Polytope of Type {14,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4}*112
Also Known As : {14,4|2}. if this polytope has another name.
Group : SmallGroup(112,31)
Rank : 3
Schlafli Type : {14,4}
Number of vertices, edges, etc : 14, 28, 4
Order of s₀s₁s₂ : 28
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,4,2} of size 224
   {14,4,4} of size 448
   {14,4,6} of size 672
   {14,4,3} of size 672
   {14,4,8} of size 896
   {14,4,8} of size 896
   {14,4,4} of size 896
   {14,4,6} of size 1008
   {14,4,10} of size 1120
   {14,4,12} of size 1344
   {14,4,6} of size 1344
   {14,4,14} of size 1568
   {14,4,5} of size 1680
   {14,4,8} of size 1792
   {14,4,16} of size 1792
   {14,4,16} of size 1792
   {14,4,4} of size 1792
   {14,4,8} of size 1792
Vertex Figure Of :
   {2,14,4} of size 224
   {4,14,4} of size 448
   {6,14,4} of size 672
   {7,14,4} of size 784
   {8,14,4} of size 896
   {10,14,4} of size 1120
   {12,14,4} of size 1344
   {14,14,4} of size 1568
   {14,14,4} of size 1568
   {14,14,4} of size 1568
   {16,14,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {14,2}*56
   4-fold quotients : {7,2}*28
   7-fold quotients : {2,4}*16
   14-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,4}*224, {14,8}*224
   3-fold covers : {14,12}*336, {42,4}*336a
   4-fold covers : {56,4}*448a, {28,4}*448, {56,4}*448b, {28,8}*448a, {28,8}*448b, {14,16}*448
   5-fold covers : {14,20}*560, {70,4}*560
   6-fold covers : {14,24}*672, {28,12}*672, {84,4}*672a, {42,8}*672
   7-fold covers : {98,4}*784, {14,28}*784a, {14,28}*784c
   8-fold covers : {56,4}*896a, {56,8}*896a, {56,8}*896b, {28,8}*896a, {56,8}*896c, {56,8}*896d, {112,4}*896a, {112,4}*896b, {28,4}*896, {56,4}*896b, {28,8}*896b, {28,16}*896a, {28,16}*896b, {14,32}*896
   9-fold covers : {14,36}*1008, {126,4}*1008a, {42,12}*1008a, {42,12}*1008b, {42,12}*1008c, {42,4}*1008
   10-fold covers : {14,40}*1120, {28,20}*1120, {140,4}*1120, {70,8}*1120
   11-fold covers : {14,44}*1232, {154,4}*1232
   12-fold covers : {14,48}*1344, {28,12}*1344a, {28,24}*1344a, {56,12}*1344a, {28,24}*1344b, {56,12}*1344b, {168,4}*1344a, {84,4}*1344a, {168,4}*1344b, {84,8}*1344a, {84,8}*1344b, {42,16}*1344, {28,12}*1344b, {42,12}*1344b, {42,4}*1344b
   13-fold covers : {14,52}*1456, {182,4}*1456
   14-fold covers : {196,4}*1568, {98,8}*1568, {14,56}*1568a, {28,28}*1568a, {28,28}*1568c, {14,56}*1568c
   15-fold covers : {14,60}*1680, {42,20}*1680a, {70,12}*1680, {210,4}*1680a
   16-fold covers : {56,8}*1792a, {28,8}*1792a, {56,8}*1792b, {56,4}*1792a, {56,8}*1792c, {56,8}*1792d, {28,16}*1792a, {112,4}*1792a, {28,16}*1792b, {112,4}*1792b, {112,8}*1792a, {56,16}*1792a, {112,8}*1792b, {56,16}*1792b, {56,16}*1792c, {112,8}*1792c, {112,8}*1792d, {56,16}*1792d, {56,16}*1792e, {112,8}*1792e, {112,8}*1792f, {56,16}*1792f, {28,32}*1792a, {224,4}*1792a, {28,32}*1792b, {224,4}*1792b, {28,4}*1792, {56,4}*1792b, {28,8}*1792b, {28,8}*1792c, {56,8}*1792e, {56,4}*1792c, {56,4}*1792d, {28,8}*1792d, {56,8}*1792f, {56,8}*1792g, {56,8}*1792h, {14,64}*1792
   17-fold covers : {14,68}*1904, {238,4}*1904
Permutation Representation (GAP) :

s0 := ( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28);;
s1 := ( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)(18,23)
(20,21)(22,26)(24,27);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)(16,22)
(19,23)(20,24)(25,27)(26,28);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*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(28)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28);
s1 := Sym(28)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)
(18,23)(20,21)(22,26)(24,27);
s2 := Sym(28)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)
(16,22)(19,23)(20,24)(25,27)(26,28);
poly := sub<Sym(28)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*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.
to this polytope