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

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

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