Polytope of Type {2,57,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,57,6}*1368
if this polytope has a name.
Group : SmallGroup(1368,201)
Rank : 4
Schlafli Type : {2,57,6}
Number of vertices, edges, etc : 2, 57, 171, 6
Order of s₀s₁s₂s₃ : 114
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) :
   3-fold quotients : {2,57,2}*456
   9-fold quotients : {2,19,2}*152
   19-fold quotients : {2,3,6}*72
   57-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)( 11, 14)
( 12, 13)( 22, 41)( 23, 59)( 24, 58)( 25, 57)( 26, 56)( 27, 55)( 28, 54)
( 29, 53)( 30, 52)( 31, 51)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 46)
( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 60,117)( 61,135)( 62,134)( 63,133)
( 64,132)( 65,131)( 66,130)( 67,129)( 68,128)( 69,127)( 70,126)( 71,125)
( 72,124)( 73,123)( 74,122)( 75,121)( 76,120)( 77,119)( 78,118)( 79,155)
( 80,173)( 81,172)( 82,171)( 83,170)( 84,169)( 85,168)( 86,167)( 87,166)
( 88,165)( 89,164)( 90,163)( 91,162)( 92,161)( 93,160)( 94,159)( 95,158)
( 96,157)( 97,156)( 98,136)( 99,154)(100,153)(101,152)(102,151)(103,150)
(104,149)(105,148)(106,147)(107,146)(108,145)(109,144)(110,143)(111,142)
(112,141)(113,140)(114,139)(115,138)(116,137);;
s2 := (  3, 80)(  4, 79)(  5, 97)(  6, 96)(  7, 95)(  8, 94)(  9, 93)( 10, 92)
( 11, 91)( 12, 90)( 13, 89)( 14, 88)( 15, 87)( 16, 86)( 17, 85)( 18, 84)
( 19, 83)( 20, 82)( 21, 81)( 22, 61)( 23, 60)( 24, 78)( 25, 77)( 26, 76)
( 27, 75)( 28, 74)( 29, 73)( 30, 72)( 31, 71)( 32, 70)( 33, 69)( 34, 68)
( 35, 67)( 36, 66)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 99)( 42, 98)
( 43,116)( 44,115)( 45,114)( 46,113)( 47,112)( 48,111)( 49,110)( 50,109)
( 51,108)( 52,107)( 53,106)( 54,105)( 55,104)( 56,103)( 57,102)( 58,101)
( 59,100)(117,137)(118,136)(119,154)(120,153)(121,152)(122,151)(123,150)
(124,149)(125,148)(126,147)(127,146)(128,145)(129,144)(130,143)(131,142)
(132,141)(133,140)(134,139)(135,138)(155,156)(157,173)(158,172)(159,171)
(160,170)(161,169)(162,168)(163,167)(164,166);;
s3 := ( 60,117)( 61,118)( 62,119)( 63,120)( 64,121)( 65,122)( 66,123)( 67,124)
( 68,125)( 69,126)( 70,127)( 71,128)( 72,129)( 73,130)( 74,131)( 75,132)
( 76,133)( 77,134)( 78,135)( 79,136)( 80,137)( 81,138)( 82,139)( 83,140)
( 84,141)( 85,142)( 86,143)( 87,144)( 88,145)( 89,146)( 90,147)( 91,148)
( 92,149)( 93,150)( 94,151)( 95,152)( 96,153)( 97,154)( 98,155)( 99,156)
(100,157)(101,158)(102,159)(103,160)(104,161)(105,162)(106,163)(107,164)
(108,165)(109,166)(110,167)(111,168)(112,169)(113,170)(114,171)(115,172)
(116,173);;
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, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(173)!(1,2);
s1 := Sym(173)!(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)
( 11, 14)( 12, 13)( 22, 41)( 23, 59)( 24, 58)( 25, 57)( 26, 56)( 27, 55)
( 28, 54)( 29, 53)( 30, 52)( 31, 51)( 32, 50)( 33, 49)( 34, 48)( 35, 47)
( 36, 46)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 60,117)( 61,135)( 62,134)
( 63,133)( 64,132)( 65,131)( 66,130)( 67,129)( 68,128)( 69,127)( 70,126)
( 71,125)( 72,124)( 73,123)( 74,122)( 75,121)( 76,120)( 77,119)( 78,118)
( 79,155)( 80,173)( 81,172)( 82,171)( 83,170)( 84,169)( 85,168)( 86,167)
( 87,166)( 88,165)( 89,164)( 90,163)( 91,162)( 92,161)( 93,160)( 94,159)
( 95,158)( 96,157)( 97,156)( 98,136)( 99,154)(100,153)(101,152)(102,151)
(103,150)(104,149)(105,148)(106,147)(107,146)(108,145)(109,144)(110,143)
(111,142)(112,141)(113,140)(114,139)(115,138)(116,137);
s2 := Sym(173)!(  3, 80)(  4, 79)(  5, 97)(  6, 96)(  7, 95)(  8, 94)(  9, 93)
( 10, 92)( 11, 91)( 12, 90)( 13, 89)( 14, 88)( 15, 87)( 16, 86)( 17, 85)
( 18, 84)( 19, 83)( 20, 82)( 21, 81)( 22, 61)( 23, 60)( 24, 78)( 25, 77)
( 26, 76)( 27, 75)( 28, 74)( 29, 73)( 30, 72)( 31, 71)( 32, 70)( 33, 69)
( 34, 68)( 35, 67)( 36, 66)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 99)
( 42, 98)( 43,116)( 44,115)( 45,114)( 46,113)( 47,112)( 48,111)( 49,110)
( 50,109)( 51,108)( 52,107)( 53,106)( 54,105)( 55,104)( 56,103)( 57,102)
( 58,101)( 59,100)(117,137)(118,136)(119,154)(120,153)(121,152)(122,151)
(123,150)(124,149)(125,148)(126,147)(127,146)(128,145)(129,144)(130,143)
(131,142)(132,141)(133,140)(134,139)(135,138)(155,156)(157,173)(158,172)
(159,171)(160,170)(161,169)(162,168)(163,167)(164,166);
s3 := Sym(173)!( 60,117)( 61,118)( 62,119)( 63,120)( 64,121)( 65,122)( 66,123)
( 67,124)( 68,125)( 69,126)( 70,127)( 71,128)( 72,129)( 73,130)( 74,131)
( 75,132)( 76,133)( 77,134)( 78,135)( 79,136)( 80,137)( 81,138)( 82,139)
( 83,140)( 84,141)( 85,142)( 86,143)( 87,144)( 88,145)( 89,146)( 90,147)
( 91,148)( 92,149)( 93,150)( 94,151)( 95,152)( 96,153)( 97,154)( 98,155)
( 99,156)(100,157)(101,158)(102,159)(103,160)(104,161)(105,162)(106,163)
(107,164)(108,165)(109,166)(110,167)(111,168)(112,169)(113,170)(114,171)
(115,172)(116,173);
poly := sub<Sym(173)|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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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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