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Polytope of Type {6,148}

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