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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,4}*128
if this polytope has a name.
Group : SmallGroup(128,2194)
Rank : 5
Schlafli Type : {4,2,2,4}
Number of vertices, edges, etc : 4, 4, 2, 4, 4
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,2,4,2} of size 256
   {4,2,2,4,3} of size 384
   {4,2,2,4,4} of size 512
   {4,2,2,4,6} of size 768
   {4,2,2,4,3} of size 768
   {4,2,2,4,6} of size 768
   {4,2,2,4,6} of size 768
   {4,2,2,4,4} of size 1152
   {4,2,2,4,6} of size 1152
   {4,2,2,4,9} of size 1152
   {4,2,2,4,10} of size 1280
   {4,2,2,4,14} of size 1792
   {4,2,2,4,15} of size 1920
   {4,2,2,4,5} of size 1920
   {4,2,2,4,6} of size 1920
Vertex Figure Of :
   {2,4,2,2,4} of size 256
   {3,4,2,2,4} of size 384
   {4,4,2,2,4} of size 512
   {6,4,2,2,4} of size 768
   {3,4,2,2,4} of size 768
   {6,4,2,2,4} of size 768
   {6,4,2,2,4} of size 768
   {4,4,2,2,4} of size 1152
   {6,4,2,2,4} of size 1152
   {9,4,2,2,4} of size 1152
   {10,4,2,2,4} of size 1280
   {14,4,2,2,4} of size 1792
   {15,4,2,2,4} of size 1920
   {5,4,2,2,4} of size 1920
   {6,4,2,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   4-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,4,4}*256, {4,4,2,4}*256, {4,2,2,8}*256, {8,2,2,4}*256
   3-fold covers : {4,2,2,12}*384, {12,2,2,4}*384, {4,2,6,4}*384a, {4,6,2,4}*384a
   4-fold covers : {4,4,4,4}*512, {8,2,2,8}*512, {4,2,2,16}*512, {16,2,2,4}*512
   5-fold covers : {4,2,2,20}*640, {20,2,2,4}*640, {4,2,10,4}*640, {4,10,2,4}*640
   6-fold covers : {4,4,6,4}*768a, {4,6,4,4}*768a, {4,4,2,12}*768, {12,2,4,4}*768, {4,2,4,12}*768a, {4,2,12,4}*768a, {4,12,2,4}*768a, {12,4,2,4}*768a, {4,2,6,8}*768, {4,6,2,8}*768a, {8,2,6,4}*768a, {8,6,2,4}*768, {8,2,2,12}*768, {12,2,2,8}*768, {4,2,2,24}*768, {24,2,2,4}*768
   7-fold covers : {4,2,2,28}*896, {28,2,2,4}*896, {4,2,14,4}*896, {4,14,2,4}*896
   9-fold covers : {4,2,18,4}*1152a, {4,18,2,4}*1152a, {4,2,2,36}*1152, {36,2,2,4}*1152, {4,6,6,4}*1152a, {4,6,6,4}*1152b, {4,6,6,4}*1152c, {4,2,6,12}*1152a, {12,6,2,4}*1152a, {4,2,6,12}*1152b, {4,2,6,12}*1152c, {4,6,2,12}*1152a, {12,2,6,4}*1152a, {12,6,2,4}*1152b, {12,6,2,4}*1152c, {12,2,2,12}*1152, {4,2,6,4}*1152, {4,6,2,4}*1152
   10-fold covers : {4,4,10,4}*1280, {4,10,4,4}*1280, {4,4,2,20}*1280, {20,2,4,4}*1280, {4,2,4,20}*1280, {4,2,20,4}*1280, {4,20,2,4}*1280, {20,4,2,4}*1280, {4,2,10,8}*1280, {4,10,2,8}*1280, {8,2,10,4}*1280, {8,10,2,4}*1280, {8,2,2,20}*1280, {20,2,2,8}*1280, {4,2,2,40}*1280, {40,2,2,4}*1280
   11-fold covers : {4,2,22,4}*1408, {4,22,2,4}*1408, {4,2,2,44}*1408, {44,2,2,4}*1408
   13-fold covers : {4,2,26,4}*1664, {4,26,2,4}*1664, {4,2,2,52}*1664, {52,2,2,4}*1664
   14-fold covers : {4,4,14,4}*1792, {4,14,4,4}*1792, {4,4,2,28}*1792, {28,2,4,4}*1792, {4,2,4,28}*1792, {4,2,28,4}*1792, {4,28,2,4}*1792, {28,4,2,4}*1792, {4,2,14,8}*1792, {4,14,2,8}*1792, {8,2,14,4}*1792, {8,14,2,4}*1792, {8,2,2,28}*1792, {28,2,2,8}*1792, {4,2,2,56}*1792, {56,2,2,4}*1792
   15-fold covers : {4,2,30,4}*1920a, {4,30,2,4}*1920a, {4,2,2,60}*1920, {60,2,2,4}*1920, {4,6,10,4}*1920a, {4,10,6,4}*1920a, {4,2,10,12}*1920, {4,10,2,12}*1920, {12,2,10,4}*1920, {12,10,2,4}*1920, {4,2,6,20}*1920a, {4,6,2,20}*1920a, {20,2,6,4}*1920a, {20,6,2,4}*1920a, {12,2,2,20}*1920, {20,2,2,12}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope