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Polytope of Type {2,46,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,46,8}*1472
if this polytope has a name.
Group : SmallGroup(1472,1317)
Rank : 4
Schlafli Type : {2,46,8}
Number of vertices, edges, etc : 2, 46, 184, 8
Order of s0s1s2s3 : 184
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 : {2,46,4}*736
   4-fold quotients : {2,46,2}*368
   8-fold quotients : {2,23,2}*184
   23-fold quotients : {2,2,8}*64
   46-fold quotients : {2,2,4}*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)( 96,117)( 97,116)( 98,115)( 99,114)
(100,113)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107)(119,140)
(120,139)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,132)
(128,131)(129,130)(142,163)(143,162)(144,161)(145,160)(146,159)(147,158)
(148,157)(149,156)(150,155)(151,154)(152,153)(165,186)(166,185)(167,184)
(168,183)(169,182)(170,181)(171,180)(172,179)(173,178)(174,177)(175,176);;
s2 := (  3,  4)(  5, 25)(  6, 24)(  7, 23)(  8, 22)(  9, 21)( 10, 20)( 11, 19)
( 12, 18)( 13, 17)( 14, 16)( 26, 27)( 28, 48)( 29, 47)( 30, 46)( 31, 45)
( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 49, 73)( 50, 72)
( 51, 94)( 52, 93)( 53, 92)( 54, 91)( 55, 90)( 56, 89)( 57, 88)( 58, 87)
( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 65, 80)( 66, 79)
( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 95,142)( 96,141)( 97,163)
( 98,162)( 99,161)(100,160)(101,159)(102,158)(103,157)(104,156)(105,155)
(106,154)(107,153)(108,152)(109,151)(110,150)(111,149)(112,148)(113,147)
(114,146)(115,145)(116,144)(117,143)(118,165)(119,164)(120,186)(121,185)
(122,184)(123,183)(124,182)(125,181)(126,180)(127,179)(128,178)(129,177)
(130,176)(131,175)(132,174)(133,173)(134,172)(135,171)(136,170)(137,169)
(138,168)(139,167)(140,166);;
s3 := (  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)( 47,139)( 48,140)( 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)( 70,185)( 71,186)( 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)( 93,162)( 94,163);;
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*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 ];;
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)( 96,117)( 97,116)( 98,115)
( 99,114)(100,113)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107)
(119,140)(120,139)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)
(127,132)(128,131)(129,130)(142,163)(143,162)(144,161)(145,160)(146,159)
(147,158)(148,157)(149,156)(150,155)(151,154)(152,153)(165,186)(166,185)
(167,184)(168,183)(169,182)(170,181)(171,180)(172,179)(173,178)(174,177)
(175,176);
s2 := Sym(186)!(  3,  4)(  5, 25)(  6, 24)(  7, 23)(  8, 22)(  9, 21)( 10, 20)
( 11, 19)( 12, 18)( 13, 17)( 14, 16)( 26, 27)( 28, 48)( 29, 47)( 30, 46)
( 31, 45)( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 49, 73)
( 50, 72)( 51, 94)( 52, 93)( 53, 92)( 54, 91)( 55, 90)( 56, 89)( 57, 88)
( 58, 87)( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 65, 80)
( 66, 79)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 95,142)( 96,141)
( 97,163)( 98,162)( 99,161)(100,160)(101,159)(102,158)(103,157)(104,156)
(105,155)(106,154)(107,153)(108,152)(109,151)(110,150)(111,149)(112,148)
(113,147)(114,146)(115,145)(116,144)(117,143)(118,165)(119,164)(120,186)
(121,185)(122,184)(123,183)(124,182)(125,181)(126,180)(127,179)(128,178)
(129,177)(130,176)(131,175)(132,174)(133,173)(134,172)(135,171)(136,170)
(137,169)(138,168)(139,167)(140,166);
s3 := Sym(186)!(  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)( 47,139)( 48,140)( 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)( 70,185)( 71,186)( 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)( 93,162)( 94,163);
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*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 >; 
 

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