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Polytope of Type {3,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,8}*336a
Also Known As : {3,8}7if this polytope has another name.
Group : SmallGroup(336,208)
Rank : 3
Schlafli Type : {3,8}
Number of vertices, edges, etc : 21, 84, 56
Order of s0s1s2 : 7
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {3,8,2} of size 672
Vertex Figure Of :
   {2,3,8} of size 672
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,8}*672a, {6,8}*672d, {6,8}*672e
   3-fold covers : {3,8}*1008
   4-fold covers : {12,8}*1344a, {12,8}*1344b, {3,16}*1344a, {6,8}*1344g
   5-fold covers : {15,8}*1680
Permutation Representation (GAP) :
s0 := (3,7)(4,8)(5,6);;
s1 := (1,3)(2,8)(5,6);;
s2 := (1,2)(3,6)(4,8)(5,7);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(8)!(3,7)(4,8)(5,6);
s1 := Sym(8)!(1,3)(2,8)(5,6);
s2 := Sym(8)!(1,2)(3,6)(4,8)(5,7);
poly := sub<Sym(8)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 >; 
 
References : None.
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