Polytope of Type {92,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {92,4}*736
Also Known As : {92,4|2}. if this polytope has another name.
Group : SmallGroup(736,77)
Rank : 3
Schlafli Type : {92,4}
Number of vertices, edges, etc : 92, 184, 4
Order of s0s1s2 : 92
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {92,4,2} of size 1472
Vertex Figure Of :
   {2,92,4} of size 1472
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {92,2}*368, {46,4}*368
   4-fold quotients : {46,2}*184
   8-fold quotients : {23,2}*92
   23-fold quotients : {4,4}*32
   46-fold quotients : {2,4}*16, {4,2}*16
   92-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {92,8}*1472a, {184,4}*1472a, {92,8}*1472b, {184,4}*1472b, {92,4}*1472
Irregular Quotients (of which this is a minimal cover):
   None.

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)( 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);;
s1 := (  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);;
s2 := ( 93,116)( 94,117)( 95,118)( 96,119)( 97,120)( 98,121)( 99,122)(100,123)(101,124)(102,125)(103,126)(104,127)(105,128)(106,129)(107,130)(108,131)(109,132)(110,133)(111,134)(112,135)(113,136)(114,137)(115,138)(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);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := 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);
s1 := 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);
s2 := Sym(184)!( 93,116)( 94,117)( 95,118)( 96,119)( 97,120)( 98,121)( 99,122)(100,123)(101,124)(102,125)(103,126)(104,127)(105,128)(106,129)(107,130)(108,131)(109,132)(110,133)(111,134)(112,135)(113,136)(114,137)(115,138)(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);
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*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 >;
References : None.
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