Polytope of Type {4,2,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,5}*160
if this polytope has a name.
Group : SmallGroup(160,217)
Rank : 5
Schlafli Type : {4,2,2,5}
Number of vertices, edges, etc : 4, 4, 2, 5, 5
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,2,5,2} of size 320
   {4,2,2,5,3} of size 960
   {4,2,2,5,5} of size 960
   {4,2,2,5,10} of size 1600
   {4,2,2,5,4} of size 1920
   {4,2,2,5,6} of size 1920
   {4,2,2,5,3} of size 1920
   {4,2,2,5,5} of size 1920
   {4,2,2,5,6} of size 1920
   {4,2,2,5,6} of size 1920
   {4,2,2,5,10} of size 1920
   {4,2,2,5,10} of size 1920
Vertex Figure Of :
   {2,4,2,2,5} of size 320
   {3,4,2,2,5} of size 480
   {4,4,2,2,5} of size 640
   {6,4,2,2,5} of size 960
   {3,4,2,2,5} of size 960
   {6,4,2,2,5} of size 960
   {6,4,2,2,5} of size 960
   {8,4,2,2,5} of size 1280
   {8,4,2,2,5} of size 1280
   {4,4,2,2,5} of size 1280
   {9,4,2,2,5} of size 1440
   {4,4,2,2,5} of size 1440
   {6,4,2,2,5} of size 1440
   {10,4,2,2,5} of size 1600
   {12,4,2,2,5} of size 1920
   {12,4,2,2,5} of size 1920
   {12,4,2,2,5} of size 1920
   {6,4,2,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,2,5}*320, {8,2,2,5}*320, {4,2,2,10}*320
   3-fold covers : {12,2,2,5}*480, {4,6,2,5}*480a, {4,2,2,15}*480
   4-fold covers : {4,8,2,5}*640a, {8,4,2,5}*640a, {4,8,2,5}*640b, {8,4,2,5}*640b, {4,4,2,5}*640, {16,2,2,5}*640, {4,2,2,20}*640, {4,4,2,10}*640, {4,2,4,10}*640, {8,2,2,10}*640
   5-fold covers : {4,2,2,25}*800, {20,2,2,5}*800, {4,2,10,5}*800, {4,10,2,5}*800
   6-fold covers : {4,12,2,5}*960a, {12,4,2,5}*960a, {24,2,2,5}*960, {8,6,2,5}*960, {4,4,2,15}*960, {8,2,2,15}*960, {12,2,2,10}*960, {4,2,6,10}*960, {4,6,2,10}*960a, {4,2,2,30}*960
   7-fold covers : {28,2,2,5}*1120, {4,14,2,5}*1120, {4,2,2,35}*1120
   8-fold covers : {4,8,2,5}*1280a, {8,4,2,5}*1280a, {8,8,2,5}*1280a, {8,8,2,5}*1280b, {8,8,2,5}*1280c, {8,8,2,5}*1280d, {4,16,2,5}*1280a, {16,4,2,5}*1280a, {4,16,2,5}*1280b, {16,4,2,5}*1280b, {4,4,2,5}*1280, {4,8,2,5}*1280b, {8,4,2,5}*1280b, {32,2,2,5}*1280, {4,4,4,10}*1280, {4,4,2,20}*1280, {4,2,4,20}*1280, {4,8,2,10}*1280a, {8,4,2,10}*1280a, {4,8,2,10}*1280b, {8,4,2,10}*1280b, {4,4,2,10}*1280, {4,2,8,10}*1280, {8,2,4,10}*1280, {8,2,2,20}*1280, {4,2,2,40}*1280, {16,2,2,10}*1280
   9-fold covers : {36,2,2,5}*1440, {4,18,2,5}*1440a, {4,2,2,45}*1440, {12,6,2,5}*1440a, {12,6,2,5}*1440b, {12,6,2,5}*1440c, {12,2,2,15}*1440, {4,2,6,15}*1440, {4,6,2,15}*1440a, {4,6,2,5}*1440
   10-fold covers : {4,4,2,25}*1600, {8,2,2,25}*1600, {4,2,2,50}*1600, {4,20,2,5}*1600, {20,4,2,5}*1600, {40,2,2,5}*1600, {8,2,10,5}*1600, {8,10,2,5}*1600, {4,4,10,5}*1600, {20,2,2,10}*1600, {4,2,10,10}*1600a, {4,2,10,10}*1600b, {4,10,2,10}*1600
   11-fold covers : {44,2,2,5}*1760, {4,22,2,5}*1760, {4,2,2,55}*1760
   12-fold covers : {4,8,2,15}*1920a, {8,4,2,15}*1920a, {8,12,2,5}*1920a, {12,8,2,5}*1920a, {4,24,2,5}*1920a, {24,4,2,5}*1920a, {4,8,2,15}*1920b, {8,4,2,15}*1920b, {8,12,2,5}*1920b, {12,8,2,5}*1920b, {4,24,2,5}*1920b, {24,4,2,5}*1920b, {4,4,2,15}*1920, {4,12,2,5}*1920a, {12,4,2,5}*1920a, {16,2,2,15}*1920, {16,6,2,5}*1920, {48,2,2,5}*1920, {4,4,2,30}*1920, {4,4,6,10}*1920, {4,12,2,10}*1920a, {12,4,2,10}*1920a, {4,2,4,30}*1920a, {4,2,2,60}*1920, {4,6,4,10}*1920a, {4,2,12,10}*1920, {12,2,4,10}*1920, {4,2,6,20}*1920a, {4,6,2,20}*1920a, {12,2,2,20}*1920, {8,2,2,30}*1920, {8,2,6,10}*1920, {8,6,2,10}*1920, {24,2,2,10}*1920, {12,4,2,5}*1920b, {4,2,6,15}*1920, {4,6,2,5}*1920b, {12,6,2,5}*1920a, {4,2,4,15}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope