Polytope of Type {12,2,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,8}*384
if this polytope has a name.
Group : SmallGroup(384,12181)
Rank : 4
Schlafli Type : {12,2,8}
Number of vertices, edges, etc : 12, 12, 8, 8
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2,8,2} of size 768
Vertex Figure Of :
   {2,12,2,8} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,2,4}*192, {6,2,8}*192
   3-fold quotients : {4,2,8}*128
   4-fold quotients : {3,2,8}*96, {12,2,2}*96, {6,2,4}*96
   6-fold quotients : {4,2,4}*64, {2,2,8}*64
   8-fold quotients : {3,2,4}*48, {6,2,2}*48
   12-fold quotients : {2,2,4}*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 : {24,2,8}*768, {12,4,8}*768a, {12,2,16}*768
   3-fold covers : {36,2,8}*1152, {12,6,8}*1152b, {12,6,8}*1152c, {12,2,24}*1152
   5-fold covers : {60,2,8}*1920, {12,10,8}*1920, {12,2,40}*1920
Permutation Representation (GAP) :

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

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