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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2,2}*128
if this polytope has a name.
Group : SmallGroup(128,2163)
Rank : 5
Schlafli Type : {4,4,2,2}
Number of vertices, edges, etc : 4, 8, 4, 2, 2
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,2,2,2} of size 256
   {4,4,2,2,3} of size 384
   {4,4,2,2,4} of size 512
   {4,4,2,2,5} of size 640
   {4,4,2,2,6} of size 768
   {4,4,2,2,7} of size 896
   {4,4,2,2,9} of size 1152
   {4,4,2,2,10} of size 1280
   {4,4,2,2,11} of size 1408
   {4,4,2,2,13} of size 1664
   {4,4,2,2,14} of size 1792
   {4,4,2,2,15} of size 1920
Vertex Figure Of :
   {2,4,4,2,2} of size 256
   {4,4,4,2,2} of size 512
   {6,4,4,2,2} of size 768
   {3,4,4,2,2} of size 768
   {6,4,4,2,2} of size 1152
   {10,4,4,2,2} of size 1280
   {14,4,4,2,2} of size 1792
   {5,4,4,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   4-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,4,2}*256, {4,4,2,4}*256, {4,8,2,2}*256a, {8,4,2,2}*256a, {4,8,2,2}*256b, {8,4,2,2}*256b, {4,4,2,2}*256
   3-fold covers : {4,12,2,2}*384a, {12,4,2,2}*384a, {4,4,2,6}*384, {4,4,6,2}*384
   4-fold covers : {4,4,4,4}*512, {4,8,2,2}*512a, {8,4,2,2}*512a, {8,8,2,2}*512a, {8,8,2,2}*512b, {8,8,2,2}*512c, {8,8,2,2}*512d, {4,8,4,2}*512a, {4,8,4,2}*512b, {4,8,4,2}*512c, {4,8,4,2}*512d, {4,4,8,2}*512a, {8,4,4,2}*512a, {4,4,8,2}*512b, {8,4,4,2}*512b, {4,4,4,2}*512a, {4,4,4,2}*512b, {4,16,2,2}*512a, {16,4,2,2}*512a, {4,16,2,2}*512b, {16,4,2,2}*512b, {4,4,2,2}*512, {4,8,2,2}*512b, {8,4,2,2}*512b
   5-fold covers : {4,20,2,2}*640, {20,4,2,2}*640, {4,4,2,10}*640, {4,4,10,2}*640
   6-fold covers : {4,4,4,6}*768, {4,4,12,2}*768, {12,4,4,2}*768, {4,12,4,2}*768a, {4,4,6,4}*768a, {4,4,2,12}*768, {4,12,2,4}*768a, {12,4,2,4}*768a, {4,8,2,6}*768a, {4,8,6,2}*768a, {8,4,2,6}*768a, {8,4,6,2}*768a, {8,12,2,2}*768a, {12,8,2,2}*768a, {4,24,2,2}*768a, {24,4,2,2}*768a, {4,8,2,6}*768b, {4,8,6,2}*768b, {8,4,2,6}*768b, {8,4,6,2}*768b, {8,12,2,2}*768b, {12,8,2,2}*768b, {4,24,2,2}*768b, {24,4,2,2}*768b, {4,4,2,6}*768, {4,4,6,2}*768a, {4,12,2,2}*768a, {12,4,2,2}*768a
   7-fold covers : {4,28,2,2}*896, {28,4,2,2}*896, {4,4,2,14}*896, {4,4,14,2}*896
   9-fold covers : {4,4,2,18}*1152, {4,4,18,2}*1152, {4,36,2,2}*1152a, {36,4,2,2}*1152a, {4,4,6,6}*1152a, {4,4,6,6}*1152b, {4,4,6,6}*1152c, {4,12,2,6}*1152a, {4,12,6,2}*1152a, {4,12,6,2}*1152b, {12,4,2,6}*1152a, {12,4,6,2}*1152, {4,12,6,2}*1152c, {12,12,2,2}*1152a, {12,12,2,2}*1152b, {12,12,2,2}*1152c, {4,4,2,2}*1152, {4,4,6,2}*1152, {4,12,2,2}*1152, {12,4,2,2}*1152
   10-fold covers : {4,4,4,10}*1280, {4,4,20,2}*1280, {20,4,4,2}*1280, {4,20,4,2}*1280, {4,4,10,4}*1280, {4,4,2,20}*1280, {4,20,2,4}*1280, {20,4,2,4}*1280, {4,8,2,10}*1280a, {4,8,10,2}*1280a, {8,4,2,10}*1280a, {8,4,10,2}*1280a, {8,20,2,2}*1280a, {20,8,2,2}*1280a, {4,40,2,2}*1280a, {40,4,2,2}*1280a, {4,8,2,10}*1280b, {4,8,10,2}*1280b, {8,4,2,10}*1280b, {8,4,10,2}*1280b, {8,20,2,2}*1280b, {20,8,2,2}*1280b, {4,40,2,2}*1280b, {40,4,2,2}*1280b, {4,4,2,10}*1280, {4,4,10,2}*1280, {4,20,2,2}*1280, {20,4,2,2}*1280
   11-fold covers : {4,4,2,22}*1408, {4,4,22,2}*1408, {4,44,2,2}*1408, {44,4,2,2}*1408
   13-fold covers : {4,4,2,26}*1664, {4,4,26,2}*1664, {4,52,2,2}*1664, {52,4,2,2}*1664
   14-fold covers : {4,4,4,14}*1792, {4,4,28,2}*1792, {28,4,4,2}*1792, {4,28,4,2}*1792, {4,4,14,4}*1792, {4,4,2,28}*1792, {4,28,2,4}*1792, {28,4,2,4}*1792, {4,8,2,14}*1792a, {4,8,14,2}*1792a, {8,4,2,14}*1792a, {8,4,14,2}*1792a, {8,28,2,2}*1792a, {28,8,2,2}*1792a, {4,56,2,2}*1792a, {56,4,2,2}*1792a, {4,8,2,14}*1792b, {4,8,14,2}*1792b, {8,4,2,14}*1792b, {8,4,14,2}*1792b, {8,28,2,2}*1792b, {28,8,2,2}*1792b, {4,56,2,2}*1792b, {56,4,2,2}*1792b, {4,4,2,14}*1792, {4,4,14,2}*1792, {4,28,2,2}*1792, {28,4,2,2}*1792
   15-fold covers : {4,4,2,30}*1920, {4,4,30,2}*1920, {4,60,2,2}*1920a, {60,4,2,2}*1920a, {4,4,6,10}*1920, {4,4,10,6}*1920, {4,12,2,10}*1920a, {4,12,10,2}*1920a, {12,4,2,10}*1920a, {12,4,10,2}*1920, {4,20,2,6}*1920, {4,20,6,2}*1920, {20,4,2,6}*1920, {20,4,6,2}*1920, {12,20,2,2}*1920, {20,12,2,2}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,6);;
s1 := (1,2)(3,5)(4,7)(6,8);;
s2 := (2,4)(3,6);;
s3 := ( 9,10);;
s4 := (11,12);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!(2,3)(4,6);
s1 := Sym(12)!(1,2)(3,5)(4,7)(6,8);
s2 := Sym(12)!(2,4)(3,6);
s3 := Sym(12)!( 9,10);
s4 := Sym(12)!(11,12);
poly := sub<Sym(12)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope