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Polytope of Type {28,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,6}*336b
if this polytope has a name.
Group : SmallGroup(336,212)
Rank : 3
Schlafli Type : {28,6}
Number of vertices, edges, etc : 28, 84, 6
Order of s0s1s2 : 21
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {28,6,2} of size 672
   {28,6,4} of size 1344
Vertex Figure Of :
   {2,28,6} of size 672
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {4,6}*48b
   14-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,6}*672
   3-fold covers : {28,18}*1008b, {84,6}*1008d
   4-fold covers : {56,6}*1344a, {28,12}*1344b, {28,6}*1344e, {56,6}*1344b, {56,6}*1344c, {28,12}*1344c
   5-fold covers : {28,30}*1680b, {140,6}*1680b
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5,27)( 6,28)( 7,25)( 8,26)( 9,23)(10,24)(11,21)(12,22)
(13,19)(14,20)(15,17)(16,18);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,25)(10,27)(11,26)(12,28)(13,21)(14,23)
(15,22)(16,24)(18,19);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(28)!( 1, 3)( 2, 4)( 5,27)( 6,28)( 7,25)( 8,26)( 9,23)(10,24)(11,21)
(12,22)(13,19)(14,20)(15,17)(16,18);
s1 := Sym(28)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,25)(10,27)(11,26)(12,28)(13,21)
(14,23)(15,22)(16,24)(18,19);
s2 := Sym(28)!( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0 >; 
 
References : None.
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