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Polytope of Type {148,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {148,6}*1776b
if this polytope has a name.
Group : SmallGroup(1776,242)
Rank : 3
Schlafli Type : {148,6}
Number of vertices, edges, etc : 148, 444, 6
Order of s0s1s2 : 111
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
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) :
   37-fold quotients : {4,6}*48b
   74-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,  3)(  2,  4)(  5,147)(  6,148)(  7,145)(  8,146)(  9,143)( 10,144)
( 11,141)( 12,142)( 13,139)( 14,140)( 15,137)( 16,138)( 17,135)( 18,136)
( 19,133)( 20,134)( 21,131)( 22,132)( 23,129)( 24,130)( 25,127)( 26,128)
( 27,125)( 28,126)( 29,123)( 30,124)( 31,121)( 32,122)( 33,119)( 34,120)
( 35,117)( 36,118)( 37,115)( 38,116)( 39,113)( 40,114)( 41,111)( 42,112)
( 43,109)( 44,110)( 45,107)( 46,108)( 47,105)( 48,106)( 49,103)( 50,104)
( 51,101)( 52,102)( 53, 99)( 54,100)( 55, 97)( 56, 98)( 57, 95)( 58, 96)
( 59, 93)( 60, 94)( 61, 91)( 62, 92)( 63, 89)( 64, 90)( 65, 87)( 66, 88)
( 67, 85)( 68, 86)( 69, 83)( 70, 84)( 71, 81)( 72, 82)( 73, 79)( 74, 80)
( 75, 77)( 76, 78);;
s1 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9,145)( 10,146)( 11,148)( 12,147)
( 13,141)( 14,142)( 15,144)( 16,143)( 17,137)( 18,138)( 19,140)( 20,139)
( 21,133)( 22,134)( 23,136)( 24,135)( 25,129)( 26,130)( 27,132)( 28,131)
( 29,125)( 30,126)( 31,128)( 32,127)( 33,121)( 34,122)( 35,124)( 36,123)
( 37,117)( 38,118)( 39,120)( 40,119)( 41,113)( 42,114)( 43,116)( 44,115)
( 45,109)( 46,110)( 47,112)( 48,111)( 49,105)( 50,106)( 51,108)( 52,107)
( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)( 59,100)( 60, 99)
( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)( 67, 92)( 68, 91)
( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 81)( 74, 82)( 75, 84)( 76, 83)
( 79, 80);;
s2 := (  2,  4)(  6,  8)( 10, 12)( 14, 16)( 18, 20)( 22, 24)( 26, 28)( 30, 32)
( 34, 36)( 38, 40)( 42, 44)( 46, 48)( 50, 52)( 54, 56)( 58, 60)( 62, 64)
( 66, 68)( 70, 72)( 74, 76)( 78, 80)( 82, 84)( 86, 88)( 90, 92)( 94, 96)
( 98,100)(102,104)(106,108)(110,112)(114,116)(118,120)(122,124)(126,128)
(130,132)(134,136)(138,140)(142,144)(146,148);;
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*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*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*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(148)!(  1,  3)(  2,  4)(  5,147)(  6,148)(  7,145)(  8,146)(  9,143)
( 10,144)( 11,141)( 12,142)( 13,139)( 14,140)( 15,137)( 16,138)( 17,135)
( 18,136)( 19,133)( 20,134)( 21,131)( 22,132)( 23,129)( 24,130)( 25,127)
( 26,128)( 27,125)( 28,126)( 29,123)( 30,124)( 31,121)( 32,122)( 33,119)
( 34,120)( 35,117)( 36,118)( 37,115)( 38,116)( 39,113)( 40,114)( 41,111)
( 42,112)( 43,109)( 44,110)( 45,107)( 46,108)( 47,105)( 48,106)( 49,103)
( 50,104)( 51,101)( 52,102)( 53, 99)( 54,100)( 55, 97)( 56, 98)( 57, 95)
( 58, 96)( 59, 93)( 60, 94)( 61, 91)( 62, 92)( 63, 89)( 64, 90)( 65, 87)
( 66, 88)( 67, 85)( 68, 86)( 69, 83)( 70, 84)( 71, 81)( 72, 82)( 73, 79)
( 74, 80)( 75, 77)( 76, 78);
s1 := Sym(148)!(  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9,145)( 10,146)( 11,148)
( 12,147)( 13,141)( 14,142)( 15,144)( 16,143)( 17,137)( 18,138)( 19,140)
( 20,139)( 21,133)( 22,134)( 23,136)( 24,135)( 25,129)( 26,130)( 27,132)
( 28,131)( 29,125)( 30,126)( 31,128)( 32,127)( 33,121)( 34,122)( 35,124)
( 36,123)( 37,117)( 38,118)( 39,120)( 40,119)( 41,113)( 42,114)( 43,116)
( 44,115)( 45,109)( 46,110)( 47,112)( 48,111)( 49,105)( 50,106)( 51,108)
( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)( 59,100)
( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)( 67, 92)
( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 81)( 74, 82)( 75, 84)
( 76, 83)( 79, 80);
s2 := Sym(148)!(  2,  4)(  6,  8)( 10, 12)( 14, 16)( 18, 20)( 22, 24)( 26, 28)
( 30, 32)( 34, 36)( 38, 40)( 42, 44)( 46, 48)( 50, 52)( 54, 56)( 58, 60)
( 62, 64)( 66, 68)( 70, 72)( 74, 76)( 78, 80)( 82, 84)( 86, 88)( 90, 92)
( 94, 96)( 98,100)(102,104)(106,108)(110,112)(114,116)(118,120)(122,124)
(126,128)(130,132)(134,136)(138,140)(142,144)(146,148);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*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*s2 >; 
 
References : None.
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