Polytope of Type {4,129}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,129}*1032
if this polytope has a name.
Group : SmallGroup(1032,43)
Rank : 3
Schlafli Type : {4,129}
Number of vertices, edges, etc : 4, 258, 129
Order of s₀s₁s₂ : 129
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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) :
   43-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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