Polytope of Type {4,92}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,92}*1472
if this polytope has a name.
Group : SmallGroup(1472,737)
Rank : 3
Schlafli Type : {4,92}
Number of vertices, edges, etc : 8, 368, 184
Order of s₀s₁s₂ : 92
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,92}*736
   4-fold quotients : {2,92}*368, {4,46}*368
   8-fold quotients : {2,46}*184
   16-fold quotients : {2,23}*92
   23-fold quotients : {4,4}*64
   46-fold quotients : {4,4}*32
   92-fold quotients : {2,4}*16, {4,2}*16
   184-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 47, 70)( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)( 54, 77)
( 55, 78)( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)
( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)(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);;
s1 := (  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)( 93,139)( 94,161)( 95,160)( 96,159)
( 97,158)( 98,157)( 99,156)(100,155)(101,154)(102,153)(103,152)(104,151)
(105,150)(106,149)(107,148)(108,147)(109,146)(110,145)(111,144)(112,143)
(113,142)(114,141)(115,140)(116,162)(117,184)(118,183)(119,182)(120,181)
(121,180)(122,179)(123,178)(124,177)(125,176)(126,175)(127,174)(128,173)
(129,172)(130,171)(131,170)(132,169)(133,168)(134,167)(135,166)(136,165)
(137,164)(138,163);;
s2 := (  1, 94)(  2, 93)(  3,115)(  4,114)(  5,113)(  6,112)(  7,111)(  8,110)
(  9,109)( 10,108)( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)( 16,102)
( 17,101)( 18,100)( 19, 99)( 20, 98)( 21, 97)( 22, 96)( 23, 95)( 24,117)
( 25,116)( 26,138)( 27,137)( 28,136)( 29,135)( 30,134)( 31,133)( 32,132)
( 33,131)( 34,130)( 35,129)( 36,128)( 37,127)( 38,126)( 39,125)( 40,124)
( 41,123)( 42,122)( 43,121)( 44,120)( 45,119)( 46,118)( 47,140)( 48,139)
( 49,161)( 50,160)( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)( 56,154)
( 57,153)( 58,152)( 59,151)( 60,150)( 61,149)( 62,148)( 63,147)( 64,146)
( 65,145)( 66,144)( 67,143)( 68,142)( 69,141)( 70,163)( 71,162)( 72,184)
( 73,183)( 74,182)( 75,181)( 76,180)( 77,179)( 78,178)( 79,177)( 80,176)
( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)( 88,168)
( 89,167)( 90,166)( 91,165)( 92,164);;
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, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(184)!( 47, 70)( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)
( 54, 77)( 55, 78)( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)
( 62, 85)( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)
(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);
s1 := Sym(184)!(  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)( 93,139)( 94,161)( 95,160)
( 96,159)( 97,158)( 98,157)( 99,156)(100,155)(101,154)(102,153)(103,152)
(104,151)(105,150)(106,149)(107,148)(108,147)(109,146)(110,145)(111,144)
(112,143)(113,142)(114,141)(115,140)(116,162)(117,184)(118,183)(119,182)
(120,181)(121,180)(122,179)(123,178)(124,177)(125,176)(126,175)(127,174)
(128,173)(129,172)(130,171)(131,170)(132,169)(133,168)(134,167)(135,166)
(136,165)(137,164)(138,163);
s2 := Sym(184)!(  1, 94)(  2, 93)(  3,115)(  4,114)(  5,113)(  6,112)(  7,111)
(  8,110)(  9,109)( 10,108)( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)
( 16,102)( 17,101)( 18,100)( 19, 99)( 20, 98)( 21, 97)( 22, 96)( 23, 95)
( 24,117)( 25,116)( 26,138)( 27,137)( 28,136)( 29,135)( 30,134)( 31,133)
( 32,132)( 33,131)( 34,130)( 35,129)( 36,128)( 37,127)( 38,126)( 39,125)
( 40,124)( 41,123)( 42,122)( 43,121)( 44,120)( 45,119)( 46,118)( 47,140)
( 48,139)( 49,161)( 50,160)( 51,159)( 52,158)( 53,157)( 54,156)( 55,155)
( 56,154)( 57,153)( 58,152)( 59,151)( 60,150)( 61,149)( 62,148)( 63,147)
( 64,146)( 65,145)( 66,144)( 67,143)( 68,142)( 69,141)( 70,163)( 71,162)
( 72,184)( 73,183)( 74,182)( 75,181)( 76,180)( 77,179)( 78,178)( 79,177)
( 80,176)( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)
( 88,168)( 89,167)( 90,166)( 91,165)( 92,164);
poly := sub<Sym(184)|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, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*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 >;

References : None.
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