Polytope of Type {5,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4}*80
if this polytope has a name.
Group : SmallGroup(80,39)
Rank : 4
Schlafli Type : {5,2,4}
Number of vertices, edges, etc : 5, 5, 4, 4
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,4,2} of size 160
   {5,2,4,3} of size 240
   {5,2,4,4} of size 320
   {5,2,4,6} of size 480
   {5,2,4,3} of size 480
   {5,2,4,6} of size 480
   {5,2,4,6} of size 480
   {5,2,4,8} of size 640
   {5,2,4,8} of size 640
   {5,2,4,4} of size 640
   {5,2,4,9} of size 720
   {5,2,4,4} of size 720
   {5,2,4,6} of size 720
   {5,2,4,10} of size 800
   {5,2,4,12} of size 960
   {5,2,4,12} of size 960
   {5,2,4,12} of size 960
   {5,2,4,6} of size 960
   {5,2,4,14} of size 1120
   {5,2,4,5} of size 1200
   {5,2,4,6} of size 1200
   {5,2,4,15} of size 1200
   {5,2,4,8} of size 1280
   {5,2,4,16} of size 1280
   {5,2,4,16} of size 1280
   {5,2,4,4} of size 1280
   {5,2,4,8} of size 1280
   {5,2,4,18} of size 1440
   {5,2,4,9} of size 1440
   {5,2,4,18} of size 1440
   {5,2,4,18} of size 1440
   {5,2,4,4} of size 1440
   {5,2,4,6} of size 1440
   {5,2,4,20} of size 1600
   {5,2,4,5} of size 1600
   {5,2,4,21} of size 1680
   {5,2,4,22} of size 1760
   {5,2,4,24} of size 1920
   {5,2,4,24} of size 1920
   {5,2,4,12} of size 1920
   {5,2,4,6} of size 1920
   {5,2,4,24} of size 1920
   {5,2,4,24} of size 1920
   {5,2,4,12} of size 1920
   {5,2,4,6} of size 1920
   {5,2,4,12} of size 1920
   {5,2,4,4} of size 2000
   {5,2,4,10} of size 2000
Vertex Figure Of :
   {2,5,2,4} of size 160
   {3,5,2,4} of size 480
   {5,5,2,4} of size 480
   {10,5,2,4} of size 800
   {4,5,2,4} of size 960
   {6,5,2,4} of size 960
   {3,5,2,4} of size 960
   {5,5,2,4} of size 960
   {6,5,2,4} of size 960
   {6,5,2,4} of size 960
   {10,5,2,4} of size 960
   {10,5,2,4} of size 960
   {4,5,2,4} of size 1280
   {5,5,2,4} of size 1280
   {4,5,2,4} of size 1920
   {6,5,2,4} of size 1920
   {6,5,2,4} of size 1920
   {10,5,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,8}*160, {10,2,4}*160
   3-fold covers : {5,2,12}*240, {15,2,4}*240
   4-fold covers : {5,2,16}*320, {20,2,4}*320, {10,4,4}*320, {10,2,8}*320
   5-fold covers : {25,2,4}*400, {5,2,20}*400, {5,10,4}*400
   6-fold covers : {5,2,24}*480, {15,2,8}*480, {10,2,12}*480, {10,6,4}*480a, {30,2,4}*480
   7-fold covers : {5,2,28}*560, {35,2,4}*560
   8-fold covers : {5,2,32}*640, {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
   9-fold covers : {5,2,36}*720, {45,2,4}*720, {15,2,12}*720, {15,6,4}*720
   10-fold covers : {25,2,8}*800, {50,2,4}*800, {5,2,40}*800, {5,10,8}*800, {10,2,20}*800, {10,10,4}*800a, {10,10,4}*800c
   11-fold covers : {5,2,44}*880, {55,2,4}*880
   12-fold covers : {5,2,48}*960, {15,2,16}*960, {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, {15,6,4}*960, {15,4,4}*960b
   13-fold covers : {5,2,52}*1040, {65,2,4}*1040
   14-fold covers : {5,2,56}*1120, {35,2,8}*1120, {10,2,28}*1120, {10,14,4}*1120, {70,2,4}*1120
   15-fold covers : {25,2,12}*1200, {75,2,4}*1200, {5,10,12}*1200, {15,2,20}*1200, {5,2,60}*1200, {15,10,4}*1200
   16-fold covers : {5,2,64}*1280, {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, {5,4,4}*1280
   17-fold covers : {5,2,68}*1360, {85,2,4}*1360
   18-fold covers : {5,2,72}*1440, {45,2,8}*1440, {10,2,36}*1440, {10,18,4}*1440a, {90,2,4}*1440, {15,2,24}*1440, {15,6,8}*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
   19-fold covers : {5,2,76}*1520, {95,2,4}*1520
   20-fold covers : {25,2,16}*1600, {100,2,4}*1600, {50,4,4}*1600, {50,2,8}*1600, {5,2,80}*1600, {5,10,16}*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
   21-fold covers : {15,2,28}*1680, {5,2,84}*1680, {35,2,12}*1680, {105,2,4}*1680
   22-fold covers : {5,2,88}*1760, {55,2,8}*1760, {10,2,44}*1760, {10,22,4}*1760, {110,2,4}*1760
   23-fold covers : {5,2,92}*1840, {115,2,4}*1840
   24-fold covers : {15,2,32}*1920, {5,2,96}*1920, {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, {15,6,8}*1920, {15,12,4}*1920, {15,8,4}*1920, {15,4,8}*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
   25-fold covers : {125,2,4}*2000, {25,2,20}*2000, {5,2,100}*2000, {5,10,20}*2000a, {25,10,4}*2000, {5,10,4}*2000a, {5,10,20}*2000b, {5,10,4}*2000b
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (7,8);;
s3 := (6,7)(8,9);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope