Polytope of Type {4,138}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,138}*1104a
Also Known As : {4,138|2}. if this polytope has another name.
Group : SmallGroup(1104,150)
Rank : 3
Schlafli Type : {4,138}
Number of vertices, edges, etc : 4, 276, 138
Order of s₀s₁s₂ : 276
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 : {2,138}*552
   3-fold quotients : {4,46}*368
   4-fold quotients : {2,69}*276
   6-fold quotients : {2,46}*184
   12-fold quotients : {2,23}*92
   23-fold quotients : {4,6}*48a
   46-fold quotients : {2,6}*24
   69-fold quotients : {4,2}*16
   92-fold quotients : {2,3}*12
   138-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope