Polytope of Type {4,10,2}

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

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

to this polytope