214)(157,213)(158,212)
(159,211)(160,210)(161,209)(162,254)(163,276)(164,275)(165,274)(166,273)
(167,272)(168,271)(169,270)(170,269)(171,268)(172,267)(173,266)(174,265)
(175,264)(176,263)(177,262)(178,261)(179,260)(180,259)(181,258)(182,257)
(183,256)(184,255)(185,231)(186,253)(187,252)(188,251)(189,250)(190,249)
(191,248)(192,247)(193,246)(194,245)(195,244)(196,243)(197,242)(198,241)
(199,240)(200,239)(201,238)(202,237)(203,236)(204,235)(205,234)(206,233)
(207,232);;
s1 := (  1,163)(  2,162)(  3,184)(  4,183)(  5,182)(  6,181)(  7,180)(  8,179)
(  9,178)( 10,177)( 11,176)( 12,175)( 13,174)( 14,173)( 15,172)( 16,171)
( 17,170)( 18,169)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)( 24,140)
( 25,139)( 26,161)( 27,160)( 28,159)( 29,158)( 30,157)( 31,156)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,151)( 37,150)( 38,149)( 39,148)( 40,147)
( 41,146)( 42,145)( 43,144)( 44,143)( 45,142)( 46,141)( 47,186)( 48,185)
( 49,207)( 50,206)( 51,205)( 52,204)( 53,203)( 54,202)( 55,201)( 56,200)
( 57,199)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)( 64,192)
( 65,191)( 66,190)( 67,189)( 68,188)( 69,187)( 70,232)( 71,231)( 72,253)
( 73,252)( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)( 80,245)
( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)( 88,237)
( 89,236)( 90,235)( 91,234)( 92,233)( 93,209)( 94,208)( 95,230)( 96,229)
( 97,228)( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,222)(104,221)
(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)(112,213)
(113,212)(114,211)(115,210)(116,255)(117,254)(118,276)(119,275)(120,274)
(121,273)(122,272)(123,271)(124,270)(125,269)(126,268)(127,267)(128,266)
(129,265)(130,264)(131,263)(132,262)(133,261)(134,260)(135,259)(136,258)
(137,257)(138,256);;
s2 := (277,278);;
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*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(278)!(  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 12, 13)( 24, 47)( 25, 69)( 26, 68)( 27, 67)
( 28, 66)( 29, 65)( 30, 64)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)
( 36, 58)( 37, 57)( 38, 56)( 39, 55)( 40, 54)( 41, 53)( 42, 52)( 43, 51)
( 44, 50)( 45, 49)( 46, 48)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)
( 76, 87)( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 93,116)( 94,138)
( 95,137)( 96,136)( 97,135)( 98,134)( 99,133)(100,132)(101,131)(102,130)
(103,129)(104,128)(105,127)(106,126)(107,125)(108,124)(109,123)(110,122)
(111,121)(112,120)(113,119)(114,118)(115,117)(139,208)(140,230)(141,229)
(142,228)(143,227)(144,226)(145,225)(146,224)(147,223)(148,222)(149,221)
(150,220)(151,219)(152,218)(153,217)(154,216)(155,215)(156,214)(157,213)
(158,212)(159,211)(160,210)(161,209)(162,254)(163,276)(164,275)(165,274)
(166,273)(167,272)(168,271)(169,270)(170,269)(171,268)(172,267)(173,266)
(174,265)(175,264)(176,263)(177,262)(178,261)(179,260)(180,259)(181,258)
(182,257)(183,256)(184,255)(185,231)(186,253)(187,252)(188,251)(189,250)
(190,249)(191,248)(192,247)(193,246)(194,245)(195,244)(196,243)(197,242)
(198,241)(199,240)(200,239)(201,238)(202,237)(203,236)(204,235)(205,234)
(206,233)(207,232);
s1 := Sym(278)!(  1,163)(  2,162)(  3,184)(  4,183)(  5,182)(  6,181)(  7,180)
(  8,179)(  9,178)( 10,177)( 11,176)( 12,175)( 13,174)( 14,173)( 15,172)
( 16,171)( 17,170)( 18,169)( 19,168)( 20,167)( 21,166)( 22,165)( 23,164)
( 24,140)( 25,139)( 26,161)( 27,160)( 28,159)( 29,158)( 30,157)( 31,156)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,151)( 37,150)( 38,149)( 39,148)
( 40,147)( 41,146)( 42,145)( 43,144)( 44,143)( 45,142)( 46,141)( 47,186)
( 48,185)( 49,207)( 50,206)( 51,205)( 52,204)( 53,203)( 54,202)( 55,201)
( 56,200)( 57,199)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)
( 64,192)( 65,191)( 66,190)( 67,189)( 68,188)( 69,187)( 70,232)( 71,231)
( 72,253)( 73,252)( 74,251)( 75,250)( 76,249)( 77,248)( 78,247)( 79,246)
( 80,245)( 81,244)( 82,243)( 83,242)( 84,241)( 85,240)( 86,239)( 87,238)
( 88,237)( 89,236)( 90,235)( 91,234)( 92,233)( 93,209)( 94,208)( 95,230)
( 96,229)( 97,228)( 98,227)( 99,226)(100,225)(101,224)(102,223)(103,222)
(104,221)(105,220)(106,219)(107,218)(108,217)(109,216)(110,215)(111,214)
(112,213)(113,212)(114,211)(115,210)(116,255)(117,254)(118,276)(119,275)
(120,274)(121,273)(122,272)(123,271)(124,270)(125,269)(126,268)(127,267)
(128,266)(129,265)(130,264)(131,263)(132,262)(133,261)(134,260)(135,259)
(136,258)(137,257)(138,256);
s2 := Sym(278)!(277,278);
poly := sub<Sym(278)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope