Polytope of Type {2,14,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,14}*784c
if this polytope has a name.
Group : SmallGroup(784,169)
Rank : 4
Schlafli Type : {2,14,14}
Number of vertices, edges, etc : 2, 14, 98, 14
Order of s₀s₁s₂s₃ : 14
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,14,2} of size 1568
Vertex Figure Of :
   {2,2,14,14} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,7,14}*392
   7-fold quotients : {2,14,2}*112
   14-fold quotients : {2,7,2}*56
   49-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,28,14}*1568b, {4,14,14}*1568b, {2,14,28}*1568c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)( 14, 48)
( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)
( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)
( 53, 58)( 54, 57)( 55, 56)( 59, 94)( 60,100)( 61, 99)( 62, 98)( 63, 97)
( 64, 96)( 65, 95)( 66, 87)( 67, 93)( 68, 92)( 69, 91)( 70, 90)( 71, 89)
( 72, 88)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81);;
s2 := (  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)( 10, 53)
( 11, 52)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)( 17, 95)( 18, 94)
( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24, 88)( 25, 87)( 26, 93)
( 27, 92)( 28, 91)( 29, 90)( 30, 89)( 31, 81)( 32, 80)( 33, 86)( 34, 85)
( 35, 84)( 36, 83)( 37, 82)( 38, 74)( 39, 73)( 40, 79)( 41, 78)( 42, 77)
( 43, 76)( 44, 75)( 45, 67)( 46, 66)( 47, 72)( 48, 71)( 49, 70)( 50, 69)
( 51, 68);;
s3 := (  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)
( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)
( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)
( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)( 95,100)
( 96, 99)( 97, 98);;
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*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(100)!(1,2);
s1 := Sym(100)!(  4,  9)(  5,  8)(  6,  7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)
( 14, 48)( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)
( 22, 40)( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 53, 58)( 54, 57)( 55, 56)( 59, 94)( 60,100)( 61, 99)( 62, 98)
( 63, 97)( 64, 96)( 65, 95)( 66, 87)( 67, 93)( 68, 92)( 69, 91)( 70, 90)
( 71, 89)( 72, 88)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)
( 79, 81);
s2 := Sym(100)!(  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)
( 10, 53)( 11, 52)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)( 17, 95)
( 18, 94)( 19,100)( 20, 99)( 21, 98)( 22, 97)( 23, 96)( 24, 88)( 25, 87)
( 26, 93)( 27, 92)( 28, 91)( 29, 90)( 30, 89)( 31, 81)( 32, 80)( 33, 86)
( 34, 85)( 35, 84)( 36, 83)( 37, 82)( 38, 74)( 39, 73)( 40, 79)( 41, 78)
( 42, 77)( 43, 76)( 44, 75)( 45, 67)( 46, 66)( 47, 72)( 48, 71)( 49, 70)
( 50, 69)( 51, 68);
s3 := Sym(100)!(  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)
( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)
( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)
( 95,100)( 96, 99)( 97, 98);
poly := sub<Sym(100)|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*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope