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Polytope of Type {14,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,6,6}*1008c
if this polytope has a name.
Group : SmallGroup(1008,922)
Rank : 4
Schlafli Type : {14,6,6}
Number of vertices, edges, etc : 14, 42, 18, 6
Order of s0s1s2s3 : 42
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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) :
   3-fold quotients : {14,6,2}*336
   7-fold quotients : {2,6,6}*144c
   9-fold quotients : {14,2,2}*112
   14-fold quotients : {2,3,6}*72
   18-fold quotients : {7,2,2}*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 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)
( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)
( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)
( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)
( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)
(114,119)(115,118)(116,117)(121,126)(122,125)(123,124);;
s1 := (  1,  2)(  3,  7)(  4,  6)(  8, 16)(  9, 15)( 10, 21)( 11, 20)( 12, 19)
( 13, 18)( 14, 17)( 22, 44)( 23, 43)( 24, 49)( 25, 48)( 26, 47)( 27, 46)
( 28, 45)( 29, 58)( 30, 57)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)
( 36, 51)( 37, 50)( 38, 56)( 39, 55)( 40, 54)( 41, 53)( 42, 52)( 64, 65)
( 66, 70)( 67, 69)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)
( 77, 80)( 85,107)( 86,106)( 87,112)( 88,111)( 89,110)( 90,109)( 91,108)
( 92,121)( 93,120)( 94,126)( 95,125)( 96,124)( 97,123)( 98,122)( 99,114)
(100,113)(101,119)(102,118)(103,117)(104,116)(105,115);;
s2 := (  1, 92)(  2, 93)(  3, 94)(  4, 95)(  5, 96)(  6, 97)(  7, 98)(  8, 85)
(  9, 86)( 10, 87)( 11, 88)( 12, 89)( 13, 90)( 14, 91)( 15, 99)( 16,100)
( 17,101)( 18,102)( 19,103)( 20,104)( 21,105)( 22, 71)( 23, 72)( 24, 73)
( 25, 74)( 26, 75)( 27, 76)( 28, 77)( 29, 64)( 30, 65)( 31, 66)( 32, 67)
( 33, 68)( 34, 69)( 35, 70)( 36, 78)( 37, 79)( 38, 80)( 39, 81)( 40, 82)
( 41, 83)( 42, 84)( 43,113)( 44,114)( 45,115)( 46,116)( 47,117)( 48,118)
( 49,119)( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)
( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126);;
s3 := (  8, 15)(  9, 16)( 10, 17)( 11, 18)( 12, 19)( 13, 20)( 14, 21)( 29, 36)
( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 50, 57)( 51, 58)
( 52, 59)( 53, 60)( 54, 61)( 55, 62)( 56, 63)( 71, 78)( 72, 79)( 73, 80)
( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 92, 99)( 93,100)( 94,101)( 95,102)
( 96,103)( 97,104)( 98,105)(113,120)(114,121)(115,122)(116,123)(117,124)
(118,125)(119,126);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s0*s1*s0*s1*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(126)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)
( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)
( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)
( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)
(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124);
s1 := Sym(126)!(  1,  2)(  3,  7)(  4,  6)(  8, 16)(  9, 15)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 22, 44)( 23, 43)( 24, 49)( 25, 48)( 26, 47)
( 27, 46)( 28, 45)( 29, 58)( 30, 57)( 31, 63)( 32, 62)( 33, 61)( 34, 60)
( 35, 59)( 36, 51)( 37, 50)( 38, 56)( 39, 55)( 40, 54)( 41, 53)( 42, 52)
( 64, 65)( 66, 70)( 67, 69)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)
( 76, 81)( 77, 80)( 85,107)( 86,106)( 87,112)( 88,111)( 89,110)( 90,109)
( 91,108)( 92,121)( 93,120)( 94,126)( 95,125)( 96,124)( 97,123)( 98,122)
( 99,114)(100,113)(101,119)(102,118)(103,117)(104,116)(105,115);
s2 := Sym(126)!(  1, 92)(  2, 93)(  3, 94)(  4, 95)(  5, 96)(  6, 97)(  7, 98)
(  8, 85)(  9, 86)( 10, 87)( 11, 88)( 12, 89)( 13, 90)( 14, 91)( 15, 99)
( 16,100)( 17,101)( 18,102)( 19,103)( 20,104)( 21,105)( 22, 71)( 23, 72)
( 24, 73)( 25, 74)( 26, 75)( 27, 76)( 28, 77)( 29, 64)( 30, 65)( 31, 66)
( 32, 67)( 33, 68)( 34, 69)( 35, 70)( 36, 78)( 37, 79)( 38, 80)( 39, 81)
( 40, 82)( 41, 83)( 42, 84)( 43,113)( 44,114)( 45,115)( 46,116)( 47,117)
( 48,118)( 49,119)( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)
( 56,112)( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126);
s3 := Sym(126)!(  8, 15)(  9, 16)( 10, 17)( 11, 18)( 12, 19)( 13, 20)( 14, 21)
( 29, 36)( 30, 37)( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 50, 57)
( 51, 58)( 52, 59)( 53, 60)( 54, 61)( 55, 62)( 56, 63)( 71, 78)( 72, 79)
( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 92, 99)( 93,100)( 94,101)
( 95,102)( 96,103)( 97,104)( 98,105)(113,120)(114,121)(115,122)(116,123)
(117,124)(118,125)(119,126);
poly := sub<Sym(126)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s0*s1*s0*s1*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.
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