Polytope of Type {2,5,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,2,2}*80
if this polytope has a name.
Group : SmallGroup(80,51)
Rank : 5
Schlafli Type : {2,5,2,2}
Number of vertices, edges, etc : 2, 5, 5, 2, 2
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,2,2,2} of size 160
   {2,5,2,2,3} of size 240
   {2,5,2,2,4} of size 320
   {2,5,2,2,5} of size 400
   {2,5,2,2,6} of size 480
   {2,5,2,2,7} of size 560
   {2,5,2,2,8} of size 640
   {2,5,2,2,9} of size 720
   {2,5,2,2,10} of size 800
   {2,5,2,2,11} of size 880
   {2,5,2,2,12} of size 960
   {2,5,2,2,13} of size 1040
   {2,5,2,2,14} of size 1120
   {2,5,2,2,15} of size 1200
   {2,5,2,2,16} of size 1280
   {2,5,2,2,17} of size 1360
   {2,5,2,2,18} of size 1440
   {2,5,2,2,19} of size 1520
   {2,5,2,2,20} of size 1600
   {2,5,2,2,21} of size 1680
   {2,5,2,2,22} of size 1760
   {2,5,2,2,23} of size 1840
   {2,5,2,2,24} of size 1920
   {2,5,2,2,25} of size 2000
Vertex Figure Of :
   {2,2,5,2,2} of size 160
   {3,2,5,2,2} of size 240
   {4,2,5,2,2} of size 320
   {5,2,5,2,2} of size 400
   {6,2,5,2,2} of size 480
   {7,2,5,2,2} of size 560
   {8,2,5,2,2} of size 640
   {9,2,5,2,2} of size 720
   {10,2,5,2,2} of size 800
   {11,2,5,2,2} of size 880
   {12,2,5,2,2} of size 960
   {13,2,5,2,2} of size 1040
   {14,2,5,2,2} of size 1120
   {15,2,5,2,2} of size 1200
   {16,2,5,2,2} of size 1280
   {17,2,5,2,2} of size 1360
   {18,2,5,2,2} of size 1440
   {19,2,5,2,2} of size 1520
   {20,2,5,2,2} of size 1600
   {21,2,5,2,2} of size 1680
   {22,2,5,2,2} of size 1760
   {23,2,5,2,2} of size 1840
   {24,2,5,2,2} of size 1920
   {25,2,5,2,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,5,2,4}*160, {2,10,2,2}*160
   3-fold covers : {2,5,2,6}*240, {2,15,2,2}*240
   4-fold covers : {2,5,2,8}*320, {2,20,2,2}*320, {2,10,2,4}*320, {2,10,4,2}*320, {4,10,2,2}*320
   5-fold covers : {2,25,2,2}*400, {2,5,2,10}*400, {2,5,10,2}*400, {10,5,2,2}*400
   6-fold covers : {2,5,2,12}*480, {2,15,2,4}*480, {2,10,2,6}*480, {2,10,6,2}*480, {6,10,2,2}*480, {2,30,2,2}*480
   7-fold covers : {2,5,2,14}*560, {2,35,2,2}*560
   8-fold covers : {2,5,2,16}*640, {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
   9-fold covers : {2,5,2,18}*720, {2,45,2,2}*720, {2,15,2,6}*720, {2,15,6,2}*720, {6,15,2,2}*720
   10-fold covers : {2,25,2,4}*800, {2,50,2,2}*800, {2,5,2,20}*800, {10,5,2,4}*800, {2,5,10,4}*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
   11-fold covers : {2,5,2,22}*880, {2,55,2,2}*880
   12-fold covers : {2,5,2,24}*960, {2,15,2,8}*960, {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, {2,15,6,2}*960, {6,15,2,2}*960, {2,15,4,2}*960, {4,15,2,2}*960
   13-fold covers : {2,5,2,26}*1040, {2,65,2,2}*1040
   14-fold covers : {2,5,2,28}*1120, {2,35,2,4}*1120, {2,10,2,14}*1120, {2,10,14,2}*1120, {14,10,2,2}*1120, {2,70,2,2}*1120
   15-fold covers : {2,25,2,6}*1200, {2,75,2,2}*1200, {2,5,10,6}*1200, {10,5,2,6}*1200, {2,5,2,30}*1200, {2,15,2,10}*1200, {2,15,10,2}*1200, {10,15,2,2}*1200
   16-fold covers : {2,5,2,32}*1280, {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, {2,5,4,2}*1280, {4,5,2,2}*1280
   17-fold covers : {2,5,2,34}*1360, {2,85,2,2}*1360
   18-fold covers : {2,5,2,36}*1440, {2,45,2,4}*1440, {2,10,2,18}*1440, {2,10,18,2}*1440, {18,10,2,2}*1440, {2,90,2,2}*1440, {2,15,2,12}*1440, {6,15,2,4}*1440, {2,15,6,4}*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
   19-fold covers : {2,5,2,38}*1520, {2,95,2,2}*1520
   20-fold covers : {2,25,2,8}*1600, {2,100,2,2}*1600, {2,50,2,4}*1600, {2,50,4,2}*1600, {4,50,2,2}*1600, {2,5,2,40}*1600, {10,5,2,8}*1600, {2,5,10,8}*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
   21-fold covers : {2,15,2,14}*1680, {2,5,2,42}*1680, {2,35,2,6}*1680, {2,105,2,2}*1680
   22-fold covers : {2,5,2,44}*1760, {2,55,2,4}*1760, {2,10,2,22}*1760, {2,10,22,2}*1760, {22,10,2,2}*1760, {2,110,2,2}*1760
   23-fold covers : {2,5,2,46}*1840, {2,115,2,2}*1840
   24-fold covers : {2,15,2,16}*1920, {2,5,2,48}*1920, {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, {6,15,2,4}*1920, {2,15,12,2}*1920, {12,15,2,2}*1920, {2,15,6,4}*1920, {2,15,4,4}*1920b, {4,15,2,4}*1920, {2,15,8,2}*1920, {8,15,2,2}*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
   25-fold covers : {2,125,2,2}*2000, {2,5,2,50}*2000, {2,25,2,10}*2000, {2,25,10,2}*2000, {10,25,2,2}*2000, {2,5,10,2}*2000, {2,5,10,10}*2000a, {10,5,2,2}*2000, {2,5,10,10}*2000b, {10,5,2,10}*2000, {10,5,10,2}*2000
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4)(5,6);;
s3 := (8,9);;
s4 := (10,11);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(11)!(1,2);
s1 := Sym(11)!(4,5)(6,7);
s2 := Sym(11)!(3,4)(5,6);
s3 := Sym(11)!(8,9);
s4 := Sym(11)!(10,11);
poly := sub<Sym(11)|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 >;

to this polytope