Polytope of Type {5,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,2}*40
if this polytope has a name.
Group : SmallGroup(40,13)
Rank : 4
Schlafli Type : {5,2,2}
Number of vertices, edges, etc : 5, 5, 2, 2
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,2,2,2} of size 80
{5,2,2,3} of size 120
{5,2,2,4} of size 160
{5,2,2,5} of size 200
{5,2,2,6} of size 240
{5,2,2,7} of size 280
{5,2,2,8} of size 320
{5,2,2,9} of size 360
{5,2,2,10} of size 400
{5,2,2,11} of size 440
{5,2,2,12} of size 480
{5,2,2,13} of size 520
{5,2,2,14} of size 560
{5,2,2,15} of size 600
{5,2,2,16} of size 640
{5,2,2,17} of size 680
{5,2,2,18} of size 720
{5,2,2,19} of size 760
{5,2,2,20} of size 800
{5,2,2,21} of size 840
{5,2,2,22} of size 880
{5,2,2,23} of size 920
{5,2,2,24} of size 960
{5,2,2,25} of size 1000
{5,2,2,26} of size 1040
{5,2,2,27} of size 1080
{5,2,2,28} of size 1120
{5,2,2,29} of size 1160
{5,2,2,30} of size 1200
{5,2,2,31} of size 1240
{5,2,2,32} of size 1280
{5,2,2,33} of size 1320
{5,2,2,34} of size 1360
{5,2,2,35} of size 1400
{5,2,2,36} of size 1440
{5,2,2,37} of size 1480
{5,2,2,38} of size 1520
{5,2,2,39} of size 1560
{5,2,2,40} of size 1600
{5,2,2,41} of size 1640
{5,2,2,42} of size 1680
{5,2,2,43} of size 1720
{5,2,2,44} of size 1760
{5,2,2,45} of size 1800
{5,2,2,46} of size 1840
{5,2,2,47} of size 1880
{5,2,2,48} of size 1920
{5,2,2,49} of size 1960
{5,2,2,50} of size 2000
Vertex Figure Of :
{2,5,2,2} of size 80
{3,5,2,2} of size 240
{5,5,2,2} of size 240
{10,5,2,2} of size 400
{4,5,2,2} of size 480
{6,5,2,2} of size 480
{3,5,2,2} of size 480
{5,5,2,2} of size 480
{6,5,2,2} of size 480
{6,5,2,2} of size 480
{10,5,2,2} of size 480
{10,5,2,2} of size 480
{4,5,2,2} of size 640
{5,5,2,2} of size 640
{4,5,2,2} of size 960
{6,5,2,2} of size 960
{6,5,2,2} of size 960
{10,5,2,2} of size 960
{5,5,2,2} of size 1280
{8,5,2,2} of size 1280
{8,5,2,2} of size 1280
{10,5,2,2} of size 1280
{4,5,2,2} of size 1280
{10,5,2,2} of size 1280
{6,5,2,2} of size 1920
{8,5,2,2} of size 1920
{12,5,2,2} of size 1920
{20,5,2,2} of size 1920
{10,5,2,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,2,4}*80, {10,2,2}*80
3-fold covers : {5,2,6}*120, {15,2,2}*120
4-fold covers : {5,2,8}*160, {20,2,2}*160, {10,2,4}*160, {10,4,2}*160
5-fold covers : {25,2,2}*200, {5,2,10}*200, {5,10,2}*200
6-fold covers : {5,2,12}*240, {15,2,4}*240, {10,2,6}*240, {10,6,2}*240, {30,2,2}*240
7-fold covers : {5,2,14}*280, {35,2,2}*280
8-fold covers : {5,2,16}*320, {20,4,2}*320, {20,2,4}*320, {10,4,4}*320, {40,2,2}*320, {10,2,8}*320, {10,8,2}*320
9-fold covers : {5,2,18}*360, {45,2,2}*360, {15,2,6}*360, {15,6,2}*360
10-fold covers : {25,2,4}*400, {50,2,2}*400, {5,2,20}*400, {5,10,4}*400, {10,2,10}*400, {10,10,2}*400a, {10,10,2}*400c
11-fold covers : {5,2,22}*440, {55,2,2}*440
12-fold covers : {5,2,24}*480, {15,2,8}*480, {10,2,12}*480, {10,12,2}*480, {20,2,6}*480, {20,6,2}*480a, {10,4,6}*480, {10,6,4}*480a, {60,2,2}*480, {30,2,4}*480, {30,4,2}*480a, {15,6,2}*480, {15,4,2}*480
13-fold covers : {5,2,26}*520, {65,2,2}*520
14-fold covers : {5,2,28}*560, {35,2,4}*560, {10,2,14}*560, {10,14,2}*560, {70,2,2}*560
15-fold covers : {25,2,6}*600, {75,2,2}*600, {5,10,6}*600, {5,2,30}*600, {15,2,10}*600, {15,10,2}*600
16-fold covers : {5,2,32}*640, {20,4,4}*640, {40,4,2}*640a, {20,4,2}*640, {40,4,2}*640b, {20,8,2}*640a, {20,8,2}*640b, {40,2,4}*640, {20,2,8}*640, {10,4,8}*640a, {10,8,4}*640a, {10,4,8}*640b, {10,8,4}*640b, {10,4,4}*640, {80,2,2}*640, {10,2,16}*640, {10,16,2}*640, {5,4,2}*640
17-fold covers : {5,2,34}*680, {85,2,2}*680
18-fold covers : {5,2,36}*720, {45,2,4}*720, {10,2,18}*720, {10,18,2}*720, {90,2,2}*720, {15,2,12}*720, {15,6,4}*720, {10,6,6}*720a, {10,6,6}*720b, {10,6,6}*720c, {30,6,2}*720a, {30,2,6}*720, {30,6,2}*720b, {30,6,2}*720c
19-fold covers : {5,2,38}*760, {95,2,2}*760
20-fold covers : {25,2,8}*800, {100,2,2}*800, {50,2,4}*800, {50,4,2}*800, {5,2,40}*800, {5,10,8}*800, {10,2,20}*800, {10,20,2}*800a, {20,2,10}*800, {20,10,2}*800a, {20,10,2}*800b, {10,4,10}*800, {10,10,4}*800a, {10,10,4}*800c, {10,20,2}*800c
21-fold covers : {15,2,14}*840, {5,2,42}*840, {35,2,6}*840, {105,2,2}*840
22-fold covers : {5,2,44}*880, {55,2,4}*880, {10,2,22}*880, {10,22,2}*880, {110,2,2}*880
23-fold covers : {5,2,46}*920, {115,2,2}*920
24-fold covers : {5,2,48}*960, {15,2,16}*960, {20,2,12}*960, {10,4,12}*960, {10,12,4}*960a, {20,4,6}*960, {20,6,4}*960a, {10,2,24}*960, {10,24,2}*960, {40,2,6}*960, {40,6,2}*960, {10,6,8}*960, {10,8,6}*960, {20,12,2}*960, {60,4,2}*960a, {60,2,4}*960, {30,4,4}*960, {120,2,2}*960, {30,2,8}*960, {30,8,2}*960, {15,12,2}*960, {15,6,4}*960, {15,4,4}*960b, {15,8,2}*960, {10,4,6}*960, {10,6,4}*960e, {10,6,6}*960, {20,6,2}*960c, {30,6,2}*960, {30,4,2}*960
25-fold covers : {125,2,2}*1000, {5,2,50}*1000, {25,2,10}*1000, {25,10,2}*1000, {5,10,10}*1000a, {5,10,2}*1000, {5,10,10}*1000b
26-fold covers : {5,2,52}*1040, {65,2,4}*1040, {10,2,26}*1040, {10,26,2}*1040, {130,2,2}*1040
27-fold covers : {5,2,54}*1080, {135,2,2}*1080, {45,2,6}*1080, {45,6,2}*1080, {15,2,18}*1080, {15,6,6}*1080a, {15,6,2}*1080, {15,6,6}*1080b
28-fold covers : {5,2,56}*1120, {35,2,8}*1120, {20,2,14}*1120, {20,14,2}*1120, {10,2,28}*1120, {10,28,2}*1120, {10,4,14}*1120, {10,14,4}*1120, {140,2,2}*1120, {70,2,4}*1120, {70,4,2}*1120
29-fold covers : {5,2,58}*1160, {145,2,2}*1160
30-fold covers : {25,2,12}*1200, {75,2,4}*1200, {50,2,6}*1200, {50,6,2}*1200, {150,2,2}*1200, {5,10,12}*1200, {15,2,20}*1200, {5,2,60}*1200, {15,10,4}*1200, {10,6,10}*1200, {10,10,6}*1200a, {10,10,6}*1200c, {10,30,2}*1200a, {10,2,30}*1200, {10,30,2}*1200b, {30,2,10}*1200, {30,10,2}*1200b, {30,10,2}*1200c
31-fold covers : {5,2,62}*1240, {155,2,2}*1240
32-fold covers : {5,2,64}*1280, {10,4,8}*1280a, {10,8,4}*1280a, {20,8,2}*1280a, {40,4,2}*1280a, {10,8,8}*1280a, {10,8,8}*1280b, {10,8,8}*1280c, {40,8,2}*1280a, {40,8,2}*1280b, {40,8,2}*1280c, {10,8,8}*1280d, {40,8,2}*1280d, {40,2,8}*1280, {20,4,8}*1280a, {40,4,4}*1280a, {20,4,8}*1280b, {40,4,4}*1280b, {20,8,4}*1280a, {20,4,4}*1280a, {20,4,4}*1280b, {20,8,4}*1280b, {20,8,4}*1280c, {20,8,4}*1280d, {10,4,16}*1280a, {10,16,4}*1280a, {20,16,2}*1280a, {80,4,2}*1280a, {10,4,16}*1280b, {10,16,4}*1280b, {20,16,2}*1280b, {80,4,2}*1280b, {10,4,4}*1280, {10,4,8}*1280b, {10,8,4}*1280b, {20,4,2}*1280a, {40,4,2}*1280b, {20,8,2}*1280b, {20,2,16}*1280, {80,2,4}*1280, {10,2,32}*1280, {10,32,2}*1280, {160,2,2}*1280, {5,4,4}*1280, {5,8,2}*1280a, {5,4,2}*1280, {5,8,2}*1280b, {10,4,2}*1280a, {10,4,2}*1280b
33-fold covers : {15,2,22}*1320, {5,2,66}*1320, {55,2,6}*1320, {165,2,2}*1320
34-fold covers : {5,2,68}*1360, {85,2,4}*1360, {10,2,34}*1360, {10,34,2}*1360, {170,2,2}*1360
35-fold covers : {25,2,14}*1400, {175,2,2}*1400, {5,10,14}*1400, {5,2,70}*1400, {35,2,10}*1400, {35,10,2}*1400
36-fold covers : {5,2,72}*1440, {45,2,8}*1440, {10,2,36}*1440, {10,36,2}*1440, {20,2,18}*1440, {20,18,2}*1440a, {10,4,18}*1440, {10,18,4}*1440a, {180,2,2}*1440, {90,2,4}*1440, {90,4,2}*1440a, {15,2,24}*1440, {15,6,8}*1440, {45,4,2}*1440, {10,6,12}*1440a, {10,6,12}*1440b, {10,12,6}*1440a, {10,12,6}*1440b, {20,6,6}*1440a, {20,6,6}*1440b, {20,6,6}*1440c, {60,6,2}*1440a, {30,12,2}*1440a, {10,6,12}*1440c, {10,12,6}*1440c, {30,6,4}*1440a, {30,2,12}*1440, {30,12,2}*1440b, {60,2,6}*1440, {60,6,2}*1440b, {60,6,2}*1440c, {30,4,6}*1440, {30,6,4}*1440b, {30,6,4}*1440c, {30,12,2}*1440c, {15,6,6}*1440, {10,4,4}*1440, {10,4,6}*1440c, {10,6,4}*1440, {20,4,2}*1440, {30,4,2}*1440, {15,4,6}*1440, {15,12,2}*1440, {15,6,2}*1440e, {20,6,2}*1440
37-fold covers : {5,2,74}*1480, {185,2,2}*1480
38-fold covers : {5,2,76}*1520, {95,2,4}*1520, {10,2,38}*1520, {10,38,2}*1520, {190,2,2}*1520
39-fold covers : {15,2,26}*1560, {5,2,78}*1560, {65,2,6}*1560, {195,2,2}*1560
40-fold covers : {25,2,16}*1600, {100,4,2}*1600, {100,2,4}*1600, {50,4,4}*1600, {200,2,2}*1600, {50,2,8}*1600, {50,8,2}*1600, {5,2,80}*1600, {5,10,16}*1600, {20,2,20}*1600, {20,10,4}*1600a, {10,4,20}*1600, {10,20,4}*1600a, {20,4,10}*1600, {10,2,40}*1600, {10,40,2}*1600a, {40,2,10}*1600, {40,10,2}*1600a, {40,10,2}*1600b, {10,8,10}*1600, {10,10,8}*1600a, {20,20,2}*1600a, {20,20,2}*1600c, {20,10,4}*1600b, {10,10,8}*1600c, {10,40,2}*1600c, {10,20,4}*1600c
41-fold covers : {5,2,82}*1640, {205,2,2}*1640
42-fold covers : {15,2,28}*1680, {5,2,84}*1680, {35,2,12}*1680, {105,2,4}*1680, {10,6,14}*1680, {10,14,6}*1680, {30,2,14}*1680, {30,14,2}*1680, {10,2,42}*1680, {10,42,2}*1680, {70,2,6}*1680, {70,6,2}*1680, {210,2,2}*1680
43-fold covers : {5,2,86}*1720, {215,2,2}*1720
44-fold covers : {5,2,88}*1760, {55,2,8}*1760, {20,2,22}*1760, {20,22,2}*1760, {10,2,44}*1760, {10,44,2}*1760, {10,4,22}*1760, {10,22,4}*1760, {220,2,2}*1760, {110,2,4}*1760, {110,4,2}*1760
45-fold covers : {25,2,18}*1800, {225,2,2}*1800, {75,2,6}*1800, {75,6,2}*1800, {5,10,18}*1800, {5,2,90}*1800, {45,2,10}*1800, {45,10,2}*1800, {15,6,10}*1800, {15,10,6}*1800, {15,2,30}*1800, {15,30,2}*1800
46-fold covers : {5,2,92}*1840, {115,2,4}*1840, {10,2,46}*1840, {10,46,2}*1840, {230,2,2}*1840
47-fold covers : {5,2,94}*1880, {235,2,2}*1880
48-fold covers : {15,2,32}*1920, {5,2,96}*1920, {60,4,4}*1920, {20,12,4}*1920a, {20,4,12}*1920, {30,4,8}*1920a, {30,8,4}*1920a, {60,8,2}*1920a, {120,4,2}*1920a, {10,8,12}*1920a, {10,12,8}*1920a, {20,8,6}*1920a, {10,4,24}*1920a, {10,24,4}*1920a, {40,4,6}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {30,4,8}*1920b, {30,8,4}*1920b, {60,8,2}*1920b, {120,4,2}*1920b, {10,8,12}*1920b, {10,12,8}*1920b, {20,8,6}*1920b, {10,4,24}*1920b, {10,24,4}*1920b, {40,4,6}*1920b, {40,12,2}*1920b, {20,24,2}*1920b, {30,4,4}*1920a, {60,4,2}*1920a, {10,4,12}*1920a, {10,12,4}*1920a, {20,4,6}*1920a, {20,12,2}*1920a, {60,2,8}*1920, {120,2,4}*1920, {20,6,8}*1920, {40,6,4}*1920a, {40,2,12}*1920, {20,2,24}*1920, {30,2,16}*1920, {30,16,2}*1920, {240,2,2}*1920, {10,6,16}*1920, {10,16,6}*1920, {10,2,48}*1920, {10,48,2}*1920, {80,2,6}*1920, {80,6,2}*1920, {15,6,2}*1920, {15,6,4}*1920, {15,6,8}*1920, {15,12,4}*1920, {15,4,4}*1920b, {15,8,2}*1920a, {15,8,4}*1920, {15,4,8}*1920, {10,4,12}*1920b, {10,12,4}*1920b, {20,12,2}*1920b, {20,4,6}*1920b, {20,6,4}*1920a, {20,6,6}*1920, {20,6,2}*1920a, {60,6,2}*1920a, {10,4,6}*1920, {10,4,12}*1920c, {10,6,4}*1920b, {10,6,12}*1920a, {10,12,4}*1920c, {10,12,6}*1920a, {20,6,4}*1920b, {30,12,2}*1920a, {30,6,2}*1920, {40,6,2}*1920b, {10,6,8}*1920a, {10,6,12}*1920b, {10,8,6}*1920a, {10,12,6}*1920b, {40,6,2}*1920c, {60,6,2}*1920b, {10,6,6}*1920, {10,6,8}*1920b, {10,8,6}*1920b, {30,6,4}*1920, {20,12,2}*1920c, {30,12,2}*1920b, {60,4,2}*1920b, {30,4,4}*1920d, {30,4,2}*1920b, {60,4,2}*1920c, {30,8,2}*1920b, {30,8,2}*1920c, {5,4,6}*1920, {15,4,2}*1920
49-fold covers : {5,2,98}*1960, {245,2,2}*1960, {35,2,14}*1960, {35,14,2}*1960
50-fold covers : {125,2,4}*2000, {250,2,2}*2000, {25,2,20}*2000, {5,2,100}*2000, {5,10,20}*2000a, {25,10,4}*2000, {5,10,4}*2000a, {10,2,50}*2000, {10,50,2}*2000a, {50,2,10}*2000, {50,10,2}*2000a, {50,10,2}*2000b, {10,10,10}*2000a, {10,10,2}*2000a, {10,10,2}*2000c, {5,10,20}*2000b, {5,10,4}*2000b, {10,10,10}*2000b, {10,10,10}*2000c, {10,10,10}*2000e, {10,10,10}*2000g, {10,10,2}*2000d
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(9)!(2,3)(4,5);
s1 := Sym(9)!(1,2)(3,4);
s2 := Sym(9)!(6,7);
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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope