Polytope of Type {10,2,4}

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

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (12,13);;
s3 := (11,12)(13,14);;
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*s2*s3, 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(14)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(14)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(14)!(12,13);
s3 := Sym(14)!(11,12)(13,14);
poly := sub<Sym(14)|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*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope