Polytope of Type {2,8,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,2,2}*128
if this polytope has a name.
Group : SmallGroup(128,2306)
Rank : 5
Schlafli Type : {2,8,2,2}
Number of vertices, edges, etc : 2, 8, 8, 2, 2
Order of s₀s₁s₂s₃s₄ : 8
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,8,2,2,2} of size 256
   {2,8,2,2,3} of size 384
   {2,8,2,2,4} of size 512
   {2,8,2,2,5} of size 640
   {2,8,2,2,6} of size 768
   {2,8,2,2,7} of size 896
   {2,8,2,2,9} of size 1152
   {2,8,2,2,10} of size 1280
   {2,8,2,2,11} of size 1408
   {2,8,2,2,13} of size 1664
   {2,8,2,2,14} of size 1792
   {2,8,2,2,15} of size 1920
Vertex Figure Of :
   {2,2,8,2,2} of size 256
   {3,2,8,2,2} of size 384
   {4,2,8,2,2} of size 512
   {5,2,8,2,2} of size 640
   {6,2,8,2,2} of size 768
   {7,2,8,2,2} of size 896
   {9,2,8,2,2} of size 1152
   {10,2,8,2,2} of size 1280
   {11,2,8,2,2} of size 1408
   {13,2,8,2,2} of size 1664
   {14,2,8,2,2} of size 1792
   {15,2,8,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,2,2}*64
   4-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,8,4,2}*256a, {4,8,2,2}*256a, {2,8,2,4}*256, {2,16,2,2}*256
   3-fold covers : {2,24,2,2}*384, {2,8,2,6}*384, {2,8,6,2}*384, {6,8,2,2}*384
   4-fold covers : {2,8,4,2}*512a, {4,8,2,2}*512a, {2,8,8,2}*512b, {2,8,8,2}*512c, {8,8,2,2}*512a, {8,8,2,2}*512b, {2,8,2,8}*512, {4,8,4,2}*512a, {2,8,4,4}*512b, {2,16,4,2}*512a, {4,16,2,2}*512a, {2,16,4,2}*512b, {4,16,2,2}*512b, {2,16,2,4}*512, {2,32,2,2}*512
   5-fold covers : {2,40,2,2}*640, {2,8,2,10}*640, {2,8,10,2}*640, {10,8,2,2}*640
   6-fold covers : {2,8,4,6}*768a, {4,8,2,6}*768a, {4,8,6,2}*768a, {6,8,4,2}*768a, {2,8,12,2}*768a, {12,8,2,2}*768a, {2,24,4,2}*768a, {4,24,2,2}*768a, {6,8,2,4}*768, {2,8,6,4}*768a, {2,8,2,12}*768, {2,24,2,4}*768, {2,16,2,6}*768, {2,16,6,2}*768, {6,16,2,2}*768, {2,48,2,2}*768
   7-fold covers : {2,56,2,2}*896, {2,8,2,14}*896, {2,8,14,2}*896, {14,8,2,2}*896
   9-fold covers : {2,8,2,18}*1152, {2,8,18,2}*1152, {18,8,2,2}*1152, {2,72,2,2}*1152, {2,8,6,6}*1152a, {2,8,6,6}*1152b, {6,8,2,6}*1152, {6,8,6,2}*1152, {2,8,6,6}*1152c, {2,24,6,2}*1152a, {6,24,2,2}*1152a, {2,24,2,6}*1152, {2,24,6,2}*1152b, {2,24,6,2}*1152c, {6,24,2,2}*1152b, {6,24,2,2}*1152c, {2,8,6,2}*1152, {6,8,2,2}*1152
   10-fold covers : {2,8,4,10}*1280a, {4,8,2,10}*1280a, {4,8,10,2}*1280a, {10,8,4,2}*1280a, {2,8,20,2}*1280a, {20,8,2,2}*1280a, {2,40,4,2}*1280a, {4,40,2,2}*1280a, {10,8,2,4}*1280, {2,8,10,4}*1280, {2,8,2,20}*1280, {2,40,2,4}*1280, {2,16,2,10}*1280, {2,16,10,2}*1280, {10,16,2,2}*1280, {2,80,2,2}*1280
   11-fold covers : {2,8,2,22}*1408, {2,8,22,2}*1408, {22,8,2,2}*1408, {2,88,2,2}*1408
   13-fold covers : {2,8,2,26}*1664, {2,8,26,2}*1664, {26,8,2,2}*1664, {2,104,2,2}*1664
   14-fold covers : {2,8,4,14}*1792a, {4,8,2,14}*1792a, {4,8,14,2}*1792a, {14,8,4,2}*1792a, {2,8,28,2}*1792a, {28,8,2,2}*1792a, {2,56,4,2}*1792a, {4,56,2,2}*1792a, {14,8,2,4}*1792, {2,8,14,4}*1792, {2,8,2,28}*1792, {2,56,2,4}*1792, {2,16,2,14}*1792, {2,16,14,2}*1792, {14,16,2,2}*1792, {2,112,2,2}*1792
   15-fold covers : {2,8,2,30}*1920, {2,8,30,2}*1920, {30,8,2,2}*1920, {2,120,2,2}*1920, {2,8,6,10}*1920, {2,8,10,6}*1920, {6,8,2,10}*1920, {6,8,10,2}*1920, {10,8,2,6}*1920, {10,8,6,2}*1920, {2,24,2,10}*1920, {2,24,10,2}*1920, {10,24,2,2}*1920, {2,40,2,6}*1920, {2,40,6,2}*1920, {6,40,2,2}*1920
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (4,5)(6,7)(8,9);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s3 := (11,12);;
s4 := (13,14);;
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*s1*s0*s1, 
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!(1,2);
s1 := Sym(14)!(4,5)(6,7)(8,9);
s2 := Sym(14)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(14)!(11,12);
s4 := Sym(14)!(13,14);
poly := sub<Sym(14)|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*s1*s0*s1, 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope