Polytope of Type {12,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,2}*384a
if this polytope has a name.
Group : SmallGroup(384,11260)
Rank : 4
Schlafli Type : {12,4,2}
Number of vertices, edges, etc : 24, 48, 8, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,4,2,2} of size 768
   {12,4,2,3} of size 1152
   {12,4,2,5} of size 1920
Vertex Figure Of :
   {2,12,4,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4,2}*192a
   3-fold quotients : {4,4,2}*128
   4-fold quotients : {12,2,2}*96, {6,4,2}*96a
   6-fold quotients : {4,4,2}*64
   8-fold quotients : {6,2,2}*48
   12-fold quotients : {2,4,2}*32, {4,2,2}*32
   16-fold quotients : {3,2,2}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8,2}*768a, {24,4,2}*768a, {12,4,4}*768b, {12,4,2}*768a, {24,4,2}*768b, {12,8,2}*768b
   3-fold covers : {36,4,2}*1152a, {12,4,6}*1152a, {12,12,2}*1152a, {12,12,2}*1152c
   5-fold covers : {60,4,2}*1920a, {12,4,10}*1920a, {12,20,2}*1920a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope