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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,2,2}*160
if this polytope has a name.
Group : SmallGroup(160,237)
Rank : 5
Schlafli Type : {2,10,2,2}
Number of vertices, edges, etc : 2, 10, 10, 2, 2
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,2,2,2} of size 320
   {2,10,2,2,3} of size 480
   {2,10,2,2,4} of size 640
   {2,10,2,2,5} of size 800
   {2,10,2,2,6} of size 960
   {2,10,2,2,7} of size 1120
   {2,10,2,2,8} of size 1280
   {2,10,2,2,9} of size 1440
   {2,10,2,2,10} of size 1600
   {2,10,2,2,11} of size 1760
   {2,10,2,2,12} of size 1920
Vertex Figure Of :
   {2,2,10,2,2} of size 320
   {3,2,10,2,2} of size 480
   {4,2,10,2,2} of size 640
   {5,2,10,2,2} of size 800
   {6,2,10,2,2} of size 960
   {7,2,10,2,2} of size 1120
   {8,2,10,2,2} of size 1280
   {9,2,10,2,2} of size 1440
   {10,2,10,2,2} of size 1600
   {11,2,10,2,2} of size 1760
   {12,2,10,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,5,2,2}*80
   5-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,20,2,2}*320, {2,10,2,4}*320, {2,10,4,2}*320, {4,10,2,2}*320
   3-fold covers : {2,10,2,6}*480, {2,10,6,2}*480, {6,10,2,2}*480, {2,30,2,2}*480
   4-fold covers : {2,20,4,2}*640, {4,20,2,2}*640, {2,20,2,4}*640, {2,10,4,4}*640, {4,10,4,2}*640, {4,10,2,4}*640, {2,40,2,2}*640, {2,10,2,8}*640, {2,10,8,2}*640, {8,10,2,2}*640
   5-fold covers : {2,50,2,2}*800, {2,10,2,10}*800, {2,10,10,2}*800a, {2,10,10,2}*800c, {10,10,2,2}*800a, {10,10,2,2}*800b
   6-fold covers : {2,10,2,12}*960, {2,10,12,2}*960, {12,10,2,2}*960, {2,20,2,6}*960, {2,20,6,2}*960a, {6,20,2,2}*960a, {2,10,4,6}*960, {2,10,6,4}*960a, {4,10,2,6}*960, {4,10,6,2}*960, {6,10,2,4}*960, {6,10,4,2}*960, {2,60,2,2}*960, {2,30,2,4}*960, {2,30,4,2}*960a, {4,30,2,2}*960a
   7-fold covers : {2,10,2,14}*1120, {2,10,14,2}*1120, {14,10,2,2}*1120, {2,70,2,2}*1120
   8-fold covers : {2,20,4,4}*1280, {4,20,4,2}*1280, {4,10,4,4}*1280, {4,20,2,4}*1280, {2,10,4,8}*1280a, {2,10,8,4}*1280a, {2,20,8,2}*1280a, {8,20,2,2}*1280a, {2,40,4,2}*1280a, {4,40,2,2}*1280a, {2,10,4,8}*1280b, {2,10,8,4}*1280b, {2,20,8,2}*1280b, {8,20,2,2}*1280b, {2,40,4,2}*1280b, {4,40,2,2}*1280b, {2,10,4,4}*1280, {2,20,4,2}*1280, {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, {2,20,2,8}*1280, {2,40,2,4}*1280, {2,10,2,16}*1280, {2,10,16,2}*1280, {16,10,2,2}*1280, {2,80,2,2}*1280
   9-fold covers : {2,10,2,18}*1440, {2,10,18,2}*1440, {18,10,2,2}*1440, {2,90,2,2}*1440, {2,10,6,6}*1440a, {2,10,6,6}*1440b, {2,10,6,6}*1440c, {2,30,6,2}*1440a, {6,10,2,6}*1440, {6,10,6,2}*1440, {6,30,2,2}*1440a, {2,30,2,6}*1440, {2,30,6,2}*1440b, {2,30,6,2}*1440c, {6,30,2,2}*1440b, {6,30,2,2}*1440c
   10-fold covers : {2,100,2,2}*1600, {2,50,2,4}*1600, {2,50,4,2}*1600, {4,50,2,2}*1600, {2,10,2,20}*1600, {2,10,20,2}*1600a, {2,20,2,10}*1600, {2,20,10,2}*1600a, {2,20,10,2}*1600b, {10,20,2,2}*1600a, {10,20,2,2}*1600b, {20,10,2,2}*1600a, {2,10,4,10}*1600, {2,10,10,4}*1600a, {4,10,2,10}*1600, {4,10,10,2}*1600a, {4,10,10,2}*1600b, {10,10,2,4}*1600a, {10,10,2,4}*1600b, {10,10,4,2}*1600a, {10,10,4,2}*1600b, {2,10,10,4}*1600c, {2,10,20,2}*1600c, {20,10,2,2}*1600c
   11-fold covers : {2,10,2,22}*1760, {2,10,22,2}*1760, {22,10,2,2}*1760, {2,110,2,2}*1760
   12-fold covers : {2,30,4,4}*1920, {2,60,4,2}*1920a, {4,60,2,2}*1920a, {6,10,4,4}*1920, {2,10,4,12}*1920, {2,10,12,4}*1920a, {2,20,4,6}*1920, {4,20,2,6}*1920, {4,20,6,2}*1920, {6,20,4,2}*1920, {2,20,12,2}*1920, {12,20,2,2}*1920, {4,30,2,4}*1920a, {4,30,4,2}*1920a, {2,60,2,4}*1920, {4,10,6,4}*1920a, {4,10,4,6}*1920, {4,10,2,12}*1920, {12,10,2,4}*1920, {6,20,2,4}*1920a, {4,10,12,2}*1920, {12,10,4,2}*1920, {2,20,6,4}*1920a, {2,20,2,12}*1920, {2,30,2,8}*1920, {2,30,8,2}*1920, {8,30,2,2}*1920, {2,120,2,2}*1920, {2,10,6,8}*1920, {2,10,8,6}*1920, {6,10,2,8}*1920, {6,10,8,2}*1920, {8,10,2,6}*1920, {8,10,6,2}*1920, {2,10,2,24}*1920, {2,10,24,2}*1920, {24,10,2,2}*1920, {2,40,2,6}*1920, {2,40,6,2}*1920, {6,40,2,2}*1920, {2,10,4,6}*1920, {2,10,6,4}*1920a, {2,10,6,6}*1920, {2,20,6,2}*1920a, {2,30,6,2}*1920, {6,20,2,2}*1920a, {6,30,2,2}*1920, {2,30,4,2}*1920, {4,30,2,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);;
s3 := (13,14);;
s4 := (15,16);;
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*s1*s0*s1, 
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, 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(16)!(1,2);
s1 := Sym(16)!( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(16)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);
s3 := Sym(16)!(13,14);
s4 := Sym(16)!(15,16);
poly := sub<Sym(16)|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*s1*s0*s1, 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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