Polytope of Type {2,12,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4,2}*768a
if this polytope has a name.
Group : SmallGroup(768,1036282)
Rank : 5
Schlafli Type : {2,12,4,2}
Number of vertices, edges, etc : 2, 24, 48, 8, 2
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,4,2}*384a
   3-fold quotients : {2,4,4,2}*256
   4-fold quotients : {2,12,2,2}*192, {2,6,4,2}*192a
   6-fold quotients : {2,4,4,2}*128
   8-fold quotients : {2,6,2,2}*96
   12-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   16-fold quotients : {2,3,2,2}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(16,17)(19,20)(21,24)(22,26)(23,25);;
s2 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,22)(16,21)(17,23)(18,25)(19,24)(20,26);;
s3 := ( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24)
(13,25)(14,26);;
s4 := (27,28);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(28)!(1,2);
s1 := Sym(28)!( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(16,17)(19,20)(21,24)(22,26)
(23,25);
s2 := Sym(28)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,22)(16,21)(17,23)(18,25)(19,24)
(20,26);
s3 := Sym(28)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)
(12,24)(13,25)(14,26);
s4 := Sym(28)!(27,28);
poly := sub<Sym(28)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope