Polytope of Type {4,141}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,141}*1128
if this polytope has a name.
Group : SmallGroup(1128,32)
Rank : 3
Schlafli Type : {4,141}
Number of vertices, edges, etc : 4, 282, 141
Order of s₀s₁s₂ : 141
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) :
   47-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)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188);;
s1 := (  3,  4)(  5,185)(  6,186)(  7,188)(  8,187)(  9,181)( 10,182)( 11,184)
( 12,183)( 13,177)( 14,178)( 15,180)( 16,179)( 17,173)( 18,174)( 19,176)
( 20,175)( 21,169)( 22,170)( 23,172)( 24,171)( 25,165)( 26,166)( 27,168)
( 28,167)( 29,161)( 30,162)( 31,164)( 32,163)( 33,157)( 34,158)( 35,160)
( 36,159)( 37,153)( 38,154)( 39,156)( 40,155)( 41,149)( 42,150)( 43,152)
( 44,151)( 45,145)( 46,146)( 47,148)( 48,147)( 49,141)( 50,142)( 51,144)
( 52,143)( 53,137)( 54,138)( 55,140)( 56,139)( 57,133)( 58,134)( 59,136)
( 60,135)( 61,129)( 62,130)( 63,132)( 64,131)( 65,125)( 66,126)( 67,128)
( 68,127)( 69,121)( 70,122)( 71,124)( 72,123)( 73,117)( 74,118)( 75,120)
( 76,119)( 77,113)( 78,114)( 79,116)( 80,115)( 81,109)( 82,110)( 83,112)
( 84,111)( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)
( 92,103)( 93, 97)( 94, 98)( 95,100)( 96, 99);;
s2 := (  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,185)( 10,188)( 11,187)( 12,186)
( 13,181)( 14,184)( 15,183)( 16,182)( 17,177)( 18,180)( 19,179)( 20,178)
( 21,173)( 22,176)( 23,175)( 24,174)( 25,169)( 26,172)( 27,171)( 28,170)
( 29,165)( 30,168)( 31,167)( 32,166)( 33,161)( 34,164)( 35,163)( 36,162)
( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)( 44,154)
( 45,149)( 46,152)( 47,151)( 48,150)( 49,145)( 50,148)( 51,147)( 52,146)
( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)
( 61,133)( 62,136)( 63,135)( 64,134)( 65,129)( 66,132)( 67,131)( 68,130)
( 69,125)( 70,128)( 71,127)( 72,126)( 73,121)( 74,124)( 75,123)( 76,122)
( 77,117)( 78,120)( 79,119)( 80,118)( 81,113)( 82,116)( 83,115)( 84,114)
( 85,109)( 86,112)( 87,111)( 88,110)( 89,105)( 90,108)( 91,107)( 92,106)
( 93,101)( 94,104)( 95,103)( 96,102)( 98,100);;
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*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(188)!(  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)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188);
s1 := Sym(188)!(  3,  4)(  5,185)(  6,186)(  7,188)(  8,187)(  9,181)( 10,182)
( 11,184)( 12,183)( 13,177)( 14,178)( 15,180)( 16,179)( 17,173)( 18,174)
( 19,176)( 20,175)( 21,169)( 22,170)( 23,172)( 24,171)( 25,165)( 26,166)
( 27,168)( 28,167)( 29,161)( 30,162)( 31,164)( 32,163)( 33,157)( 34,158)
( 35,160)( 36,159)( 37,153)( 38,154)( 39,156)( 40,155)( 41,149)( 42,150)
( 43,152)( 44,151)( 45,145)( 46,146)( 47,148)( 48,147)( 49,141)( 50,142)
( 51,144)( 52,143)( 53,137)( 54,138)( 55,140)( 56,139)( 57,133)( 58,134)
( 59,136)( 60,135)( 61,129)( 62,130)( 63,132)( 64,131)( 65,125)( 66,126)
( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)( 72,123)( 73,117)( 74,118)
( 75,120)( 76,119)( 77,113)( 78,114)( 79,116)( 80,115)( 81,109)( 82,110)
( 83,112)( 84,111)( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)
( 91,104)( 92,103)( 93, 97)( 94, 98)( 95,100)( 96, 99);
s2 := Sym(188)!(  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,185)( 10,188)( 11,187)
( 12,186)( 13,181)( 14,184)( 15,183)( 16,182)( 17,177)( 18,180)( 19,179)
( 20,178)( 21,173)( 22,176)( 23,175)( 24,174)( 25,169)( 26,172)( 27,171)
( 28,170)( 29,165)( 30,168)( 31,167)( 32,166)( 33,161)( 34,164)( 35,163)
( 36,162)( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)
( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)( 49,145)( 50,148)( 51,147)
( 52,146)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)
( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)( 65,129)( 66,132)( 67,131)
( 68,130)( 69,125)( 70,128)( 71,127)( 72,126)( 73,121)( 74,124)( 75,123)
( 76,122)( 77,117)( 78,120)( 79,119)( 80,118)( 81,113)( 82,116)( 83,115)
( 84,114)( 85,109)( 86,112)( 87,111)( 88,110)( 89,105)( 90,108)( 91,107)
( 92,106)( 93,101)( 94,104)( 95,103)( 96,102)( 98,100);
poly := sub<Sym(188)|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*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