Polytope of Type {2,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10}*80
if this polytope has a name.
Group : SmallGroup(80,51)
Rank : 4
Schlafli Type : {2,2,10}
Number of vertices, edges, etc : 2, 2, 10, 10
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,10,2} of size 160
   {2,2,10,4} of size 320
   {2,2,10,5} of size 400
   {2,2,10,3} of size 480
   {2,2,10,3} of size 480
   {2,2,10,5} of size 480
   {2,2,10,5} of size 480
   {2,2,10,6} of size 480
   {2,2,10,8} of size 640
   {2,2,10,4} of size 800
   {2,2,10,10} of size 800
   {2,2,10,10} of size 800
   {2,2,10,10} of size 800
   {2,2,10,12} of size 960
   {2,2,10,4} of size 960
   {2,2,10,4} of size 960
   {2,2,10,6} of size 960
   {2,2,10,6} of size 960
   {2,2,10,3} of size 960
   {2,2,10,5} of size 960
   {2,2,10,6} of size 960
   {2,2,10,6} of size 960
   {2,2,10,6} of size 960
   {2,2,10,6} of size 960
   {2,2,10,10} of size 960
   {2,2,10,10} of size 960
   {2,2,10,10} of size 960
   {2,2,10,10} of size 960
   {2,2,10,14} of size 1120
   {2,2,10,3} of size 1200
   {2,2,10,6} of size 1200
   {2,2,10,15} of size 1200
   {2,2,10,16} of size 1280
   {2,2,10,5} of size 1280
   {2,2,10,4} of size 1280
   {2,2,10,4} of size 1280
   {2,2,10,5} of size 1280
   {2,2,10,18} of size 1440
   {2,2,10,3} of size 1440
   {2,2,10,15} of size 1440
   {2,2,10,20} of size 1600
   {2,2,10,20} of size 1600
   {2,2,10,20} of size 1600
   {2,2,10,4} of size 1600
   {2,2,10,22} of size 1760
   {2,2,10,24} of size 1920
   {2,2,10,4} of size 1920
   {2,2,10,4} of size 1920
   {2,2,10,12} of size 1920
   {2,2,10,12} of size 1920
   {2,2,10,12} of size 1920
   {2,2,10,12} of size 1920
   {2,2,10,20} of size 1920
   {2,2,10,20} of size 1920
   {2,2,10,4} of size 1920
   {2,2,10,6} of size 1920
   {2,2,10,6} of size 1920
   {2,2,10,10} of size 1920
   {2,2,10,6} of size 1920
   {2,2,10,25} of size 2000
   {2,2,10,5} of size 2000
   {2,2,10,10} of size 2000
Vertex Figure Of :
   {2,2,2,10} of size 160
   {3,2,2,10} of size 240
   {4,2,2,10} of size 320
   {5,2,2,10} of size 400
   {6,2,2,10} of size 480
   {7,2,2,10} of size 560
   {8,2,2,10} of size 640
   {9,2,2,10} of size 720
   {10,2,2,10} of size 800
   {11,2,2,10} of size 880
   {12,2,2,10} of size 960
   {13,2,2,10} of size 1040
   {14,2,2,10} of size 1120
   {15,2,2,10} of size 1200
   {16,2,2,10} of size 1280
   {17,2,2,10} of size 1360
   {18,2,2,10} of size 1440
   {19,2,2,10} of size 1520
   {20,2,2,10} of size 1600
   {21,2,2,10} of size 1680
   {22,2,2,10} of size 1760
   {23,2,2,10} of size 1840
   {24,2,2,10} of size 1920
   {25,2,2,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,5}*40
   5-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,20}*160, {2,4,10}*160, {4,2,10}*160
   3-fold covers : {2,6,10}*240, {6,2,10}*240, {2,2,30}*240
   4-fold covers : {2,4,20}*320, {4,2,20}*320, {4,4,10}*320, {2,2,40}*320, {2,8,10}*320, {8,2,10}*320
   5-fold covers : {2,2,50}*400, {2,10,10}*400a, {2,10,10}*400b, {10,2,10}*400
   6-fold covers : {2,12,10}*480, {12,2,10}*480, {2,6,20}*480a, {6,2,20}*480, {4,6,10}*480a, {6,4,10}*480, {2,2,60}*480, {2,4,30}*480a, {4,2,30}*480
   7-fold covers : {2,14,10}*560, {14,2,10}*560, {2,2,70}*560
   8-fold covers : {4,4,20}*640, {2,4,40}*640a, {2,4,20}*640, {2,4,40}*640b, {2,8,20}*640a, {2,8,20}*640b, {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, {2,2,80}*640, {2,16,10}*640, {16,2,10}*640
   9-fold covers : {2,18,10}*720, {18,2,10}*720, {2,2,90}*720, {6,6,10}*720a, {6,6,10}*720b, {6,6,10}*720c, {2,6,30}*720a, {2,6,30}*720b, {2,6,30}*720c, {6,2,30}*720
   10-fold covers : {2,2,100}*800, {2,4,50}*800, {4,2,50}*800, {2,10,20}*800a, {2,10,20}*800b, {2,20,10}*800a, {10,2,20}*800, {20,2,10}*800, {4,10,10}*800a, {10,4,10}*800, {4,10,10}*800c, {2,20,10}*800c
   11-fold covers : {2,22,10}*880, {22,2,10}*880, {2,2,110}*880
   12-fold covers : {12,2,20}*960, {4,12,10}*960a, {12,4,10}*960, {6,4,20}*960, {4,6,20}*960a, {2,24,10}*960, {24,2,10}*960, {2,6,40}*960, {6,2,40}*960, {6,8,10}*960, {8,6,10}*960, {2,12,20}*960, {2,4,60}*960a, {4,2,60}*960, {4,4,30}*960, {2,2,120}*960, {2,8,30}*960, {8,2,30}*960, {4,6,10}*960e, {6,4,10}*960, {6,6,10}*960, {2,6,20}*960c, {2,6,30}*960, {2,4,30}*960
   13-fold covers : {2,26,10}*1040, {26,2,10}*1040, {2,2,130}*1040
   14-fold covers : {2,14,20}*1120, {14,2,20}*1120, {2,28,10}*1120, {28,2,10}*1120, {4,14,10}*1120, {14,4,10}*1120, {2,2,140}*1120, {2,4,70}*1120, {4,2,70}*1120
   15-fold covers : {2,6,50}*1200, {6,2,50}*1200, {2,2,150}*1200, {6,10,10}*1200a, {6,10,10}*1200b, {10,6,10}*1200, {2,30,10}*1200a, {2,10,30}*1200b, {2,10,30}*1200c, {2,30,10}*1200b, {10,2,30}*1200, {30,2,10}*1200
   16-fold covers : {4,8,10}*1280a, {8,4,10}*1280a, {2,8,20}*1280a, {2,4,40}*1280a, {8,8,10}*1280a, {8,8,10}*1280b, {8,8,10}*1280c, {2,8,40}*1280a, {2,8,40}*1280b, {2,8,40}*1280c, {8,8,10}*1280d, {2,8,40}*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, {2,16,20}*1280a, {2,4,80}*1280a, {4,16,10}*1280b, {16,4,10}*1280b, {2,16,20}*1280b, {2,4,80}*1280b, {4,4,10}*1280, {4,8,10}*1280b, {8,4,10}*1280b, {2,4,20}*1280a, {2,4,40}*1280b, {2,8,20}*1280b, {16,2,20}*1280, {4,2,80}*1280, {2,32,10}*1280, {32,2,10}*1280, {2,2,160}*1280, {2,4,10}*1280b
   17-fold covers : {2,34,10}*1360, {34,2,10}*1360, {2,2,170}*1360
   18-fold covers : {2,36,10}*1440, {36,2,10}*1440, {2,18,20}*1440a, {18,2,20}*1440, {4,18,10}*1440a, {18,4,10}*1440, {2,2,180}*1440, {2,4,90}*1440a, {4,2,90}*1440, {6,12,10}*1440a, {6,12,10}*1440b, {12,6,10}*1440a, {12,6,10}*1440b, {6,6,20}*1440a, {6,6,20}*1440b, {6,6,20}*1440c, {2,6,60}*1440a, {2,12,30}*1440a, {6,12,10}*1440c, {12,6,10}*1440c, {4,6,30}*1440a, {2,12,30}*1440b, {12,2,30}*1440, {2,6,60}*1440b, {2,6,60}*1440c, {6,2,60}*1440, {4,6,30}*1440b, {6,4,30}*1440, {4,6,30}*1440c, {2,12,30}*1440c, {4,4,10}*1440, {4,6,10}*1440, {6,4,10}*1440c, {2,4,20}*1440, {2,4,30}*1440, {2,6,20}*1440
   19-fold covers : {2,38,10}*1520, {38,2,10}*1520, {2,2,190}*1520
   20-fold covers : {2,4,100}*1600, {4,2,100}*1600, {4,4,50}*1600, {2,2,200}*1600, {2,8,50}*1600, {8,2,50}*1600, {20,2,20}*1600, {4,10,20}*1600a, {4,20,10}*1600a, {10,4,20}*1600, {20,4,10}*1600, {2,10,40}*1600a, {2,10,40}*1600b, {2,40,10}*1600a, {10,2,40}*1600, {40,2,10}*1600, {8,10,10}*1600a, {10,8,10}*1600, {2,20,20}*1600a, {2,20,20}*1600b, {4,10,20}*1600b, {8,10,10}*1600c, {2,40,10}*1600c, {4,20,10}*1600c
   21-fold covers : {6,14,10}*1680, {14,6,10}*1680, {2,14,30}*1680, {14,2,30}*1680, {2,42,10}*1680, {42,2,10}*1680, {2,6,70}*1680, {6,2,70}*1680, {2,2,210}*1680
   22-fold covers : {2,22,20}*1760, {22,2,20}*1760, {2,44,10}*1760, {44,2,10}*1760, {4,22,10}*1760, {22,4,10}*1760, {2,2,220}*1760, {2,4,110}*1760, {4,2,110}*1760
   23-fold covers : {2,46,10}*1840, {46,2,10}*1840, {2,2,230}*1840
   24-fold covers : {4,4,60}*1920, {4,12,20}*1920a, {12,4,20}*1920, {4,8,30}*1920a, {8,4,30}*1920a, {2,8,60}*1920a, {2,4,120}*1920a, {8,12,10}*1920a, {12,8,10}*1920a, {6,8,20}*1920a, {4,24,10}*1920a, {24,4,10}*1920a, {6,4,40}*1920a, {2,12,40}*1920a, {2,24,20}*1920a, {4,8,30}*1920b, {8,4,30}*1920b, {2,8,60}*1920b, {2,4,120}*1920b, {8,12,10}*1920b, {12,8,10}*1920b, {6,8,20}*1920b, {4,24,10}*1920b, {24,4,10}*1920b, {6,4,40}*1920b, {2,12,40}*1920b, {2,24,20}*1920b, {4,4,30}*1920a, {2,4,60}*1920a, {4,12,10}*1920a, {12,4,10}*1920a, {6,4,20}*1920a, {2,12,20}*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, {2,16,30}*1920, {16,2,30}*1920, {2,2,240}*1920, {6,16,10}*1920, {16,6,10}*1920, {2,48,10}*1920, {48,2,10}*1920, {2,6,80}*1920, {6,2,80}*1920, {4,12,10}*1920b, {12,4,10}*1920b, {2,12,20}*1920b, {4,6,20}*1920a, {6,4,20}*1920b, {6,6,20}*1920, {2,6,20}*1920a, {2,6,60}*1920a, {4,6,10}*1920b, {4,6,20}*1920b, {4,12,10}*1920c, {6,4,10}*1920, {6,12,10}*1920a, {12,4,10}*1920c, {12,6,10}*1920a, {2,12,30}*1920a, {2,6,30}*1920, {2,6,40}*1920b, {6,8,10}*1920a, {6,12,10}*1920b, {8,6,10}*1920a, {12,6,10}*1920b, {2,6,40}*1920c, {2,6,60}*1920b, {6,6,10}*1920, {6,8,10}*1920b, {8,6,10}*1920b, {4,6,30}*1920, {2,12,20}*1920c, {2,12,30}*1920b, {2,4,60}*1920b, {4,4,30}*1920d, {2,4,30}*1920b, {2,4,60}*1920c, {2,8,30}*1920b, {2,8,30}*1920c
   25-fold covers : {2,2,250}*2000, {2,10,50}*2000a, {2,10,50}*2000b, {2,50,10}*2000a, {10,2,50}*2000, {50,2,10}*2000, {10,10,10}*2000a, {2,10,10}*2000b, {2,10,10}*2000c, {10,10,10}*2000b, {10,10,10}*2000c, {10,10,10}*2000d, {10,10,10}*2000g, {2,10,10}*2000d
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14);;
s3 := ( 5, 9)( 6, 7)( 8,13)(10,11)(12,14);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope