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Polytope of Type {2,42,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,42,6}*1008c
if this polytope has a name.
Group : SmallGroup(1008,942)
Rank : 4
Schlafli Type : {2,42,6}
Number of vertices, edges, etc : 2, 42, 126, 6
Order of s0s1s2s3 : 42
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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) :
   2-fold quotients : {2,21,6}*504
   3-fold quotients : {2,42,2}*336
   6-fold quotients : {2,21,2}*168
   7-fold quotients : {2,6,6}*144c
   9-fold quotients : {2,14,2}*112
   14-fold quotients : {2,3,6}*72
   18-fold quotients : {2,7,2}*56
   21-fold quotients : {2,6,2}*48
   42-fold quotients : {2,3,2}*24
   63-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 10, 17)( 11, 23)( 12, 22)( 13, 21)( 14, 20)
( 15, 19)( 16, 18)( 24, 45)( 25, 51)( 26, 50)( 27, 49)( 28, 48)( 29, 47)
( 30, 46)( 31, 59)( 32, 65)( 33, 64)( 34, 63)( 35, 62)( 36, 61)( 37, 60)
( 38, 52)( 39, 58)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 67, 72)
( 68, 71)( 69, 70)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)
( 79, 81)( 87,108)( 88,114)( 89,113)( 90,112)( 91,111)( 92,110)( 93,109)
( 94,122)( 95,128)( 96,127)( 97,126)( 98,125)( 99,124)(100,123)(101,115)
(102,121)(103,120)(104,119)(105,118)(106,117)(107,116);;
s2 := (  3, 95)(  4, 94)(  5,100)(  6, 99)(  7, 98)(  8, 97)(  9, 96)( 10, 88)
( 11, 87)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)( 17,102)( 18,101)
( 19,107)( 20,106)( 21,105)( 22,104)( 23,103)( 24, 74)( 25, 73)( 26, 79)
( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 67)( 32, 66)( 33, 72)( 34, 71)
( 35, 70)( 36, 69)( 37, 68)( 38, 81)( 39, 80)( 40, 86)( 41, 85)( 42, 84)
( 43, 83)( 44, 82)( 45,116)( 46,115)( 47,121)( 48,120)( 49,119)( 50,118)
( 51,117)( 52,109)( 53,108)( 54,114)( 55,113)( 56,112)( 57,111)( 58,110)
( 59,123)( 60,122)( 61,128)( 62,127)( 63,126)( 64,125)( 65,124);;
s3 := ( 24, 45)( 25, 46)( 26, 47)( 27, 48)( 28, 49)( 29, 50)( 30, 51)( 31, 52)
( 32, 53)( 33, 54)( 34, 55)( 35, 56)( 36, 57)( 37, 58)( 38, 59)( 39, 60)
( 40, 61)( 41, 62)( 42, 63)( 43, 64)( 44, 65)( 87,108)( 88,109)( 89,110)
( 90,111)( 91,112)( 92,113)( 93,114)( 94,115)( 95,116)( 96,117)( 97,118)
( 98,119)( 99,120)(100,121)(101,122)(102,123)(103,124)(104,125)(105,126)
(106,127)(107,128);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(128)!(1,2);
s1 := Sym(128)!(  4,  9)(  5,  8)(  6,  7)( 10, 17)( 11, 23)( 12, 22)( 13, 21)
( 14, 20)( 15, 19)( 16, 18)( 24, 45)( 25, 51)( 26, 50)( 27, 49)( 28, 48)
( 29, 47)( 30, 46)( 31, 59)( 32, 65)( 33, 64)( 34, 63)( 35, 62)( 36, 61)
( 37, 60)( 38, 52)( 39, 58)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 67, 72)( 68, 71)( 69, 70)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)
( 78, 82)( 79, 81)( 87,108)( 88,114)( 89,113)( 90,112)( 91,111)( 92,110)
( 93,109)( 94,122)( 95,128)( 96,127)( 97,126)( 98,125)( 99,124)(100,123)
(101,115)(102,121)(103,120)(104,119)(105,118)(106,117)(107,116);
s2 := Sym(128)!(  3, 95)(  4, 94)(  5,100)(  6, 99)(  7, 98)(  8, 97)(  9, 96)
( 10, 88)( 11, 87)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)( 17,102)
( 18,101)( 19,107)( 20,106)( 21,105)( 22,104)( 23,103)( 24, 74)( 25, 73)
( 26, 79)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 67)( 32, 66)( 33, 72)
( 34, 71)( 35, 70)( 36, 69)( 37, 68)( 38, 81)( 39, 80)( 40, 86)( 41, 85)
( 42, 84)( 43, 83)( 44, 82)( 45,116)( 46,115)( 47,121)( 48,120)( 49,119)
( 50,118)( 51,117)( 52,109)( 53,108)( 54,114)( 55,113)( 56,112)( 57,111)
( 58,110)( 59,123)( 60,122)( 61,128)( 62,127)( 63,126)( 64,125)( 65,124);
s3 := Sym(128)!( 24, 45)( 25, 46)( 26, 47)( 27, 48)( 28, 49)( 29, 50)( 30, 51)
( 31, 52)( 32, 53)( 33, 54)( 34, 55)( 35, 56)( 36, 57)( 37, 58)( 38, 59)
( 39, 60)( 40, 61)( 41, 62)( 42, 63)( 43, 64)( 44, 65)( 87,108)( 88,109)
( 89,110)( 90,111)( 91,112)( 92,113)( 93,114)( 94,115)( 95,116)( 96,117)
( 97,118)( 98,119)( 99,120)(100,121)(101,122)(102,123)(103,124)(104,125)
(105,126)(106,127)(107,128);
poly := sub<Sym(128)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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