Polytope of Type {111,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {111,6}*1776
if this polytope has a name.
Group : SmallGroup(1776,242)
Rank : 3
Schlafli Type : {111,6}
Number of vertices, edges, etc : 148, 444, 8
Order of s₀s₁s₂ : 148
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   12-fold quotients : {37,2}*148
   37-fold quotients : {3,6}*48
   74-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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