Polytope of Type {6,28}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,28}*336b
if this polytope has a name.
Group : SmallGroup(336,212)
Rank : 3
Schlafli Type : {6,28}
Number of vertices, edges, etc : 6, 84, 28
Order of s₀s₁s₂ : 21
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,28,2} of size 672
Vertex Figure Of :
   {2,6,28} of size 672
   {4,6,28} of size 1344
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {6,4}*48b
   14-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,28}*672
   3-fold covers : {18,28}*1008b, {6,84}*1008d
   4-fold covers : {6,56}*1344a, {12,28}*1344b, {6,28}*1344e, {6,56}*1344b, {6,56}*1344c, {12,28}*1344c
   5-fold covers : {30,28}*1680b, {6,140}*1680b
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,28}

Twisty Puzzle