Polytope of Type {2,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,5}*40
if this polytope has a name.
Group : SmallGroup(40,13)
Rank : 4
Schlafli Type : {2,2,5}
Number of vertices, edges, etc : 2, 2, 5, 5
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,5,2} of size 80
   {2,2,5,3} of size 240
   {2,2,5,5} of size 240
   {2,2,5,10} of size 400
   {2,2,5,4} of size 480
   {2,2,5,6} of size 480
   {2,2,5,3} of size 480
   {2,2,5,5} of size 480
   {2,2,5,6} of size 480
   {2,2,5,6} of size 480
   {2,2,5,10} of size 480
   {2,2,5,10} of size 480
   {2,2,5,4} of size 640
   {2,2,5,5} of size 640
   {2,2,5,4} of size 960
   {2,2,5,6} of size 960
   {2,2,5,6} of size 960
   {2,2,5,10} of size 960
   {2,2,5,5} of size 1280
   {2,2,5,8} of size 1280
   {2,2,5,8} of size 1280
   {2,2,5,10} of size 1280
   {2,2,5,4} of size 1280
   {2,2,5,10} of size 1280
   {2,2,5,6} of size 1920
   {2,2,5,8} of size 1920
   {2,2,5,12} of size 1920
   {2,2,5,20} of size 1920
   {2,2,5,10} of size 2000
Vertex Figure Of :
   {2,2,2,5} of size 80
   {3,2,2,5} of size 120
   {4,2,2,5} of size 160
   {5,2,2,5} of size 200
   {6,2,2,5} of size 240
   {7,2,2,5} of size 280
   {8,2,2,5} of size 320
   {9,2,2,5} of size 360
   {10,2,2,5} of size 400
   {11,2,2,5} of size 440
   {12,2,2,5} of size 480
   {13,2,2,5} of size 520
   {14,2,2,5} of size 560
   {15,2,2,5} of size 600
   {16,2,2,5} of size 640
   {17,2,2,5} of size 680
   {18,2,2,5} of size 720
   {19,2,2,5} of size 760
   {20,2,2,5} of size 800
   {21,2,2,5} of size 840
   {22,2,2,5} of size 880
   {23,2,2,5} of size 920
   {24,2,2,5} of size 960
   {25,2,2,5} of size 1000
   {26,2,2,5} of size 1040
   {27,2,2,5} of size 1080
   {28,2,2,5} of size 1120
   {29,2,2,5} of size 1160
   {30,2,2,5} of size 1200
   {31,2,2,5} of size 1240
   {32,2,2,5} of size 1280
   {33,2,2,5} of size 1320
   {34,2,2,5} of size 1360
   {35,2,2,5} of size 1400
   {36,2,2,5} of size 1440
   {37,2,2,5} of size 1480
   {38,2,2,5} of size 1520
   {39,2,2,5} of size 1560
   {40,2,2,5} of size 1600
   {41,2,2,5} of size 1640
   {42,2,2,5} of size 1680
   {43,2,2,5} of size 1720
   {44,2,2,5} of size 1760
   {45,2,2,5} of size 1800
   {46,2,2,5} of size 1840
   {47,2,2,5} of size 1880
   {48,2,2,5} of size 1920
   {49,2,2,5} of size 1960
   {50,2,2,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,5}*80, {2,2,10}*80
   3-fold covers : {6,2,5}*120, {2,2,15}*120
   4-fold covers : {8,2,5}*160, {2,2,20}*160, {2,4,10}*160, {4,2,10}*160
   5-fold covers : {2,2,25}*200, {2,10,5}*200, {10,2,5}*200
   6-fold covers : {12,2,5}*240, {4,2,15}*240, {2,6,10}*240, {6,2,10}*240, {2,2,30}*240
   7-fold covers : {14,2,5}*280, {2,2,35}*280
   8-fold covers : {16,2,5}*320, {2,4,20}*320, {4,2,20}*320, {4,4,10}*320, {2,2,40}*320, {2,8,10}*320, {8,2,10}*320
   9-fold covers : {18,2,5}*360, {2,2,45}*360, {2,6,15}*360, {6,2,15}*360
   10-fold covers : {4,2,25}*400, {2,2,50}*400, {20,2,5}*400, {4,10,5}*400, {2,10,10}*400a, {2,10,10}*400b, {10,2,10}*400
   11-fold covers : {22,2,5}*440, {2,2,55}*440
   12-fold covers : {24,2,5}*480, {8,2,15}*480, {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, {2,6,15}*480, {2,4,15}*480
   13-fold covers : {26,2,5}*520, {2,2,65}*520
   14-fold covers : {28,2,5}*560, {4,2,35}*560, {2,14,10}*560, {14,2,10}*560, {2,2,70}*560
   15-fold covers : {6,2,25}*600, {2,2,75}*600, {6,10,5}*600, {2,10,15}*600, {10,2,15}*600, {30,2,5}*600
   16-fold covers : {32,2,5}*640, {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, {2,4,5}*640
   17-fold covers : {34,2,5}*680, {2,2,85}*680
   18-fold covers : {36,2,5}*720, {4,2,45}*720, {2,18,10}*720, {18,2,10}*720, {2,2,90}*720, {12,2,15}*720, {4,6,15}*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
   19-fold covers : {38,2,5}*760, {2,2,95}*760
   20-fold covers : {8,2,25}*800, {2,2,100}*800, {2,4,50}*800, {4,2,50}*800, {40,2,5}*800, {8,10,5}*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
   21-fold covers : {14,2,15}*840, {42,2,5}*840, {6,2,35}*840, {2,2,105}*840
   22-fold covers : {44,2,5}*880, {4,2,55}*880, {2,22,10}*880, {22,2,10}*880, {2,2,110}*880
   23-fold covers : {46,2,5}*920, {2,2,115}*920
   24-fold covers : {48,2,5}*960, {16,2,15}*960, {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, {2,12,15}*960, {4,6,15}*960, {4,4,15}*960b, {2,8,15}*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
   25-fold covers : {2,2,125}*1000, {2,10,25}*1000, {10,2,25}*1000, {50,2,5}*1000, {2,10,5}*1000, {10,10,5}*1000a, {10,10,5}*1000b
   26-fold covers : {52,2,5}*1040, {4,2,65}*1040, {2,26,10}*1040, {26,2,10}*1040, {2,2,130}*1040
   27-fold covers : {54,2,5}*1080, {2,2,135}*1080, {2,6,45}*1080, {6,2,45}*1080, {18,2,15}*1080, {6,6,15}*1080a, {2,6,15}*1080, {6,6,15}*1080b
   28-fold covers : {56,2,5}*1120, {8,2,35}*1120, {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
   29-fold covers : {58,2,5}*1160, {2,2,145}*1160
   30-fold covers : {12,2,25}*1200, {4,2,75}*1200, {2,6,50}*1200, {6,2,50}*1200, {2,2,150}*1200, {12,10,5}*1200, {20,2,15}*1200, {60,2,5}*1200, {4,10,15}*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
   31-fold covers : {62,2,5}*1240, {2,2,155}*1240
   32-fold covers : {64,2,5}*1280, {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, {4,4,5}*1280, {2,8,5}*1280a, {2,4,5}*1280, {2,4,10}*1280a, {2,8,5}*1280b, {2,4,10}*1280b
   33-fold covers : {22,2,15}*1320, {66,2,5}*1320, {6,2,55}*1320, {2,2,165}*1320
   34-fold covers : {68,2,5}*1360, {4,2,85}*1360, {2,34,10}*1360, {34,2,10}*1360, {2,2,170}*1360
   35-fold covers : {14,2,25}*1400, {2,2,175}*1400, {14,10,5}*1400, {2,10,35}*1400, {10,2,35}*1400, {70,2,5}*1400
   36-fold covers : {72,2,5}*1440, {8,2,45}*1440, {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, {24,2,15}*1440, {8,6,15}*1440, {2,4,45}*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, {6,6,15}*1440, {4,4,10}*1440, {4,6,10}*1440, {6,4,10}*1440c, {2,4,20}*1440, {2,4,30}*1440, {6,4,15}*1440, {2,12,15}*1440, {2,6,15}*1440e, {2,6,20}*1440
   37-fold covers : {74,2,5}*1480, {2,2,185}*1480
   38-fold covers : {76,2,5}*1520, {4,2,95}*1520, {2,38,10}*1520, {38,2,10}*1520, {2,2,190}*1520
   39-fold covers : {26,2,15}*1560, {78,2,5}*1560, {6,2,65}*1560, {2,2,195}*1560
   40-fold covers : {16,2,25}*1600, {2,4,100}*1600, {4,2,100}*1600, {4,4,50}*1600, {2,2,200}*1600, {2,8,50}*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, {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
   41-fold covers : {82,2,5}*1640, {2,2,205}*1640
   42-fold covers : {28,2,15}*1680, {84,2,5}*1680, {12,2,35}*1680, {4,2,105}*1680, {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
   43-fold covers : {86,2,5}*1720, {2,2,215}*1720
   44-fold covers : {88,2,5}*1760, {8,2,55}*1760, {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
   45-fold covers : {18,2,25}*1800, {2,2,225}*1800, {2,6,75}*1800, {6,2,75}*1800, {18,10,5}*1800, {2,10,45}*1800, {10,2,45}*1800, {90,2,5}*1800, {6,10,15}*1800, {10,6,15}*1800, {2,30,15}*1800, {30,2,15}*1800
   46-fold covers : {92,2,5}*1840, {4,2,115}*1840, {2,46,10}*1840, {46,2,10}*1840, {2,2,230}*1840
   47-fold covers : {94,2,5}*1880, {2,2,235}*1880
   48-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, {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, {2,6,15}*1920, {4,6,15}*1920, {8,6,15}*1920, {4,12,15}*1920, {4,4,15}*1920b, {2,8,15}*1920a, {4,8,15}*1920, {8,4,15}*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, {6,4,5}*1920, {2,4,15}*1920
   49-fold covers : {98,2,5}*1960, {2,2,245}*1960, {2,14,35}*1960, {14,2,35}*1960
   50-fold covers : {4,2,125}*2000, {2,2,250}*2000, {20,2,25}*2000, {100,2,5}*2000, {20,10,5}*2000a, {4,10,25}*2000, {4,10,5}*2000a, {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, {20,10,5}*2000b, {4,10,5}*2000b, {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 := (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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(9)!(1,2);
s1 := Sym(9)!(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*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 >;

to this polytope