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Polytope of Type {6,6,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,14}*1008c
if this polytope has a name.
Group : SmallGroup(1008,922)
Rank : 4
Schlafli Type : {6,6,14}
Number of vertices, edges, etc : 6, 18, 42, 14
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) :
   2-fold quotients : {3,6,14}*504
   3-fold quotients : {6,2,14}*336
   6-fold quotients : {3,2,14}*168, {6,2,7}*168
   7-fold quotients : {6,6,2}*144c
   9-fold quotients : {2,2,14}*112
   12-fold quotients : {3,2,7}*84
   14-fold quotients : {3,6,2}*72
   18-fold quotients : {2,2,7}*56
   21-fold quotients : {6,2,2}*48
   42-fold quotients : {3,2,2}*24
   63-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  8, 15)(  9, 16)( 10, 17)( 11, 18)( 12, 19)( 13, 20)( 14, 21)( 22, 43)
( 23, 44)( 24, 45)( 25, 46)( 26, 47)( 27, 48)( 28, 49)( 29, 57)( 30, 58)
( 31, 59)( 32, 60)( 33, 61)( 34, 62)( 35, 63)( 36, 50)( 37, 51)( 38, 52)
( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 71, 78)( 72, 79)( 73, 80)( 74, 81)
( 75, 82)( 76, 83)( 77, 84)( 85,106)( 86,107)( 87,108)( 88,109)( 89,110)
( 90,111)( 91,112)( 92,120)( 93,121)( 94,122)( 95,123)( 96,124)( 97,125)
( 98,126)( 99,113)(100,114)(101,115)(102,116)(103,117)(104,118)(105,119);;
s1 := (  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);;
s2 := (  2,  7)(  3,  6)(  4,  5)(  8, 15)(  9, 21)( 10, 20)( 11, 19)( 12, 18)
( 13, 17)( 14, 16)( 23, 28)( 24, 27)( 25, 26)( 29, 36)( 30, 42)( 31, 41)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 44, 49)( 45, 48)( 46, 47)( 50, 57)
( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 65, 70)( 66, 69)
( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 86, 91)( 87, 90)( 88, 89)( 92, 99)( 93,105)( 94,104)( 95,103)( 96,102)
( 97,101)( 98,100)(107,112)(108,111)(109,110)(113,120)(114,126)(115,125)
(116,124)(117,123)(118,122)(119,121);;
s3 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)
( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)
( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)
( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)
( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111)
(113,114)(115,119)(116,118)(120,121)(122,126)(123,125);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(126)!(  8, 15)(  9, 16)( 10, 17)( 11, 18)( 12, 19)( 13, 20)( 14, 21)
( 22, 43)( 23, 44)( 24, 45)( 25, 46)( 26, 47)( 27, 48)( 28, 49)( 29, 57)
( 30, 58)( 31, 59)( 32, 60)( 33, 61)( 34, 62)( 35, 63)( 36, 50)( 37, 51)
( 38, 52)( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 71, 78)( 72, 79)( 73, 80)
( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 85,106)( 86,107)( 87,108)( 88,109)
( 89,110)( 90,111)( 91,112)( 92,120)( 93,121)( 94,122)( 95,123)( 96,124)
( 97,125)( 98,126)( 99,113)(100,114)(101,115)(102,116)(103,117)(104,118)
(105,119);
s1 := 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);
s2 := Sym(126)!(  2,  7)(  3,  6)(  4,  5)(  8, 15)(  9, 21)( 10, 20)( 11, 19)
( 12, 18)( 13, 17)( 14, 16)( 23, 28)( 24, 27)( 25, 26)( 29, 36)( 30, 42)
( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 44, 49)( 45, 48)( 46, 47)
( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 65, 70)
( 66, 69)( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)( 86, 91)( 87, 90)( 88, 89)( 92, 99)( 93,105)( 94,104)( 95,103)
( 96,102)( 97,101)( 98,100)(107,112)(108,111)(109,110)(113,120)(114,126)
(115,125)(116,124)(117,123)(118,122)(119,121);
s3 := Sym(126)!(  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)
( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)
( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)
( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)
( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)
( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)
(109,111)(113,114)(115,119)(116,118)(120,121)(122,126)(123,125);
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope