Polytope of Type {2,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4}*384a
if this polytope has a name.
Group : SmallGroup(384,11260)
Rank : 4
Schlafli Type : {2,12,4}
Number of vertices, edges, etc : 2, 24, 48, 8
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,4,2} of size 768
Vertex Figure Of :
   {2,2,12,4} of size 768
   {3,2,12,4} of size 1152
   {5,2,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,4}*192a
   3-fold quotients : {2,4,4}*128
   4-fold quotients : {2,12,2}*96, {2,6,4}*96a
   6-fold quotients : {2,4,4}*64
   8-fold quotients : {2,6,2}*48
   12-fold quotients : {2,2,4}*32, {2,4,2}*32
   16-fold quotients : {2,3,2}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,8}*768a, {2,24,4}*768a, {4,12,4}*768a, {2,12,4}*768a, {2,24,4}*768b, {2,12,8}*768b
   3-fold covers : {2,36,4}*1152a, {6,12,4}*1152a, {6,12,4}*1152b, {2,12,12}*1152a, {2,12,12}*1152c
   5-fold covers : {2,60,4}*1920a, {10,12,4}*1920a, {2,12,20}*1920a
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);;
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, 
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(26)!(1,2);
s1 := Sym(26)!( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(16,17)(19,20)(21,24)(22,26)
(23,25);
s2 := Sym(26)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,22)(16,21)(17,23)(18,25)(19,24)
(20,26);
s3 := Sym(26)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)
(12,24)(13,25)(14,26);
poly := sub<Sym(26)|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, 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