Polytope of Type {2,14,4}

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

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

Permutation Representation (Magma) :

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

to this polytope