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Polytope of Type {138,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {138,4}*1104a
Also Known As : {138,4|2}. if this polytope has another name.
Group : SmallGroup(1104,150)
Rank : 3
Schlafli Type : {138,4}
Number of vertices, edges, etc : 138, 276, 4
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 : {138,2}*552
   3-fold quotients : {46,4}*368
   4-fold quotients : {69,2}*276
   6-fold quotients : {46,2}*184
   12-fold quotients : {23,2}*92
   23-fold quotients : {6,4}*48a
   46-fold quotients : {6,2}*24
   69-fold quotients : {2,4}*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)(140,161)(141,160)(142,159)(143,158)
(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(162,185)
(163,207)(164,206)(165,205)(166,204)(167,203)(168,202)(169,201)(170,200)
(171,199)(172,198)(173,197)(174,196)(175,195)(176,194)(177,193)(178,192)
(179,191)(180,190)(181,189)(182,188)(183,187)(184,186)(209,230)(210,229)
(211,228)(212,227)(213,226)(214,225)(215,224)(216,223)(217,222)(218,221)
(219,220)(231,254)(232,276)(233,275)(234,274)(235,273)(236,272)(237,271)
(238,270)(239,269)(240,268)(241,267)(242,266)(243,265)(244,264)(245,263)
(246,262)(247,261)(248,260)(249,259)(250,258)(251,257)(252,256)(253,255);;
s1 := (  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)(139,232)(140,231)(141,253)(142,252)
(143,251)(144,250)(145,249)(146,248)(147,247)(148,246)(149,245)(150,244)
(151,243)(152,242)(153,241)(154,240)(155,239)(156,238)(157,237)(158,236)
(159,235)(160,234)(161,233)(162,209)(163,208)(164,230)(165,229)(166,228)
(167,227)(168,226)(169,225)(170,224)(171,223)(172,222)(173,221)(174,220)
(175,219)(176,218)(177,217)(178,216)(179,215)(180,214)(181,213)(182,212)
(183,211)(184,210)(185,255)(186,254)(187,276)(188,275)(189,274)(190,273)
(191,272)(192,271)(193,270)(194,269)(195,268)(196,267)(197,266)(198,265)
(199,264)(200,263)(201,262)(202,261)(203,260)(204,259)(205,258)(206,257)
(207,256);;
s2 := (  1,139)(  2,140)(  3,141)(  4,142)(  5,143)(  6,144)(  7,145)(  8,146)
(  9,147)( 10,148)( 11,149)( 12,150)( 13,151)( 14,152)( 15,153)( 16,154)
( 17,155)( 18,156)( 19,157)( 20,158)( 21,159)( 22,160)( 23,161)( 24,162)
( 25,163)( 26,164)( 27,165)( 28,166)( 29,167)( 30,168)( 31,169)( 32,170)
( 33,171)( 34,172)( 35,173)( 36,174)( 37,175)( 38,176)( 39,177)( 40,178)
( 41,179)( 42,180)( 43,181)( 44,182)( 45,183)( 46,184)( 47,185)( 48,186)
( 49,187)( 50,188)( 51,189)( 52,190)( 53,191)( 54,192)( 55,193)( 56,194)
( 57,195)( 58,196)( 59,197)( 60,198)( 61,199)( 62,200)( 63,201)( 64,202)
( 65,203)( 66,204)( 67,205)( 68,206)( 69,207)( 70,208)( 71,209)( 72,210)
( 73,211)( 74,212)( 75,213)( 76,214)( 77,215)( 78,216)( 79,217)( 80,218)
( 81,219)( 82,220)( 83,221)( 84,222)( 85,223)( 86,224)( 87,225)( 88,226)
( 89,227)( 90,228)( 91,229)( 92,230)( 93,231)( 94,232)( 95,233)( 96,234)
( 97,235)( 98,236)( 99,237)(100,238)(101,239)(102,240)(103,241)(104,242)
(105,243)(106,244)(107,245)(108,246)(109,247)(110,248)(111,249)(112,250)
(113,251)(114,252)(115,253)(116,254)(117,255)(118,256)(119,257)(120,258)
(121,259)(122,260)(123,261)(124,262)(125,263)(126,264)(127,265)(128,266)
(129,267)(130,268)(131,269)(132,270)(133,271)(134,272)(135,273)(136,274)
(137,275)(138,276);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(276)!(  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)(140,161)(141,160)(142,159)
(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)
(162,185)(163,207)(164,206)(165,205)(166,204)(167,203)(168,202)(169,201)
(170,200)(171,199)(172,198)(173,197)(174,196)(175,195)(176,194)(177,193)
(178,192)(179,191)(180,190)(181,189)(182,188)(183,187)(184,186)(209,230)
(210,229)(211,228)(212,227)(213,226)(214,225)(215,224)(216,223)(217,222)
(218,221)(219,220)(231,254)(232,276)(233,275)(234,274)(235,273)(236,272)
(237,271)(238,270)(239,269)(240,268)(241,267)(242,266)(243,265)(244,264)
(245,263)(246,262)(247,261)(248,260)(249,259)(250,258)(251,257)(252,256)
(253,255);
s1 := 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)(139,232)(140,231)(141,253)
(142,252)(143,251)(144,250)(145,249)(146,248)(147,247)(148,246)(149,245)
(150,244)(151,243)(152,242)(153,241)(154,240)(155,239)(156,238)(157,237)
(158,236)(159,235)(160,234)(161,233)(162,209)(163,208)(164,230)(165,229)
(166,228)(167,227)(168,226)(169,225)(170,224)(171,223)(172,222)(173,221)
(174,220)(175,219)(176,218)(177,217)(178,216)(179,215)(180,214)(181,213)
(182,212)(183,211)(184,210)(185,255)(186,254)(187,276)(188,275)(189,274)
(190,273)(191,272)(192,271)(193,270)(194,269)(195,268)(196,267)(197,266)
(198,265)(199,264)(200,263)(201,262)(202,261)(203,260)(204,259)(205,258)
(206,257)(207,256);
s2 := Sym(276)!(  1,139)(  2,140)(  3,141)(  4,142)(  5,143)(  6,144)(  7,145)
(  8,146)(  9,147)( 10,148)( 11,149)( 12,150)( 13,151)( 14,152)( 15,153)
( 16,154)( 17,155)( 18,156)( 19,157)( 20,158)( 21,159)( 22,160)( 23,161)
( 24,162)( 25,163)( 26,164)( 27,165)( 28,166)( 29,167)( 30,168)( 31,169)
( 32,170)( 33,171)( 34,172)( 35,173)( 36,174)( 37,175)( 38,176)( 39,177)
( 40,178)( 41,179)( 42,180)( 43,181)( 44,182)( 45,183)( 46,184)( 47,185)
( 48,186)( 49,187)( 50,188)( 51,189)( 52,190)( 53,191)( 54,192)( 55,193)
( 56,194)( 57,195)( 58,196)( 59,197)( 60,198)( 61,199)( 62,200)( 63,201)
( 64,202)( 65,203)( 66,204)( 67,205)( 68,206)( 69,207)( 70,208)( 71,209)
( 72,210)( 73,211)( 74,212)( 75,213)( 76,214)( 77,215)( 78,216)( 79,217)
( 80,218)( 81,219)( 82,220)( 83,221)( 84,222)( 85,223)( 86,224)( 87,225)
( 88,226)( 89,227)( 90,228)( 91,229)( 92,230)( 93,231)( 94,232)( 95,233)
( 96,234)( 97,235)( 98,236)( 99,237)(100,238)(101,239)(102,240)(103,241)
(104,242)(105,243)(106,244)(107,245)(108,246)(109,247)(110,248)(111,249)
(112,250)(113,251)(114,252)(115,253)(116,254)(117,255)(118,256)(119,257)
(120,258)(121,259)(122,260)(123,261)(124,262)(125,263)(126,264)(127,265)
(128,266)(129,267)(130,268)(131,269)(132,270)(133,271)(134,272)(135,273)
(136,274)(137,275)(138,276);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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 >; 
 
References : None.
to this polytope