Polytope of Type {2,14,14,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,14,2}*1568b
if this polytope has a name.
Group : SmallGroup(1568,925)
Rank : 5
Schlafli Type : {2,14,14,2}
Number of vertices, edges, etc : 2, 14, 98, 14, 2
Order of s0s1s2s3s4 : 14
Order of s0s1s2s3s4s3s2s1 : 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 : {2,14,7,2}*784
7-fold quotients : {2,2,14,2}*224
14-fold quotients : {2,2,7,2}*112
49-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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);;
s2 := ( 3, 4)( 5, 9)( 6, 8)( 10, 46)( 11, 45)( 12, 51)( 13, 50)( 14, 49)
( 15, 48)( 16, 47)( 17, 39)( 18, 38)( 19, 44)( 20, 43)( 21, 42)( 22, 41)
( 23, 40)( 24, 32)( 25, 31)( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)
( 52, 53)( 54, 58)( 55, 57)( 59, 95)( 60, 94)( 61,100)( 62, 99)( 63, 98)
( 64, 97)( 65, 96)( 66, 88)( 67, 87)( 68, 93)( 69, 92)( 70, 91)( 71, 90)
( 72, 89)( 73, 81)( 74, 80)( 75, 86)( 76, 85)( 77, 84)( 78, 83)( 79, 82);;
s3 := ( 3, 59)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)( 10, 52)
( 11, 58)( 12, 57)( 13, 56)( 14, 55)( 15, 54)( 16, 53)( 17, 94)( 18,100)
( 19, 99)( 20, 98)( 21, 97)( 22, 96)( 23, 95)( 24, 87)( 25, 93)( 26, 92)
( 27, 91)( 28, 90)( 29, 89)( 30, 88)( 31, 80)( 32, 86)( 33, 85)( 34, 84)
( 35, 83)( 36, 82)( 37, 81)( 38, 73)( 39, 79)( 40, 78)( 41, 77)( 42, 76)
( 43, 75)( 44, 74)( 45, 66)( 46, 72)( 47, 71)( 48, 70)( 49, 69)( 50, 68)
( 51, 67);;
s4 := (101,102);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s3*s1*s2*s1*s2*s3*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,
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(102)!(1,2);
s1 := Sym(102)!( 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);
s2 := Sym(102)!( 3, 4)( 5, 9)( 6, 8)( 10, 46)( 11, 45)( 12, 51)( 13, 50)
( 14, 49)( 15, 48)( 16, 47)( 17, 39)( 18, 38)( 19, 44)( 20, 43)( 21, 42)
( 22, 41)( 23, 40)( 24, 32)( 25, 31)( 26, 37)( 27, 36)( 28, 35)( 29, 34)
( 30, 33)( 52, 53)( 54, 58)( 55, 57)( 59, 95)( 60, 94)( 61,100)( 62, 99)
( 63, 98)( 64, 97)( 65, 96)( 66, 88)( 67, 87)( 68, 93)( 69, 92)( 70, 91)
( 71, 90)( 72, 89)( 73, 81)( 74, 80)( 75, 86)( 76, 85)( 77, 84)( 78, 83)
( 79, 82);
s3 := Sym(102)!( 3, 59)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)
( 10, 52)( 11, 58)( 12, 57)( 13, 56)( 14, 55)( 15, 54)( 16, 53)( 17, 94)
( 18,100)( 19, 99)( 20, 98)( 21, 97)( 22, 96)( 23, 95)( 24, 87)( 25, 93)
( 26, 92)( 27, 91)( 28, 90)( 29, 89)( 30, 88)( 31, 80)( 32, 86)( 33, 85)
( 34, 84)( 35, 83)( 36, 82)( 37, 81)( 38, 73)( 39, 79)( 40, 78)( 41, 77)
( 42, 76)( 43, 75)( 44, 74)( 45, 66)( 46, 72)( 47, 71)( 48, 70)( 49, 69)
( 50, 68)( 51, 67);
s4 := Sym(102)!(101,102);
poly := sub<Sym(102)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s3*s1*s2*s1*s2*s3*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,
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 >;
to this polytope