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Polytope of Type {3,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,10}*360
if this polytope has a name.
Group : SmallGroup(360,121)
Rank : 3
Schlafli Type : {3,10}
Number of vertices, edges, etc : 18, 90, 60
Order of s0s1s2 : 15
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {3,10,2} of size 720
Vertex Figure Of :
   {2,3,10} of size 720
   {4,3,10} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,10}*120a
   6-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,10}*720b, {6,10}*720b, {6,10}*720c
   3-fold covers : {9,10}*1080
   4-fold covers : {12,10}*1440e, {12,10}*1440f, {3,20}*1440a, {3,20}*1440b, {6,10}*1440f
   5-fold covers : {15,10}*1800a
Permutation Representation (GAP) :
s0 := (2,3)(5,6)(7,8);;
s1 := (1,2)(4,5)(7,8);;
s2 := (5,7)(6,8);;
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*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(8)!(2,3)(5,6)(7,8);
s1 := Sym(8)!(1,2)(4,5)(7,8);
s2 := Sym(8)!(5,7)(6,8);
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*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope