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Polytope of Type {46,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {46,8}*736
Also Known As : {46,8|2}. if this polytope has another name.
Group : SmallGroup(736,105)
Rank : 3
Schlafli Type : {46,8}
Number of vertices, edges, etc : 46, 184, 8
Order of s0s1s2 : 184
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {46,8,2} of size 1472
Vertex Figure Of :
   {2,46,8} of size 1472
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {46,4}*368
   4-fold quotients : {46,2}*184
   8-fold quotients : {23,2}*92
   23-fold quotients : {2,8}*32
   46-fold quotients : {2,4}*16
   92-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {92,8}*1472a, {46,16}*1472
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)(140,161)(141,160)(142,159)(143,158)(144,157)(145,156)
(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)(165,182)
(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)(173,174);;
s1 := (  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)
( 10, 16)( 11, 15)( 12, 14)( 24, 25)( 26, 46)( 27, 45)( 28, 44)( 29, 43)
( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 71)( 48, 70)
( 49, 92)( 50, 91)( 51, 90)( 52, 89)( 53, 88)( 54, 87)( 55, 86)( 56, 85)
( 57, 84)( 58, 83)( 59, 82)( 60, 81)( 61, 80)( 62, 79)( 63, 78)( 64, 77)
( 65, 76)( 66, 75)( 67, 74)( 68, 73)( 69, 72)( 93,140)( 94,139)( 95,161)
( 96,160)( 97,159)( 98,158)( 99,157)(100,156)(101,155)(102,154)(103,153)
(104,152)(105,151)(106,150)(107,149)(108,148)(109,147)(110,146)(111,145)
(112,144)(113,143)(114,142)(115,141)(116,163)(117,162)(118,184)(119,183)
(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)(127,175)
(128,174)(129,173)(130,172)(131,171)(132,170)(133,169)(134,168)(135,167)
(136,166)(137,165)(138,164);;
s2 := (  1, 93)(  2, 94)(  3, 95)(  4, 96)(  5, 97)(  6, 98)(  7, 99)(  8,100)
(  9,101)( 10,102)( 11,103)( 12,104)( 13,105)( 14,106)( 15,107)( 16,108)
( 17,109)( 18,110)( 19,111)( 20,112)( 21,113)( 22,114)( 23,115)( 24,116)
( 25,117)( 26,118)( 27,119)( 28,120)( 29,121)( 30,122)( 31,123)( 32,124)
( 33,125)( 34,126)( 35,127)( 36,128)( 37,129)( 38,130)( 39,131)( 40,132)
( 41,133)( 42,134)( 43,135)( 44,136)( 45,137)( 46,138)( 47,162)( 48,163)
( 49,164)( 50,165)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)( 56,171)
( 57,172)( 58,173)( 59,174)( 60,175)( 61,176)( 62,177)( 63,178)( 64,179)
( 65,180)( 66,181)( 67,182)( 68,183)( 69,184)( 70,139)( 71,140)( 72,141)
( 73,142)( 74,143)( 75,144)( 76,145)( 77,146)( 78,147)( 79,148)( 80,149)
( 81,150)( 82,151)( 83,152)( 84,153)( 85,154)( 86,155)( 87,156)( 88,157)
( 89,158)( 90,159)( 91,160)( 92,161);;
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*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 ];;
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)( 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)(140,161)(141,160)(142,159)(143,158)(144,157)
(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)(163,184)(164,183)
(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)(172,175)
(173,174);
s1 := Sym(184)!(  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)
(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 24, 25)( 26, 46)( 27, 45)( 28, 44)
( 29, 43)( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 71)
( 48, 70)( 49, 92)( 50, 91)( 51, 90)( 52, 89)( 53, 88)( 54, 87)( 55, 86)
( 56, 85)( 57, 84)( 58, 83)( 59, 82)( 60, 81)( 61, 80)( 62, 79)( 63, 78)
( 64, 77)( 65, 76)( 66, 75)( 67, 74)( 68, 73)( 69, 72)( 93,140)( 94,139)
( 95,161)( 96,160)( 97,159)( 98,158)( 99,157)(100,156)(101,155)(102,154)
(103,153)(104,152)(105,151)(106,150)(107,149)(108,148)(109,147)(110,146)
(111,145)(112,144)(113,143)(114,142)(115,141)(116,163)(117,162)(118,184)
(119,183)(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)
(127,175)(128,174)(129,173)(130,172)(131,171)(132,170)(133,169)(134,168)
(135,167)(136,166)(137,165)(138,164);
s2 := Sym(184)!(  1, 93)(  2, 94)(  3, 95)(  4, 96)(  5, 97)(  6, 98)(  7, 99)
(  8,100)(  9,101)( 10,102)( 11,103)( 12,104)( 13,105)( 14,106)( 15,107)
( 16,108)( 17,109)( 18,110)( 19,111)( 20,112)( 21,113)( 22,114)( 23,115)
( 24,116)( 25,117)( 26,118)( 27,119)( 28,120)( 29,121)( 30,122)( 31,123)
( 32,124)( 33,125)( 34,126)( 35,127)( 36,128)( 37,129)( 38,130)( 39,131)
( 40,132)( 41,133)( 42,134)( 43,135)( 44,136)( 45,137)( 46,138)( 47,162)
( 48,163)( 49,164)( 50,165)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)
( 56,171)( 57,172)( 58,173)( 59,174)( 60,175)( 61,176)( 62,177)( 63,178)
( 64,179)( 65,180)( 66,181)( 67,182)( 68,183)( 69,184)( 70,139)( 71,140)
( 72,141)( 73,142)( 74,143)( 75,144)( 76,145)( 77,146)( 78,147)( 79,148)
( 80,149)( 81,150)( 82,151)( 83,152)( 84,153)( 85,154)( 86,155)( 87,156)
( 88,157)( 89,158)( 90,159)( 91,160)( 92,161);
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*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 >; 
 
References : None.
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