Polytope of Type {141,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {141,4}*1128
if this polytope has a name.
Group : SmallGroup(1128,32)
Rank : 3
Schlafli Type : {141,4}
Number of vertices, edges, etc : 141, 282, 4
Order of s₀s₁s₂ : 141
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   47-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  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);;
s1 := (  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);;
s2 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := 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);
s1 := 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);
s2 := Sym(188)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope