Polytope of Type {92,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {92,6}*1104a
Also Known As : {92,6|2}. if this polytope has another name.
Group : SmallGroup(1104,108)
Rank : 3
Schlafli Type : {92,6}
Number of vertices, edges, etc : 92, 276, 6
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 : {46,6}*552
   3-fold quotients : {92,2}*368
   6-fold quotients : {46,2}*184
   12-fold quotients : {23,2}*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 := (  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)
( 10, 15)( 11, 14)( 12, 13)( 25, 46)( 26, 45)( 27, 44)( 28, 43)( 29, 42)
( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)( 49, 68)
( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 57, 60)
( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)
( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 94,115)( 95,114)( 96,113)( 97,112)
( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)(117,138)
(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)(125,130)
(126,129)(127,128)(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)(162,231)(163,253)(164,252)(165,251)(166,250)(167,249)(168,248)
(169,247)(170,246)(171,245)(172,244)(173,243)(174,242)(175,241)(176,240)
(177,239)(178,238)(179,237)(180,236)(181,235)(182,234)(183,233)(184,232)
(185,254)(186,276)(187,275)(188,274)(189,273)(190,272)(191,271)(192,270)
(193,269)(194,268)(195,267)(196,266)(197,265)(198,264)(199,263)(200,262)
(201,261)(202,260)(203,259)(204,258)(205,257)(206,256)(207,255);;
s1 := (  1,140)(  2,139)(  3,161)(  4,160)(  5,159)(  6,158)(  7,157)(  8,156)
(  9,155)( 10,154)( 11,153)( 12,152)( 13,151)( 14,150)( 15,149)( 16,148)
( 17,147)( 18,146)( 19,145)( 20,144)( 21,143)( 22,142)( 23,141)( 24,186)
( 25,185)( 26,207)( 27,206)( 28,205)( 29,204)( 30,203)( 31,202)( 32,201)
( 33,200)( 34,199)( 35,198)( 36,197)( 37,196)( 38,195)( 39,194)( 40,193)
( 41,192)( 42,191)( 43,190)( 44,189)( 45,188)( 46,187)( 47,163)( 48,162)
( 49,184)( 50,183)( 51,182)( 52,181)( 53,180)( 54,179)( 55,178)( 56,177)
( 57,176)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)( 64,169)
( 65,168)( 66,167)( 67,166)( 68,165)( 69,164)( 70,209)( 71,208)( 72,230)
( 73,229)( 74,228)( 75,227)( 76,226)( 77,225)( 78,224)( 79,223)( 80,222)
( 81,221)( 82,220)( 83,219)( 84,218)( 85,217)( 86,216)( 87,215)( 88,214)
( 89,213)( 90,212)( 91,211)( 92,210)( 93,255)( 94,254)( 95,276)( 96,275)
( 97,274)( 98,273)( 99,272)(100,271)(101,270)(102,269)(103,268)(104,267)
(105,266)(106,265)(107,264)(108,263)(109,262)(110,261)(111,260)(112,259)
(113,258)(114,257)(115,256)(116,232)(117,231)(118,253)(119,252)(120,251)
(121,250)(122,249)(123,248)(124,247)(125,246)(126,245)(127,244)(128,243)
(129,242)(130,241)(131,240)(132,239)(133,238)(134,237)(135,236)(136,235)
(137,234)(138,233);;
s2 := (  1, 24)(  2, 25)(  3, 26)(  4, 27)(  5, 28)(  6, 29)(  7, 30)(  8, 31)
(  9, 32)( 10, 33)( 11, 34)( 12, 35)( 13, 36)( 14, 37)( 15, 38)( 16, 39)
( 17, 40)( 18, 41)( 19, 42)( 20, 43)( 21, 44)( 22, 45)( 23, 46)( 70, 93)
( 71, 94)( 72, 95)( 73, 96)( 74, 97)( 75, 98)( 76, 99)( 77,100)( 78,101)
( 79,102)( 80,103)( 81,104)( 82,105)( 83,106)( 84,107)( 85,108)( 86,109)
( 87,110)( 88,111)( 89,112)( 90,113)( 91,114)( 92,115)(139,162)(140,163)
(141,164)(142,165)(143,166)(144,167)(145,168)(146,169)(147,170)(148,171)
(149,172)(150,173)(151,174)(152,175)(153,176)(154,177)(155,178)(156,179)
(157,180)(158,181)(159,182)(160,183)(161,184)(208,231)(209,232)(210,233)
(211,234)(212,235)(213,236)(214,237)(215,238)(216,239)(217,240)(218,241)
(219,242)(220,243)(221,244)(222,245)(223,246)(224,247)(225,248)(226,249)
(227,250)(228,251)(229,252)(230,253);;
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*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 ];;
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)( 25, 46)( 26, 45)( 27, 44)( 28, 43)
( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 48, 69)
( 49, 68)( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)
( 57, 60)( 58, 59)( 71, 92)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)
( 77, 86)( 78, 85)( 79, 84)( 80, 83)( 81, 82)( 94,115)( 95,114)( 96,113)
( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106)(104,105)
(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)
(125,130)(126,129)(127,128)(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)(162,231)(163,253)(164,252)(165,251)(166,250)(167,249)
(168,248)(169,247)(170,246)(171,245)(172,244)(173,243)(174,242)(175,241)
(176,240)(177,239)(178,238)(179,237)(180,236)(181,235)(182,234)(183,233)
(184,232)(185,254)(186,276)(187,275)(188,274)(189,273)(190,272)(191,271)
(192,270)(193,269)(194,268)(195,267)(196,266)(197,265)(198,264)(199,263)
(200,262)(201,261)(202,260)(203,259)(204,258)(205,257)(206,256)(207,255);
s1 := Sym(276)!(  1,140)(  2,139)(  3,161)(  4,160)(  5,159)(  6,158)(  7,157)
(  8,156)(  9,155)( 10,154)( 11,153)( 12,152)( 13,151)( 14,150)( 15,149)
( 16,148)( 17,147)( 18,146)( 19,145)( 20,144)( 21,143)( 22,142)( 23,141)
( 24,186)( 25,185)( 26,207)( 27,206)( 28,205)( 29,204)( 30,203)( 31,202)
( 32,201)( 33,200)( 34,199)( 35,198)( 36,197)( 37,196)( 38,195)( 39,194)
( 40,193)( 41,192)( 42,191)( 43,190)( 44,189)( 45,188)( 46,187)( 47,163)
( 48,162)( 49,184)( 50,183)( 51,182)( 52,181)( 53,180)( 54,179)( 55,178)
( 56,177)( 57,176)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)
( 64,169)( 65,168)( 66,167)( 67,166)( 68,165)( 69,164)( 70,209)( 71,208)
( 72,230)( 73,229)( 74,228)( 75,227)( 76,226)( 77,225)( 78,224)( 79,223)
( 80,222)( 81,221)( 82,220)( 83,219)( 84,218)( 85,217)( 86,216)( 87,215)
( 88,214)( 89,213)( 90,212)( 91,211)( 92,210)( 93,255)( 94,254)( 95,276)
( 96,275)( 97,274)( 98,273)( 99,272)(100,271)(101,270)(102,269)(103,268)
(104,267)(105,266)(106,265)(107,264)(108,263)(109,262)(110,261)(111,260)
(112,259)(113,258)(114,257)(115,256)(116,232)(117,231)(118,253)(119,252)
(120,251)(121,250)(122,249)(123,248)(124,247)(125,246)(126,245)(127,244)
(128,243)(129,242)(130,241)(131,240)(132,239)(133,238)(134,237)(135,236)
(136,235)(137,234)(138,233);
s2 := Sym(276)!(  1, 24)(  2, 25)(  3, 26)(  4, 27)(  5, 28)(  6, 29)(  7, 30)
(  8, 31)(  9, 32)( 10, 33)( 11, 34)( 12, 35)( 13, 36)( 14, 37)( 15, 38)
( 16, 39)( 17, 40)( 18, 41)( 19, 42)( 20, 43)( 21, 44)( 22, 45)( 23, 46)
( 70, 93)( 71, 94)( 72, 95)( 73, 96)( 74, 97)( 75, 98)( 76, 99)( 77,100)
( 78,101)( 79,102)( 80,103)( 81,104)( 82,105)( 83,106)( 84,107)( 85,108)
( 86,109)( 87,110)( 88,111)( 89,112)( 90,113)( 91,114)( 92,115)(139,162)
(140,163)(141,164)(142,165)(143,166)(144,167)(145,168)(146,169)(147,170)
(148,171)(149,172)(150,173)(151,174)(152,175)(153,176)(154,177)(155,178)
(156,179)(157,180)(158,181)(159,182)(160,183)(161,184)(208,231)(209,232)
(210,233)(211,234)(212,235)(213,236)(214,237)(215,238)(216,239)(217,240)
(218,241)(219,242)(220,243)(221,244)(222,245)(223,246)(224,247)(225,248)
(226,249)(227,250)(228,251)(229,252)(230,253);
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*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 >;

References : None.
to this polytope