Polytope of Type {4,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,10}*160
if this polytope has a name.
Group : SmallGroup(160,217)
Rank : 4
Schlafli Type : {4,2,10}
Number of vertices, edges, etc : 4, 4, 10, 10
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,10,2} of size 320
   {4,2,10,4} of size 640
   {4,2,10,5} of size 800
   {4,2,10,3} of size 960
   {4,2,10,3} of size 960
   {4,2,10,5} of size 960
   {4,2,10,5} of size 960
   {4,2,10,6} of size 960
   {4,2,10,8} of size 1280
   {4,2,10,4} of size 1600
   {4,2,10,10} of size 1600
   {4,2,10,10} of size 1600
   {4,2,10,10} of size 1600
   {4,2,10,12} of size 1920
   {4,2,10,4} of size 1920
   {4,2,10,4} of size 1920
   {4,2,10,6} of size 1920
   {4,2,10,6} of size 1920
   {4,2,10,3} of size 1920
   {4,2,10,5} of size 1920
   {4,2,10,6} of size 1920
   {4,2,10,6} of size 1920
   {4,2,10,6} of size 1920
   {4,2,10,6} of size 1920
   {4,2,10,10} of size 1920
   {4,2,10,10} of size 1920
   {4,2,10,10} of size 1920
   {4,2,10,10} of size 1920
Vertex Figure Of :
   {2,4,2,10} of size 320
   {3,4,2,10} of size 480
   {4,4,2,10} of size 640
   {6,4,2,10} of size 960
   {3,4,2,10} of size 960
   {6,4,2,10} of size 960
   {6,4,2,10} of size 960
   {8,4,2,10} of size 1280
   {8,4,2,10} of size 1280
   {4,4,2,10} of size 1280
   {9,4,2,10} of size 1440
   {4,4,2,10} of size 1440
   {6,4,2,10} of size 1440
   {10,4,2,10} of size 1600
   {12,4,2,10} of size 1920
   {12,4,2,10} of size 1920
   {12,4,2,10} of size 1920
   {6,4,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,5}*80, {2,2,10}*80
   4-fold quotients : {2,2,5}*40
   5-fold quotients : {4,2,2}*32
   10-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,20}*320, {4,4,10}*320, {8,2,10}*320
   3-fold covers : {12,2,10}*480, {4,6,10}*480a, {4,2,30}*480
   4-fold covers : {4,4,20}*640, {4,2,40}*640, {8,2,20}*640, {4,8,10}*640a, {8,4,10}*640a, {4,8,10}*640b, {8,4,10}*640b, {4,4,10}*640, {16,2,10}*640
   5-fold covers : {4,2,50}*800, {20,2,10}*800, {4,10,10}*800a, {4,10,10}*800c
   6-fold covers : {12,2,20}*960, {4,12,10}*960a, {12,4,10}*960, {4,6,20}*960a, {24,2,10}*960, {8,6,10}*960, {4,2,60}*960, {4,4,30}*960, {8,2,30}*960
   7-fold covers : {28,2,10}*1120, {4,14,10}*1120, {4,2,70}*1120
   8-fold covers : {4,8,10}*1280a, {8,4,10}*1280a, {8,8,10}*1280a, {8,8,10}*1280b, {8,8,10}*1280c, {8,8,10}*1280d, {8,2,40}*1280, {8,4,20}*1280a, {4,4,40}*1280a, {8,4,20}*1280b, {4,4,40}*1280b, {4,8,20}*1280a, {4,4,20}*1280a, {4,4,20}*1280b, {4,8,20}*1280b, {4,8,20}*1280c, {4,8,20}*1280d, {4,16,10}*1280a, {16,4,10}*1280a, {4,16,10}*1280b, {16,4,10}*1280b, {4,4,10}*1280, {4,8,10}*1280b, {8,4,10}*1280b, {16,2,20}*1280, {4,2,80}*1280, {32,2,10}*1280
   9-fold covers : {36,2,10}*1440, {4,18,10}*1440a, {4,2,90}*1440, {12,6,10}*1440a, {12,6,10}*1440b, {12,6,10}*1440c, {4,6,30}*1440a, {12,2,30}*1440, {4,6,30}*1440b, {4,6,30}*1440c, {4,6,10}*1440
   10-fold covers : {4,2,100}*1600, {4,4,50}*1600, {8,2,50}*1600, {20,2,20}*1600, {4,10,20}*1600a, {4,20,10}*1600a, {20,4,10}*1600, {40,2,10}*1600, {8,10,10}*1600a, {4,10,20}*1600b, {8,10,10}*1600c, {4,20,10}*1600c
   11-fold covers : {44,2,10}*1760, {4,22,10}*1760, {4,2,110}*1760
   12-fold covers : {4,4,60}*1920, {4,12,20}*1920a, {12,4,20}*1920, {4,8,30}*1920a, {8,4,30}*1920a, {8,12,10}*1920a, {12,8,10}*1920a, {4,24,10}*1920a, {24,4,10}*1920a, {4,8,30}*1920b, {8,4,30}*1920b, {8,12,10}*1920b, {12,8,10}*1920b, {4,24,10}*1920b, {24,4,10}*1920b, {4,4,30}*1920a, {4,12,10}*1920a, {12,4,10}*1920a, {8,2,60}*1920, {4,2,120}*1920, {8,6,20}*1920, {4,6,40}*1920a, {12,2,40}*1920, {24,2,20}*1920, {16,2,30}*1920, {16,6,10}*1920, {48,2,10}*1920, {12,4,10}*1920b, {4,6,10}*1920b, {4,6,20}*1920b, {12,6,10}*1920a, {4,6,30}*1920, {4,4,30}*1920d
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14);;
s3 := ( 5, 9)( 6, 7)( 8,13)(10,11)(12,14);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope