Polytope of Type {4,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14,2}*224
if this polytope has a name.
Group : SmallGroup(224,178)
Rank : 4
Schlafli Type : {4,14,2}
Number of vertices, edges, etc : 4, 28, 14, 2
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,14,2,2} of size 448
   {4,14,2,3} of size 672
   {4,14,2,4} of size 896
   {4,14,2,5} of size 1120
   {4,14,2,6} of size 1344
   {4,14,2,7} of size 1568
   {4,14,2,8} of size 1792
Vertex Figure Of :
   {2,4,14,2} of size 448
   {4,4,14,2} of size 896
   {6,4,14,2} of size 1344
   {3,4,14,2} of size 1344
   {8,4,14,2} of size 1792
   {8,4,14,2} of size 1792
   {4,4,14,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,14,2}*112
   4-fold quotients : {2,7,2}*56
   7-fold quotients : {4,2,2}*32
   14-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,28,2}*448, {4,14,4}*448, {8,14,2}*448
   3-fold covers : {12,14,2}*672, {4,14,6}*672, {4,42,2}*672a
   4-fold covers : {4,28,4}*896, {4,56,2}*896a, {4,28,2}*896, {4,56,2}*896b, {8,28,2}*896a, {8,28,2}*896b, {4,14,8}*896, {8,14,4}*896, {16,14,2}*896
   5-fold covers : {20,14,2}*1120, {4,14,10}*1120, {4,70,2}*1120
   6-fold covers : {4,14,12}*1344, {12,14,4}*1344, {4,28,6}*1344, {24,14,2}*1344, {8,14,6}*1344, {12,28,2}*1344, {4,84,2}*1344a, {4,42,4}*1344a, {8,42,2}*1344
   7-fold covers : {4,98,2}*1568, {28,14,2}*1568a, {4,14,14}*1568a, {4,14,14}*1568b, {28,14,2}*1568c
   8-fold covers : {8,28,2}*1792a, {4,56,2}*1792a, {8,56,2}*1792a, {8,56,2}*1792b, {8,56,2}*1792c, {8,56,2}*1792d, {8,14,8}*1792, {4,28,8}*1792a, {8,28,4}*1792a, {4,28,8}*1792b, {8,28,4}*1792b, {4,56,4}*1792a, {4,28,4}*1792a, {4,28,4}*1792b, {4,56,4}*1792b, {4,56,4}*1792c, {4,56,4}*1792d, {16,28,2}*1792a, {4,112,2}*1792a, {16,28,2}*1792b, {4,112,2}*1792b, {4,28,2}*1792, {4,56,2}*1792b, {8,28,2}*1792b, {4,14,16}*1792, {16,14,4}*1792, {32,14,2}*1792
Permutation Representation (GAP) :

s0 := ( 2, 5)( 6,11)( 7,12)(13,19)(14,20)(21,25)(22,26);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,18)(12,17)(15,22)(16,21)
(19,24)(20,23)(25,28)(26,27);;
s2 := ( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)( 9,15)(10,17)(12,19)(14,21)(18,23)
(20,25)(24,27);;
s3 := (29,30);;
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, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(30)!( 2, 5)( 6,11)( 7,12)(13,19)(14,20)(21,25)(22,26);
s1 := Sym(30)!( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,18)(12,17)(15,22)
(16,21)(19,24)(20,23)(25,28)(26,27);
s2 := Sym(30)!( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)( 9,15)(10,17)(12,19)(14,21)
(18,23)(20,25)(24,27);
s3 := Sym(30)!(29,30);
poly := sub<Sym(30)|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, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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 >;

to this polytope