Polytope of Type {4,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,5}*80
if this polytope has a name.
Group : SmallGroup(80,39)
Rank : 4
Schlafli Type : {4,2,5}
Number of vertices, edges, etc : 4, 4, 5, 5
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,5,2} of size 160
   {4,2,5,3} of size 480
   {4,2,5,5} of size 480
   {4,2,5,10} of size 800
   {4,2,5,4} of size 960
   {4,2,5,6} of size 960
   {4,2,5,3} of size 960
   {4,2,5,5} of size 960
   {4,2,5,6} of size 960
   {4,2,5,6} of size 960
   {4,2,5,10} of size 960
   {4,2,5,10} of size 960
   {4,2,5,4} of size 1280
   {4,2,5,5} of size 1280
   {4,2,5,4} of size 1920
   {4,2,5,6} of size 1920
   {4,2,5,6} of size 1920
   {4,2,5,10} of size 1920
Vertex Figure Of :
   {2,4,2,5} of size 160
   {3,4,2,5} of size 240
   {4,4,2,5} of size 320
   {6,4,2,5} of size 480
   {3,4,2,5} of size 480
   {6,4,2,5} of size 480
   {6,4,2,5} of size 480
   {8,4,2,5} of size 640
   {8,4,2,5} of size 640
   {4,4,2,5} of size 640
   {9,4,2,5} of size 720
   {4,4,2,5} of size 720
   {6,4,2,5} of size 720
   {10,4,2,5} of size 800
   {12,4,2,5} of size 960
   {12,4,2,5} of size 960
   {12,4,2,5} of size 960
   {6,4,2,5} of size 960
   {14,4,2,5} of size 1120
   {5,4,2,5} of size 1200
   {6,4,2,5} of size 1200
   {15,4,2,5} of size 1200
   {8,4,2,5} of size 1280
   {16,4,2,5} of size 1280
   {16,4,2,5} of size 1280
   {4,4,2,5} of size 1280
   {8,4,2,5} of size 1280
   {18,4,2,5} of size 1440
   {9,4,2,5} of size 1440
   {18,4,2,5} of size 1440
   {18,4,2,5} of size 1440
   {4,4,2,5} of size 1440
   {6,4,2,5} of size 1440
   {20,4,2,5} of size 1600
   {5,4,2,5} of size 1600
   {21,4,2,5} of size 1680
   {22,4,2,5} of size 1760
   {24,4,2,5} of size 1920
   {24,4,2,5} of size 1920
   {12,4,2,5} of size 1920
   {6,4,2,5} of size 1920
   {24,4,2,5} of size 1920
   {24,4,2,5} of size 1920
   {12,4,2,5} of size 1920
   {6,4,2,5} of size 1920
   {12,4,2,5} of size 1920
   {4,4,2,5} of size 2000
   {10,4,2,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,5}*160, {4,2,10}*160
   3-fold covers : {12,2,5}*240, {4,2,15}*240
   4-fold covers : {16,2,5}*320, {4,2,20}*320, {4,4,10}*320, {8,2,10}*320
   5-fold covers : {4,2,25}*400, {20,2,5}*400, {4,10,5}*400
   6-fold covers : {24,2,5}*480, {8,2,15}*480, {12,2,10}*480, {4,6,10}*480a, {4,2,30}*480
   7-fold covers : {28,2,5}*560, {4,2,35}*560
   8-fold covers : {32,2,5}*640, {4,4,20}*640, {4,2,40}*640, {8,2,20}*640, {4,8,10}*640a, {8,4,10}*640a, {4,8,10}*640b, {8,4,10}*640b, {4,4,10}*640, {16,2,10}*640
   9-fold covers : {36,2,5}*720, {4,2,45}*720, {12,2,15}*720, {4,6,15}*720
   10-fold covers : {8,2,25}*800, {4,2,50}*800, {40,2,5}*800, {8,10,5}*800, {20,2,10}*800, {4,10,10}*800a, {4,10,10}*800c
   11-fold covers : {44,2,5}*880, {4,2,55}*880
   12-fold covers : {48,2,5}*960, {16,2,15}*960, {12,2,20}*960, {4,12,10}*960a, {12,4,10}*960, {4,6,20}*960a, {24,2,10}*960, {8,6,10}*960, {4,2,60}*960, {4,4,30}*960, {8,2,30}*960, {4,6,15}*960, {4,4,15}*960b
   13-fold covers : {52,2,5}*1040, {4,2,65}*1040
   14-fold covers : {56,2,5}*1120, {8,2,35}*1120, {28,2,10}*1120, {4,14,10}*1120, {4,2,70}*1120
   15-fold covers : {12,2,25}*1200, {4,2,75}*1200, {12,10,5}*1200, {20,2,15}*1200, {60,2,5}*1200, {4,10,15}*1200
   16-fold covers : {64,2,5}*1280, {4,8,10}*1280a, {8,4,10}*1280a, {8,8,10}*1280a, {8,8,10}*1280b, {8,8,10}*1280c, {8,8,10}*1280d, {8,2,40}*1280, {8,4,20}*1280a, {4,4,40}*1280a, {8,4,20}*1280b, {4,4,40}*1280b, {4,8,20}*1280a, {4,4,20}*1280a, {4,4,20}*1280b, {4,8,20}*1280b, {4,8,20}*1280c, {4,8,20}*1280d, {4,16,10}*1280a, {16,4,10}*1280a, {4,16,10}*1280b, {16,4,10}*1280b, {4,4,10}*1280, {4,8,10}*1280b, {8,4,10}*1280b, {16,2,20}*1280, {4,2,80}*1280, {32,2,10}*1280, {4,4,5}*1280
   17-fold covers : {68,2,5}*1360, {4,2,85}*1360
   18-fold covers : {72,2,5}*1440, {8,2,45}*1440, {36,2,10}*1440, {4,18,10}*1440a, {4,2,90}*1440, {24,2,15}*1440, {8,6,15}*1440, {12,6,10}*1440a, {12,6,10}*1440b, {12,6,10}*1440c, {4,6,30}*1440a, {12,2,30}*1440, {4,6,30}*1440b, {4,6,30}*1440c, {4,6,10}*1440
   19-fold covers : {76,2,5}*1520, {4,2,95}*1520
   20-fold covers : {16,2,25}*1600, {4,2,100}*1600, {4,4,50}*1600, {8,2,50}*1600, {80,2,5}*1600, {16,10,5}*1600, {20,2,20}*1600, {4,10,20}*1600a, {4,20,10}*1600a, {20,4,10}*1600, {40,2,10}*1600, {8,10,10}*1600a, {4,10,20}*1600b, {8,10,10}*1600c, {4,20,10}*1600c
   21-fold covers : {28,2,15}*1680, {84,2,5}*1680, {12,2,35}*1680, {4,2,105}*1680
   22-fold covers : {88,2,5}*1760, {8,2,55}*1760, {44,2,10}*1760, {4,22,10}*1760, {4,2,110}*1760
   23-fold covers : {92,2,5}*1840, {4,2,115}*1840
   24-fold covers : {32,2,15}*1920, {96,2,5}*1920, {4,4,60}*1920, {4,12,20}*1920a, {12,4,20}*1920, {4,8,30}*1920a, {8,4,30}*1920a, {8,12,10}*1920a, {12,8,10}*1920a, {4,24,10}*1920a, {24,4,10}*1920a, {4,8,30}*1920b, {8,4,30}*1920b, {8,12,10}*1920b, {12,8,10}*1920b, {4,24,10}*1920b, {24,4,10}*1920b, {4,4,30}*1920a, {4,12,10}*1920a, {12,4,10}*1920a, {8,2,60}*1920, {4,2,120}*1920, {8,6,20}*1920, {4,6,40}*1920a, {12,2,40}*1920, {24,2,20}*1920, {16,2,30}*1920, {16,6,10}*1920, {48,2,10}*1920, {8,6,15}*1920, {4,12,15}*1920, {4,8,15}*1920, {8,4,15}*1920, {12,4,10}*1920b, {4,6,10}*1920b, {4,6,20}*1920b, {12,6,10}*1920a, {4,6,30}*1920, {4,4,30}*1920d
   25-fold covers : {4,2,125}*2000, {20,2,25}*2000, {100,2,5}*2000, {20,10,5}*2000a, {4,10,25}*2000, {4,10,5}*2000a, {20,10,5}*2000b, {4,10,5}*2000b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope