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Polytope of Type {8,46}

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