Polytope of Type {14,16,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,16,2,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1076041)
Rank : 5
Schlafli Type : {14,16,2,2}
Number of vertices, edges, etc : 14, 112, 16, 2, 2
Order of s0s1s2s3s4 : 112
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 : {14,8,2,2}*896
4-fold quotients : {14,4,2,2}*448
7-fold quotients : {2,16,2,2}*256
8-fold quotients : {14,2,2,2}*224
14-fold quotients : {2,8,2,2}*128
16-fold quotients : {7,2,2,2}*112
28-fold quotients : {2,4,2,2}*64
56-fold quotients : {2,2,2,2}*32
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);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 23)( 16, 22)
( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 44)( 30, 43)( 31, 49)
( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 51)( 37, 50)( 38, 56)( 39, 55)
( 40, 54)( 41, 53)( 42, 52)( 57, 86)( 58, 85)( 59, 91)( 60, 90)( 61, 89)
( 62, 88)( 63, 87)( 64, 93)( 65, 92)( 66, 98)( 67, 97)( 68, 96)( 69, 95)
( 70, 94)( 71,107)( 72,106)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)
( 78,100)( 79, 99)( 80,105)( 81,104)( 82,103)( 83,102)( 84,101);;
s2 := ( 1, 57)( 2, 58)( 3, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)( 8, 64)
( 9, 65)( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 78)( 16, 79)
( 17, 80)( 18, 81)( 19, 82)( 20, 83)( 21, 84)( 22, 71)( 23, 72)( 24, 73)
( 25, 74)( 26, 75)( 27, 76)( 28, 77)( 29, 99)( 30,100)( 31,101)( 32,102)
( 33,103)( 34,104)( 35,105)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)
( 41,111)( 42,112)( 43, 85)( 44, 86)( 45, 87)( 46, 88)( 47, 89)( 48, 90)
( 49, 91)( 50, 92)( 51, 93)( 52, 94)( 53, 95)( 54, 96)( 55, 97)( 56, 98);;
s3 := (113,114);;
s4 := (115,116);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*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*s0*s1,
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(116)!( 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);
s1 := Sym(116)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 23)
( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 44)( 30, 43)
( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 51)( 37, 50)( 38, 56)
( 39, 55)( 40, 54)( 41, 53)( 42, 52)( 57, 86)( 58, 85)( 59, 91)( 60, 90)
( 61, 89)( 62, 88)( 63, 87)( 64, 93)( 65, 92)( 66, 98)( 67, 97)( 68, 96)
( 69, 95)( 70, 94)( 71,107)( 72,106)( 73,112)( 74,111)( 75,110)( 76,109)
( 77,108)( 78,100)( 79, 99)( 80,105)( 81,104)( 82,103)( 83,102)( 84,101);
s2 := Sym(116)!( 1, 57)( 2, 58)( 3, 59)( 4, 60)( 5, 61)( 6, 62)( 7, 63)
( 8, 64)( 9, 65)( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 78)
( 16, 79)( 17, 80)( 18, 81)( 19, 82)( 20, 83)( 21, 84)( 22, 71)( 23, 72)
( 24, 73)( 25, 74)( 26, 75)( 27, 76)( 28, 77)( 29, 99)( 30,100)( 31,101)
( 32,102)( 33,103)( 34,104)( 35,105)( 36,106)( 37,107)( 38,108)( 39,109)
( 40,110)( 41,111)( 42,112)( 43, 85)( 44, 86)( 45, 87)( 46, 88)( 47, 89)
( 48, 90)( 49, 91)( 50, 92)( 51, 93)( 52, 94)( 53, 95)( 54, 96)( 55, 97)
( 56, 98);
s3 := Sym(116)!(113,114);
s4 := Sym(116)!(115,116);
poly := sub<Sym(116)|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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*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*s0*s1,
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 >;
to this polytope