Polytope of Type {21,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {21,6}*336
if this polytope has a name.
Group : SmallGroup(336,212)
Rank : 3
Schlafli Type : {21,6}
Number of vertices, edges, etc : 28, 84, 8
Order of s₀s₁s₂ : 28
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {21,6,2} of size 672
   {21,6,4} of size 1344
   {21,6,3} of size 1680
Vertex Figure Of :
   {2,21,6} of size 672
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {3,6}*48
   12-fold quotients : {7,2}*28
   14-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {21,12}*672, {42,6}*672
   3-fold covers : {21,6}*1008b
   4-fold covers : {21,6}*1344, {84,6}*1344a, {42,12}*1344a, {42,6}*1344, {84,6}*1344b, {42,12}*1344b
   5-fold covers : {105,6}*1680
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope