Polytope of Type {2,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,10}*600
if this polytope has a name.
Group : SmallGroup(600,154)
Rank : 4
Schlafli Type : {2,6,10}
Number of vertices, edges, etc : 2, 15, 75, 25
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,10,2} of size 1200
Vertex Figure Of :
   {2,2,6,10} of size 1200
   {3,2,6,10} of size 1800
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,10}*1200a
   3-fold covers : {2,18,10}*1800, {6,6,10}*1800, {2,6,30}*1800
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 8,25)( 9,26)(10,27)(11,23)(12,24)(13,22)(14,18)(15,19)(16,20)(17,21);;
s2 := ( 4,10)( 5,17)( 6,19)( 7,26)( 8,20)( 9,27)(12,13)(15,21)(16,23)(18,24);;
s3 := ( 3, 4)( 5, 7)( 8,24)( 9,23)(10,27)(11,26)(12,25)(13,19)(14,18)(15,22)
(16,21)(17,20);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s1*s2*s3*s1*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(27)!(1,2);
s1 := Sym(27)!( 8,25)( 9,26)(10,27)(11,23)(12,24)(13,22)(14,18)(15,19)(16,20)
(17,21);
s2 := Sym(27)!( 4,10)( 5,17)( 6,19)( 7,26)( 8,20)( 9,27)(12,13)(15,21)(16,23)
(18,24);
s3 := Sym(27)!( 3, 4)( 5, 7)( 8,24)( 9,23)(10,27)(11,26)(12,25)(13,19)(14,18)
(15,22)(16,21)(17,20);
poly := sub<Sym(27)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s1*s2*s3*s1*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope