Polytope of Type {3,2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,8}*576
if this polytope has a name.
Group : SmallGroup(576,6606)
Rank : 5
Schlafli Type : {3,2,6,8}
Number of vertices, edges, etc : 3, 3, 6, 24, 8
Order of s₀s₁s₂s₃s₄ : 24
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,6,8,2} of size 1152
Vertex Figure Of :
   {2,3,2,6,8} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,6,4}*288a
   3-fold quotients : {3,2,2,8}*192
   4-fold quotients : {3,2,6,2}*144
   6-fold quotients : {3,2,2,4}*96
   8-fold quotients : {3,2,3,2}*72
   12-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,12,8}*1152a, {3,2,6,16}*1152, {6,2,6,8}*1152
   3-fold covers : {3,2,18,8}*1728, {9,2,6,8}*1728, {3,6,6,8}*1728a, {3,2,6,24}*1728a, {3,2,6,24}*1728c, {3,6,6,8}*1728b
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(26,27);;
s3 := ( 4, 6)( 5,12)( 8, 9)(10,13)(11,18)(14,15)(16,19)(17,24)(20,21)(22,25)
(23,26);;
s4 := ( 4, 5)( 6, 9)( 7,10)( 8,11)(12,15)(13,16)(14,17)(18,21)(19,22)(20,23)
(24,26)(25,27);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(27)!(2,3);
s1 := Sym(27)!(1,2);
s2 := Sym(27)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(26,27);
s3 := Sym(27)!( 4, 6)( 5,12)( 8, 9)(10,13)(11,18)(14,15)(16,19)(17,24)(20,21)
(22,25)(23,26);
s4 := Sym(27)!( 4, 5)( 6, 9)( 7,10)( 8,11)(12,15)(13,16)(14,17)(18,21)(19,22)
(20,23)(24,26)(25,27);
poly := sub<Sym(27)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope