Questions?
See the FAQ
or other info.

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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,2,5}*160
if this polytope has a name.
Group : SmallGroup(160,217)
Rank : 5
Schlafli Type : {2,4,2,5}
Number of vertices, edges, etc : 2, 4, 4, 5, 5
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,2,5,2} of size 320
   {2,4,2,5,3} of size 960
   {2,4,2,5,5} of size 960
   {2,4,2,5,10} of size 1600
   {2,4,2,5,4} of size 1920
   {2,4,2,5,6} of size 1920
   {2,4,2,5,3} of size 1920
   {2,4,2,5,5} of size 1920
   {2,4,2,5,6} of size 1920
   {2,4,2,5,6} of size 1920
   {2,4,2,5,10} of size 1920
   {2,4,2,5,10} of size 1920
Vertex Figure Of :
   {2,2,4,2,5} of size 320
   {3,2,4,2,5} of size 480
   {4,2,4,2,5} of size 640
   {5,2,4,2,5} of size 800
   {6,2,4,2,5} of size 960
   {7,2,4,2,5} of size 1120
   {8,2,4,2,5} of size 1280
   {9,2,4,2,5} of size 1440
   {10,2,4,2,5} of size 1600
   {11,2,4,2,5} of size 1760
   {12,2,4,2,5} 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, {2,8,2,5}*320, {2,4,2,10}*320
   3-fold covers : {2,12,2,5}*480, {6,4,2,5}*480a, {2,4,2,15}*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, {2,16,2,5}*640, {2,4,2,20}*640, {2,4,4,10}*640, {4,4,2,10}*640, {2,8,2,10}*640
   5-fold covers : {2,4,2,25}*800, {2,20,2,5}*800, {10,4,2,5}*800, {2,4,10,5}*800
   6-fold covers : {4,12,2,5}*960a, {12,4,2,5}*960a, {2,24,2,5}*960, {6,8,2,5}*960, {4,4,2,15}*960, {2,8,2,15}*960, {2,12,2,10}*960, {2,4,6,10}*960a, {6,4,2,10}*960a, {2,4,2,30}*960
   7-fold covers : {2,28,2,5}*1120, {14,4,2,5}*1120, {2,4,2,35}*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, {2,32,2,5}*1280, {4,4,4,10}*1280, {2,4,4,20}*1280, {4,4,2,20}*1280, {2,4,8,10}*1280a, {2,8,4,10}*1280a, {4,8,2,10}*1280a, {8,4,2,10}*1280a, {2,4,8,10}*1280b, {2,8,4,10}*1280b, {4,8,2,10}*1280b, {8,4,2,10}*1280b, {2,4,4,10}*1280, {4,4,2,10}*1280, {2,8,2,20}*1280, {2,4,2,40}*1280, {2,16,2,10}*1280
   9-fold covers : {2,36,2,5}*1440, {18,4,2,5}*1440a, {2,4,2,45}*1440, {6,12,2,5}*1440a, {6,12,2,5}*1440b, {6,12,2,5}*1440c, {2,12,2,15}*1440, {6,4,2,15}*1440a, {2,4,6,15}*1440, {6,4,2,5}*1440
   10-fold covers : {4,4,2,25}*1600, {2,8,2,25}*1600, {2,4,2,50}*1600, {4,20,2,5}*1600, {20,4,2,5}*1600, {2,40,2,5}*1600, {10,8,2,5}*1600, {2,8,10,5}*1600, {4,4,10,5}*1600, {2,20,2,10}*1600, {2,4,10,10}*1600a, {10,4,2,10}*1600, {2,4,10,10}*1600c
   11-fold covers : {2,44,2,5}*1760, {22,4,2,5}*1760, {2,4,2,55}*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, {2,16,2,15}*1920, {6,16,2,5}*1920, {2,48,2,5}*1920, {2,4,4,30}*1920, {4,4,2,30}*1920, {4,4,6,10}*1920, {6,4,4,10}*1920, {2,4,12,10}*1920a, {2,12,4,10}*1920, {4,12,2,10}*1920a, {12,4,2,10}*1920a, {2,4,2,60}*1920, {6,4,2,20}*1920a, {2,4,6,20}*1920a, {2,12,2,20}*1920, {2,8,2,30}*1920, {2,8,6,10}*1920, {6,8,2,10}*1920, {2,24,2,10}*1920, {4,12,2,5}*1920b, {6,4,2,5}*1920b, {6,12,2,5}*1920a, {2,4,6,15}*1920, {2,4,4,15}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4)(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*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, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(11)!(1,2);
s1 := Sym(11)!(4,5);
s2 := Sym(11)!(3,4)(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*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, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

to this polytope