Polytope of Type {2,10,4}

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

s0 := (1,2);;
s1 := ( 5, 6)( 8, 9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22);;
s2 := ( 3, 5)( 4,13)( 6,10)( 7, 8)( 9,19)(12,17)(14,15)(16,20)(18,21);;
s3 := ( 3, 4)( 5, 8)( 6, 9)( 7,12)(10,15)(11,16)(13,17)(14,18)(19,21)(20,22);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(22)!(1,2);
s1 := Sym(22)!( 5, 6)( 8, 9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22);
s2 := Sym(22)!( 3, 5)( 4,13)( 6,10)( 7, 8)( 9,19)(12,17)(14,15)(16,20)(18,21);
s3 := Sym(22)!( 3, 4)( 5, 8)( 6, 9)( 7,12)(10,15)(11,16)(13,17)(14,18)(19,21)
(20,22);
poly := sub<Sym(22)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope