Polytope of Type {10,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,2}*160
if this polytope has a name.
Group : SmallGroup(160,217)
Rank : 4
Schlafli Type : {10,4,2}
Number of vertices, edges, etc : 10, 20, 4, 2
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,4,2,2} of size 320
   {10,4,2,3} of size 480
   {10,4,2,4} of size 640
   {10,4,2,5} of size 800
   {10,4,2,6} of size 960
   {10,4,2,7} of size 1120
   {10,4,2,8} of size 1280
   {10,4,2,9} of size 1440
   {10,4,2,10} of size 1600
   {10,4,2,11} of size 1760
   {10,4,2,12} of size 1920
Vertex Figure Of :
   {2,10,4,2} of size 320
   {4,10,4,2} of size 640
   {5,10,4,2} of size 800
   {3,10,4,2} of size 960
   {5,10,4,2} of size 960
   {6,10,4,2} of size 960
   {8,10,4,2} of size 1280
   {10,10,4,2} of size 1600
   {10,10,4,2} of size 1600
   {10,10,4,2} of size 1600
   {12,10,4,2} of size 1920
   {4,10,4,2} of size 1920
   {6,10,4,2} of size 1920
   {3,10,4,2} of size 1920
   {5,10,4,2} of size 1920
   {6,10,4,2} of size 1920
   {6,10,4,2} of size 1920
   {10,10,4,2} of size 1920
   {10,10,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,2,2}*80
   4-fold quotients : {5,2,2}*40
   5-fold quotients : {2,4,2}*32
   10-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,4,2}*320, {10,4,4}*320, {10,8,2}*320
   3-fold covers : {10,12,2}*480, {10,4,6}*480, {30,4,2}*480a
   4-fold covers : {20,4,4}*640, {40,4,2}*640a, {20,4,2}*640, {40,4,2}*640b, {20,8,2}*640a, {20,8,2}*640b, {10,4,8}*640a, {10,8,4}*640a, {10,4,8}*640b, {10,8,4}*640b, {10,4,4}*640, {10,16,2}*640
   5-fold covers : {50,4,2}*800, {10,20,2}*800a, {10,4,10}*800, {10,20,2}*800c
   6-fold covers : {10,4,12}*960, {10,12,4}*960a, {20,4,6}*960, {10,24,2}*960, {10,8,6}*960, {20,12,2}*960, {60,4,2}*960a, {30,4,4}*960, {30,8,2}*960
   7-fold covers : {10,28,2}*1120, {10,4,14}*1120, {70,4,2}*1120
   8-fold covers : {10,4,8}*1280a, {10,8,4}*1280a, {20,8,2}*1280a, {40,4,2}*1280a, {10,8,8}*1280a, {10,8,8}*1280b, {10,8,8}*1280c, {40,8,2}*1280a, {40,8,2}*1280b, {40,8,2}*1280c, {10,8,8}*1280d, {40,8,2}*1280d, {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, {20,16,2}*1280a, {80,4,2}*1280a, {10,4,16}*1280b, {10,16,4}*1280b, {20,16,2}*1280b, {80,4,2}*1280b, {10,4,4}*1280, {10,4,8}*1280b, {10,8,4}*1280b, {20,4,2}*1280a, {40,4,2}*1280b, {20,8,2}*1280b, {10,32,2}*1280
   9-fold covers : {10,36,2}*1440, {10,4,18}*1440, {90,4,2}*1440a, {10,12,6}*1440a, {10,12,6}*1440b, {30,12,2}*1440a, {10,12,6}*1440c, {30,12,2}*1440b, {30,4,6}*1440, {30,12,2}*1440c, {10,4,6}*1440c, {30,4,2}*1440
   10-fold covers : {100,4,2}*1600, {50,4,4}*1600, {50,8,2}*1600, {10,4,20}*1600, {10,20,4}*1600a, {20,4,10}*1600, {10,40,2}*1600a, {10,8,10}*1600, {20,20,2}*1600a, {20,20,2}*1600c, {10,40,2}*1600c, {10,20,4}*1600c
   11-fold covers : {10,44,2}*1760, {10,4,22}*1760, {110,4,2}*1760
   12-fold covers : {60,4,4}*1920, {20,12,4}*1920a, {20,4,12}*1920, {30,4,8}*1920a, {30,8,4}*1920a, {60,8,2}*1920a, {120,4,2}*1920a, {10,8,12}*1920a, {10,12,8}*1920a, {20,8,6}*1920a, {10,4,24}*1920a, {10,24,4}*1920a, {40,4,6}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {30,4,8}*1920b, {30,8,4}*1920b, {60,8,2}*1920b, {120,4,2}*1920b, {10,8,12}*1920b, {10,12,8}*1920b, {20,8,6}*1920b, {10,4,24}*1920b, {10,24,4}*1920b, {40,4,6}*1920b, {40,12,2}*1920b, {20,24,2}*1920b, {30,4,4}*1920a, {60,4,2}*1920a, {10,4,12}*1920a, {10,12,4}*1920a, {20,4,6}*1920a, {20,12,2}*1920a, {30,16,2}*1920, {10,16,6}*1920, {10,48,2}*1920, {10,12,4}*1920b, {20,12,2}*1920b, {10,4,6}*1920, {10,12,6}*1920a, {30,12,2}*1920b, {30,4,2}*1920b
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);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
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(22)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20);
s1 := Sym(22)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,17)(10,15)(12,13)(14,18)(16,19);
s2 := Sym(22)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,15)(12,16)(17,19)
(18,20);
s3 := Sym(22)!(21,22);
poly := sub<Sym(22)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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 >;

to this polytope