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Polytope of Type {10,4,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,2,2}*320
if this polytope has a name.
Group : SmallGroup(320,1612)
Rank : 5
Schlafli Type : {10,4,2,2}
Number of vertices, edges, etc : 10, 20, 4, 2, 2
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,4,2,2,2} of size 640
   {10,4,2,2,3} of size 960
   {10,4,2,2,4} of size 1280
   {10,4,2,2,5} of size 1600
   {10,4,2,2,6} of size 1920
Vertex Figure Of :
   {2,10,4,2,2} of size 640
   {4,10,4,2,2} of size 1280
   {5,10,4,2,2} of size 1600
   {6,10,4,2,2} of size 1920
   {3,10,4,2,2} of size 1920
   {5,10,4,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,2,2,2}*160
   4-fold quotients : {5,2,2,2}*80
   5-fold quotients : {2,4,2,2}*64
   10-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,4,2,2}*640, {10,4,4,2}*640, {10,4,2,4}*640, {10,8,2,2}*640
   3-fold covers : {10,12,2,2}*960, {10,4,2,6}*960, {10,4,6,2}*960, {30,4,2,2}*960a
   4-fold covers : {10,4,4,4}*1280, {20,4,4,2}*1280, {20,4,2,4}*1280, {10,4,8,2}*1280a, {10,8,4,2}*1280a, {20,8,2,2}*1280a, {40,4,2,2}*1280a, {10,4,8,2}*1280b, {10,8,4,2}*1280b, {20,8,2,2}*1280b, {40,4,2,2}*1280b, {10,4,4,2}*1280, {20,4,2,2}*1280, {10,4,2,8}*1280, {10,8,2,4}*1280, {10,16,2,2}*1280
   5-fold covers : {50,4,2,2}*1600, {10,20,2,2}*1600a, {10,4,2,10}*1600, {10,4,10,2}*1600, {10,20,2,2}*1600c
   6-fold covers : {30,4,4,2}*1920, {60,4,2,2}*1920a, {10,4,4,6}*1920, {10,4,12,2}*1920, {10,12,4,2}*1920a, {20,4,2,6}*1920, {20,4,6,2}*1920, {20,12,2,2}*1920, {30,4,2,4}*1920a, {10,4,6,4}*1920a, {10,4,2,12}*1920, {10,12,2,4}*1920, {30,8,2,2}*1920, {10,8,2,6}*1920, {10,8,6,2}*1920, {10,24,2,2}*1920
Permutation Representation (GAP) :
s0 := ( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20);;
s1 := ( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,17)(10,15)(12,13)(14,18)(16,19);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,15)(12,16)(17,19)(18,20);;
s3 := (21,22);;
s4 := (23,24);;
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*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, 
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, 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(24)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20);
s1 := Sym(24)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,17)(10,15)(12,13)(14,18)(16,19);
s2 := Sym(24)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,15)(12,16)(17,19)
(18,20);
s3 := Sym(24)!(21,22);
s4 := Sym(24)!(23,24);
poly := sub<Sym(24)|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*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, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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