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

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

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

Permutation Representation (Magma) :

s0 := Sym(14)!(2,3)(4,5)(6,7);
s1 := Sym(14)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(14)!( 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*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, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope