Polytope of Type {2,5,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,2}*40
if this polytope has a name.
Group : SmallGroup(40,13)
Rank : 4
Schlafli Type : {2,5,2}
Number of vertices, edges, etc : 2, 5, 5, 2
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,2,2} of size 80
   {2,5,2,3} of size 120
   {2,5,2,4} of size 160
   {2,5,2,5} of size 200
   {2,5,2,6} of size 240
   {2,5,2,7} of size 280
   {2,5,2,8} of size 320
   {2,5,2,9} of size 360
   {2,5,2,10} of size 400
   {2,5,2,11} of size 440
   {2,5,2,12} of size 480
   {2,5,2,13} of size 520
   {2,5,2,14} of size 560
   {2,5,2,15} of size 600
   {2,5,2,16} of size 640
   {2,5,2,17} of size 680
   {2,5,2,18} of size 720
   {2,5,2,19} of size 760
   {2,5,2,20} of size 800
   {2,5,2,21} of size 840
   {2,5,2,22} of size 880
   {2,5,2,23} of size 920
   {2,5,2,24} of size 960
   {2,5,2,25} of size 1000
   {2,5,2,26} of size 1040
   {2,5,2,27} of size 1080
   {2,5,2,28} of size 1120
   {2,5,2,29} of size 1160
   {2,5,2,30} of size 1200
   {2,5,2,31} of size 1240
   {2,5,2,32} of size 1280
   {2,5,2,33} of size 1320
   {2,5,2,34} of size 1360
   {2,5,2,35} of size 1400
   {2,5,2,36} of size 1440
   {2,5,2,37} of size 1480
   {2,5,2,38} of size 1520
   {2,5,2,39} of size 1560
   {2,5,2,40} of size 1600
   {2,5,2,41} of size 1640
   {2,5,2,42} of size 1680
   {2,5,2,43} of size 1720
   {2,5,2,44} of size 1760
   {2,5,2,45} of size 1800
   {2,5,2,46} of size 1840
   {2,5,2,47} of size 1880
   {2,5,2,48} of size 1920
   {2,5,2,49} of size 1960
   {2,5,2,50} of size 2000
Vertex Figure Of :
   {2,2,5,2} of size 80
   {3,2,5,2} of size 120
   {4,2,5,2} of size 160
   {5,2,5,2} of size 200
   {6,2,5,2} of size 240
   {7,2,5,2} of size 280
   {8,2,5,2} of size 320
   {9,2,5,2} of size 360
   {10,2,5,2} of size 400
   {11,2,5,2} of size 440
   {12,2,5,2} of size 480
   {13,2,5,2} of size 520
   {14,2,5,2} of size 560
   {15,2,5,2} of size 600
   {16,2,5,2} of size 640
   {17,2,5,2} of size 680
   {18,2,5,2} of size 720
   {19,2,5,2} of size 760
   {20,2,5,2} of size 800
   {21,2,5,2} of size 840
   {22,2,5,2} of size 880
   {23,2,5,2} of size 920
   {24,2,5,2} of size 960
   {25,2,5,2} of size 1000
   {26,2,5,2} of size 1040
   {27,2,5,2} of size 1080
   {28,2,5,2} of size 1120
   {29,2,5,2} of size 1160
   {30,2,5,2} of size 1200
   {31,2,5,2} of size 1240
   {32,2,5,2} of size 1280
   {33,2,5,2} of size 1320
   {34,2,5,2} of size 1360
   {35,2,5,2} of size 1400
   {36,2,5,2} of size 1440
   {37,2,5,2} of size 1480
   {38,2,5,2} of size 1520
   {39,2,5,2} of size 1560
   {40,2,5,2} of size 1600
   {41,2,5,2} of size 1640
   {42,2,5,2} of size 1680
   {43,2,5,2} of size 1720
   {44,2,5,2} of size 1760
   {45,2,5,2} of size 1800
   {46,2,5,2} of size 1840
   {47,2,5,2} of size 1880
   {48,2,5,2} of size 1920
   {49,2,5,2} of size 1960
   {50,2,5,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,10,2}*80
   3-fold covers : {2,15,2}*120
   4-fold covers : {2,20,2}*160, {2,10,4}*160, {4,10,2}*160
   5-fold covers : {2,25,2}*200, {2,5,10}*200, {10,5,2}*200
   6-fold covers : {2,10,6}*240, {6,10,2}*240, {2,30,2}*240
   7-fold covers : {2,35,2}*280
   8-fold covers : {2,20,4}*320, {4,20,2}*320, {4,10,4}*320, {2,40,2}*320, {2,10,8}*320, {8,10,2}*320
   9-fold covers : {2,45,2}*360, {2,15,6}*360, {6,15,2}*360
   10-fold covers : {2,50,2}*400, {2,10,10}*400a, {2,10,10}*400c, {10,10,2}*400a, {10,10,2}*400b
   11-fold covers : {2,55,2}*440
   12-fold covers : {2,10,12}*480, {12,10,2}*480, {2,20,6}*480a, {6,20,2}*480a, {4,10,6}*480, {6,10,4}*480, {2,60,2}*480, {2,30,4}*480a, {4,30,2}*480a, {2,15,6}*480, {6,15,2}*480, {2,15,4}*480, {4,15,2}*480
   13-fold covers : {2,65,2}*520
   14-fold covers : {2,10,14}*560, {14,10,2}*560, {2,70,2}*560
   15-fold covers : {2,75,2}*600, {2,15,10}*600, {10,15,2}*600
   16-fold covers : {4,20,4}*640, {2,40,4}*640a, {4,40,2}*640a, {2,20,4}*640, {4,20,2}*640, {2,40,4}*640b, {4,40,2}*640b, {2,20,8}*640a, {8,20,2}*640a, {2,20,8}*640b, {8,20,2}*640b, {4,10,8}*640, {8,10,4}*640, {2,80,2}*640, {2,10,16}*640, {16,10,2}*640, {2,5,4}*640, {4,5,2}*640
   17-fold covers : {2,85,2}*680
   18-fold covers : {2,10,18}*720, {18,10,2}*720, {2,90,2}*720, {6,10,6}*720, {2,30,6}*720a, {6,30,2}*720a, {2,30,6}*720b, {2,30,6}*720c, {6,30,2}*720b, {6,30,2}*720c
   19-fold covers : {2,95,2}*760
   20-fold covers : {2,100,2}*800, {2,50,4}*800, {4,50,2}*800, {2,10,20}*800a, {2,20,10}*800a, {2,20,10}*800b, {10,20,2}*800a, {10,20,2}*800b, {20,10,2}*800a, {4,10,10}*800a, {4,10,10}*800b, {10,10,4}*800a, {10,10,4}*800b, {2,10,20}*800c, {20,10,2}*800c
   21-fold covers : {2,105,2}*840
   22-fold covers : {2,10,22}*880, {22,10,2}*880, {2,110,2}*880
   23-fold covers : {2,115,2}*920
   24-fold covers : {4,20,6}*960, {6,20,4}*960, {4,10,12}*960, {12,10,4}*960, {2,10,24}*960, {24,10,2}*960, {2,40,6}*960, {6,40,2}*960, {6,10,8}*960, {8,10,6}*960, {2,20,12}*960, {12,20,2}*960, {2,60,4}*960a, {4,60,2}*960a, {4,30,4}*960a, {2,120,2}*960, {2,30,8}*960, {8,30,2}*960, {2,15,12}*960, {12,15,2}*960, {2,15,8}*960, {8,15,2}*960, {2,20,6}*960c, {2,30,6}*960, {6,20,2}*960c, {6,30,2}*960, {2,30,4}*960, {4,30,2}*960
   25-fold covers : {2,125,2}*1000, {2,25,10}*1000, {10,25,2}*1000, {2,5,10}*1000, {10,5,2}*1000, {10,5,10}*1000
   26-fold covers : {2,10,26}*1040, {26,10,2}*1040, {2,130,2}*1040
   27-fold covers : {2,135,2}*1080, {2,45,6}*1080, {6,45,2}*1080, {2,15,6}*1080, {6,15,2}*1080, {6,15,6}*1080
   28-fold covers : {2,20,14}*1120, {14,20,2}*1120, {2,10,28}*1120, {28,10,2}*1120, {4,10,14}*1120, {14,10,4}*1120, {2,140,2}*1120, {2,70,4}*1120, {4,70,2}*1120
   29-fold covers : {2,145,2}*1160
   30-fold covers : {2,50,6}*1200, {6,50,2}*1200, {2,150,2}*1200, {6,10,10}*1200a, {6,10,10}*1200c, {10,10,6}*1200a, {10,10,6}*1200b, {2,10,30}*1200a, {30,10,2}*1200a, {2,10,30}*1200b, {2,30,10}*1200b, {2,30,10}*1200c, {10,30,2}*1200b, {10,30,2}*1200c, {30,10,2}*1200b
   31-fold covers : {2,155,2}*1240
   32-fold covers : {2,20,8}*1280a, {8,20,2}*1280a, {2,40,4}*1280a, {4,40,2}*1280a, {2,40,8}*1280a, {8,40,2}*1280a, {2,40,8}*1280b, {2,40,8}*1280c, {8,40,2}*1280b, {8,40,2}*1280c, {2,40,8}*1280d, {8,40,2}*1280d, {8,10,8}*1280, {4,20,8}*1280a, {8,20,4}*1280a, {4,20,8}*1280b, {8,20,4}*1280b, {4,40,4}*1280a, {4,20,4}*1280a, {4,20,4}*1280b, {4,40,4}*1280b, {4,40,4}*1280c, {4,40,4}*1280d, {2,20,16}*1280a, {16,20,2}*1280a, {2,80,4}*1280a, {4,80,2}*1280a, {2,20,16}*1280b, {16,20,2}*1280b, {2,80,4}*1280b, {4,80,2}*1280b, {2,20,4}*1280a, {2,40,4}*1280b, {4,20,2}*1280a, {4,40,2}*1280b, {2,20,8}*1280b, {8,20,2}*1280b, {4,10,16}*1280, {16,10,4}*1280, {2,10,32}*1280, {32,10,2}*1280, {2,160,2}*1280, {2,5,8}*1280a, {8,5,2}*1280a, {2,5,4}*1280, {2,5,8}*1280b, {2,10,4}*1280a, {4,5,2}*1280, {4,10,2}*1280a, {8,5,2}*1280b, {2,10,4}*1280b, {4,10,2}*1280b
   33-fold covers : {2,165,2}*1320
   34-fold covers : {2,10,34}*1360, {34,10,2}*1360, {2,170,2}*1360
   35-fold covers : {2,175,2}*1400, {2,35,10}*1400, {10,35,2}*1400
   36-fold covers : {2,10,36}*1440, {36,10,2}*1440, {2,20,18}*1440a, {18,20,2}*1440a, {4,10,18}*1440, {18,10,4}*1440, {2,180,2}*1440, {2,90,4}*1440a, {4,90,2}*1440a, {2,45,4}*1440, {4,45,2}*1440, {6,10,12}*1440, {12,10,6}*1440, {6,20,6}*1440, {2,60,6}*1440a, {6,60,2}*1440a, {2,30,12}*1440a, {12,30,2}*1440a, {4,30,6}*1440a, {6,30,4}*1440a, {2,30,12}*1440b, {12,30,2}*1440b, {2,60,6}*1440b, {2,60,6}*1440c, {6,60,2}*1440b, {6,60,2}*1440c, {4,30,6}*1440b, {4,30,6}*1440c, {6,30,4}*1440b, {6,30,4}*1440c, {2,30,12}*1440c, {12,30,2}*1440c, {2,20,4}*1440, {2,30,4}*1440, {4,20,2}*1440, {4,30,2}*1440, {4,15,6}*1440b, {6,15,4}*1440b, {2,15,12}*1440, {12,15,2}*1440, {2,15,6}*1440e, {6,15,2}*1440e, {2,20,6}*1440, {6,20,2}*1440
   37-fold covers : {2,185,2}*1480
   38-fold covers : {2,10,38}*1520, {38,10,2}*1520, {2,190,2}*1520
   39-fold covers : {2,195,2}*1560
   40-fold covers : {2,100,4}*1600, {4,100,2}*1600, {4,50,4}*1600, {2,200,2}*1600, {2,50,8}*1600, {8,50,2}*1600, {4,10,20}*1600a, {20,10,4}*1600a, {4,20,10}*1600a, {4,20,10}*1600b, {10,20,4}*1600a, {10,20,4}*1600b, {2,10,40}*1600a, {2,40,10}*1600a, {2,40,10}*1600b, {10,40,2}*1600a, {10,40,2}*1600b, {40,10,2}*1600a, {8,10,10}*1600a, {8,10,10}*1600b, {10,10,8}*1600a, {10,10,8}*1600b, {2,20,20}*1600a, {2,20,20}*1600c, {20,20,2}*1600a, {20,20,2}*1600b, {4,10,20}*1600c, {20,10,4}*1600c, {2,10,40}*1600c, {40,10,2}*1600c
   41-fold covers : {2,205,2}*1640
   42-fold covers : {6,10,14}*1680, {14,10,6}*1680, {2,30,14}*1680, {14,30,2}*1680, {2,10,42}*1680, {42,10,2}*1680, {2,70,6}*1680, {6,70,2}*1680, {2,210,2}*1680
   43-fold covers : {2,215,2}*1720
   44-fold covers : {2,20,22}*1760, {22,20,2}*1760, {2,10,44}*1760, {44,10,2}*1760, {4,10,22}*1760, {22,10,4}*1760, {2,220,2}*1760, {2,110,4}*1760, {4,110,2}*1760
   45-fold covers : {2,225,2}*1800, {2,75,6}*1800, {6,75,2}*1800, {2,45,10}*1800, {10,45,2}*1800, {6,15,10}*1800, {10,15,6}*1800, {2,15,30}*1800, {30,15,2}*1800
   46-fold covers : {2,10,46}*1840, {46,10,2}*1840, {2,230,2}*1840
   47-fold covers : {2,235,2}*1880
   48-fold covers : {4,60,4}*1920a, {4,20,12}*1920, {12,20,4}*1920, {2,60,8}*1920a, {8,60,2}*1920a, {2,120,4}*1920a, {4,120,2}*1920a, {6,20,8}*1920a, {8,20,6}*1920a, {4,40,6}*1920a, {6,40,4}*1920a, {2,40,12}*1920a, {12,40,2}*1920a, {2,20,24}*1920a, {24,20,2}*1920a, {2,60,8}*1920b, {8,60,2}*1920b, {2,120,4}*1920b, {4,120,2}*1920b, {6,20,8}*1920b, {8,20,6}*1920b, {4,40,6}*1920b, {6,40,4}*1920b, {2,40,12}*1920b, {12,40,2}*1920b, {2,20,24}*1920b, {24,20,2}*1920b, {2,60,4}*1920a, {4,60,2}*1920a, {4,20,6}*1920a, {6,20,4}*1920a, {2,20,12}*1920a, {12,20,2}*1920a, {4,30,8}*1920a, {8,30,4}*1920a, {8,10,12}*1920, {12,10,8}*1920, {4,10,24}*1920, {24,10,4}*1920, {2,30,16}*1920, {16,30,2}*1920, {2,240,2}*1920, {6,10,16}*1920, {16,10,6}*1920, {2,10,48}*1920, {48,10,2}*1920, {2,80,6}*1920, {6,80,2}*1920, {2,15,6}*1920, {6,15,2}*1920, {4,15,6}*1920, {6,15,4}*1920, {2,15,8}*1920a, {8,15,2}*1920a, {2,20,12}*1920b, {12,20,2}*1920b, {2,20,6}*1920a, {2,60,6}*1920a, {6,20,2}*1920a, {6,60,2}*1920a, {4,20,6}*1920c, {4,30,6}*1920, {6,20,4}*1920c, {6,30,4}*1920, {2,30,12}*1920a, {12,30,2}*1920a, {2,30,6}*1920, {2,40,6}*1920b, {6,30,2}*1920, {6,40,2}*1920b, {2,40,6}*1920c, {2,60,6}*1920b, {6,40,2}*1920c, {6,60,2}*1920b, {2,20,12}*1920c, {2,30,12}*1920b, {12,20,2}*1920c, {12,30,2}*1920b, {2,60,4}*1920b, {4,60,2}*1920b, {4,30,4}*1920a, {4,30,4}*1920b, {2,30,4}*1920b, {2,60,4}*1920c, {4,30,2}*1920b, {4,60,2}*1920c, {2,30,8}*1920b, {8,30,2}*1920b, {2,30,8}*1920c, {8,30,2}*1920c, {2,15,4}*1920, {4,15,2}*1920, {4,15,4}*1920c
   49-fold covers : {2,245,2}*1960, {2,35,14}*1960, {14,35,2}*1960
   50-fold covers : {2,250,2}*2000, {2,10,50}*2000a, {2,50,10}*2000a, {2,50,10}*2000b, {10,50,2}*2000a, {10,50,2}*2000b, {50,10,2}*2000a, {2,10,10}*2000a, {2,10,10}*2000c, {10,10,2}*2000b, {10,10,2}*2000c, {10,10,10}*2000b, {10,10,10}*2000d, {10,10,10}*2000e, {10,10,10}*2000f, {2,10,10}*2000d, {10,10,2}*2000d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope