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Polytope of Type {2,92,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,92,4}*1472
if this polytope has a name.
Group : SmallGroup(1472,1036)
Rank : 4
Schlafli Type : {2,92,4}
Number of vertices, edges, etc : 2, 92, 184, 4
Order of s0s1s2s3 : 92
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,92,2}*736, {2,46,4}*736
   4-fold quotients : {2,46,2}*368
   8-fold quotients : {2,23,2}*184
   23-fold quotients : {2,4,4}*64
   46-fold quotients : {2,2,4}*32, {2,4,2}*32
   92-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)( 11, 18)
( 12, 17)( 13, 16)( 14, 15)( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)
( 32, 43)( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 50, 71)( 51, 70)
( 52, 69)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 73, 94)( 74, 93)( 75, 92)( 76, 91)( 77, 90)( 78, 89)( 79, 88)
( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 95,141)( 96,163)( 97,162)( 98,161)
( 99,160)(100,159)(101,158)(102,157)(103,156)(104,155)(105,154)(106,153)
(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,146)(114,145)
(115,144)(116,143)(117,142)(118,164)(119,186)(120,185)(121,184)(122,183)
(123,182)(124,181)(125,180)(126,179)(127,178)(128,177)(129,176)(130,175)
(131,174)(132,173)(133,172)(134,171)(135,170)(136,169)(137,168)(138,167)
(139,166)(140,165);;
s2 := (  3, 96)(  4, 95)(  5,117)(  6,116)(  7,115)(  8,114)(  9,113)( 10,112)
( 11,111)( 12,110)( 13,109)( 14,108)( 15,107)( 16,106)( 17,105)( 18,104)
( 19,103)( 20,102)( 21,101)( 22,100)( 23, 99)( 24, 98)( 25, 97)( 26,119)
( 27,118)( 28,140)( 29,139)( 30,138)( 31,137)( 32,136)( 33,135)( 34,134)
( 35,133)( 36,132)( 37,131)( 38,130)( 39,129)( 40,128)( 41,127)( 42,126)
( 43,125)( 44,124)( 45,123)( 46,122)( 47,121)( 48,120)( 49,142)( 50,141)
( 51,163)( 52,162)( 53,161)( 54,160)( 55,159)( 56,158)( 57,157)( 58,156)
( 59,155)( 60,154)( 61,153)( 62,152)( 63,151)( 64,150)( 65,149)( 66,148)
( 67,147)( 68,146)( 69,145)( 70,144)( 71,143)( 72,165)( 73,164)( 74,186)
( 75,185)( 76,184)( 77,183)( 78,182)( 79,181)( 80,180)( 81,179)( 82,178)
( 83,177)( 84,176)( 85,175)( 86,174)( 87,173)( 88,172)( 89,171)( 90,170)
( 91,169)( 92,168)( 93,167)( 94,166);;
s3 := ( 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)(116,139)(117,140)(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)(162,185)(163,186);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(186)!(1,2);
s1 := Sym(186)!(  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)
( 11, 18)( 12, 17)( 13, 16)( 14, 15)( 27, 48)( 28, 47)( 29, 46)( 30, 45)
( 31, 44)( 32, 43)( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 50, 71)
( 51, 70)( 52, 69)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)
( 59, 62)( 60, 61)( 73, 94)( 74, 93)( 75, 92)( 76, 91)( 77, 90)( 78, 89)
( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 95,141)( 96,163)( 97,162)
( 98,161)( 99,160)(100,159)(101,158)(102,157)(103,156)(104,155)(105,154)
(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,146)
(114,145)(115,144)(116,143)(117,142)(118,164)(119,186)(120,185)(121,184)
(122,183)(123,182)(124,181)(125,180)(126,179)(127,178)(128,177)(129,176)
(130,175)(131,174)(132,173)(133,172)(134,171)(135,170)(136,169)(137,168)
(138,167)(139,166)(140,165);
s2 := Sym(186)!(  3, 96)(  4, 95)(  5,117)(  6,116)(  7,115)(  8,114)(  9,113)
( 10,112)( 11,111)( 12,110)( 13,109)( 14,108)( 15,107)( 16,106)( 17,105)
( 18,104)( 19,103)( 20,102)( 21,101)( 22,100)( 23, 99)( 24, 98)( 25, 97)
( 26,119)( 27,118)( 28,140)( 29,139)( 30,138)( 31,137)( 32,136)( 33,135)
( 34,134)( 35,133)( 36,132)( 37,131)( 38,130)( 39,129)( 40,128)( 41,127)
( 42,126)( 43,125)( 44,124)( 45,123)( 46,122)( 47,121)( 48,120)( 49,142)
( 50,141)( 51,163)( 52,162)( 53,161)( 54,160)( 55,159)( 56,158)( 57,157)
( 58,156)( 59,155)( 60,154)( 61,153)( 62,152)( 63,151)( 64,150)( 65,149)
( 66,148)( 67,147)( 68,146)( 69,145)( 70,144)( 71,143)( 72,165)( 73,164)
( 74,186)( 75,185)( 76,184)( 77,183)( 78,182)( 79,181)( 80,180)( 81,179)
( 82,178)( 83,177)( 84,176)( 85,175)( 86,174)( 87,173)( 88,172)( 89,171)
( 90,170)( 91,169)( 92,168)( 93,167)( 94,166);
s3 := Sym(186)!( 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)(116,139)(117,140)
(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)(162,185)(163,186);
poly := sub<Sym(186)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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