Polytope of Type {20,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,2,3}*240
if this polytope has a name.
Group : SmallGroup(240,137)
Rank : 4
Schlafli Type : {20,2,3}
Number of vertices, edges, etc : 20, 20, 3, 3
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,2,3,2} of size 480
   {20,2,3,3} of size 960
   {20,2,3,4} of size 960
   {20,2,3,6} of size 1440
   {20,2,3,4} of size 1920
   {20,2,3,6} of size 1920
Vertex Figure Of :
   {2,20,2,3} of size 480
   {4,20,2,3} of size 960
   {6,20,2,3} of size 1440
   {6,20,2,3} of size 1440
   {8,20,2,3} of size 1920
   {8,20,2,3} of size 1920
   {4,20,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,2,3}*120
   4-fold quotients : {5,2,3}*60
   5-fold quotients : {4,2,3}*48
   10-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {40,2,3}*480, {20,2,6}*480
   3-fold covers : {20,2,9}*720, {20,6,3}*720, {60,2,3}*720
   4-fold covers : {80,2,3}*960, {20,2,12}*960, {20,4,6}*960, {40,2,6}*960, {20,4,3}*960
   5-fold covers : {100,2,3}*1200, {20,2,15}*1200
   6-fold covers : {40,2,9}*1440, {20,2,18}*1440, {40,6,3}*1440, {120,2,3}*1440, {20,6,6}*1440a, {20,6,6}*1440c, {60,2,6}*1440
   7-fold covers : {20,2,21}*1680, {140,2,3}*1680
   8-fold covers : {160,2,3}*1920, {20,4,12}*1920, {20,8,6}*1920a, {40,4,6}*1920a, {20,8,6}*1920b, {40,4,6}*1920b, {20,4,6}*1920a, {40,2,12}*1920, {20,2,24}*1920, {80,2,6}*1920, {20,8,3}*1920, {40,4,3}*1920, {20,4,6}*1920b
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)(18,20);;
s2 := (22,23);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(23)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);
s1 := Sym(23)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)
(18,20);
s2 := Sym(23)!(22,23);
s3 := Sym(23)!(21,22);
poly := sub<Sym(23)|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, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope