Polytope of Type {20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20}*40
Also Known As : 20-gon, {20}. if this polytope has another name.
Group : SmallGroup(40,6)
Rank : 2
Schlafli Type : {20}
Number of vertices, edges, etc : 20, 20
Order of s0s1 : 20
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{20,2} of size 80
{20,4} of size 160
{20,6} of size 240
{20,6} of size 240
{20,4} of size 320
{20,8} of size 320
{20,8} of size 320
{20,6} of size 360
{20,10} of size 400
{20,10} of size 400
{20,10} of size 400
{20,12} of size 480
{20,6} of size 480
{20,6} of size 480
{20,10} of size 480
{20,10} of size 480
{20,3} of size 480
{20,5} of size 480
{20,6} of size 480
{20,14} of size 560
{20,8} of size 640
{20,4} of size 640
{20,8} of size 640
{20,16} of size 640
{20,16} of size 640
{20,4} of size 640
{20,4} of size 640
{20,4} of size 640
{20,4} of size 640
{20,5} of size 640
{20,5} of size 640
{20,18} of size 720
{20,18} of size 720
{20,4} of size 720
{20,6} of size 720
{20,20} of size 800
{20,20} of size 800
{20,20} of size 800
{20,4} of size 800
{20,22} of size 880
{20,12} of size 960
{20,24} of size 960
{20,24} of size 960
{20,4} of size 960
{20,4} of size 960
{20,4} of size 960
{20,4} of size 960
{20,6} of size 960
{20,6} of size 960
{20,6} of size 960
{20,10} of size 960
{20,6} of size 960
{20,10} of size 960
{20,12} of size 960
{20,6} of size 960
{20,12} of size 960
{20,4} of size 1000
{20,10} of size 1000
{20,10} of size 1000
{20,10} of size 1000
{20,10} of size 1000
{20,10} of size 1000
{20,26} of size 1040
{20,6} of size 1080
{20,28} of size 1120
{20,6} of size 1200
{20,6} of size 1200
{20,30} of size 1200
{20,30} of size 1200
{20,30} of size 1200
{20,5} of size 1200
{20,6} of size 1200
{20,10} of size 1200
{20,15} of size 1200
{20,30} of size 1200
{20,3} of size 1200
{20,6} of size 1200
{20,8} of size 1280
{20,16} of size 1280
{20,16} of size 1280
{20,32} of size 1280
{20,32} of size 1280
{20,4} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,5} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,10} of size 1280
{20,10} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,4} of size 1280
{20,10} of size 1280
{20,4} of size 1280
{20,4} of size 1280
{20,10} of size 1280
{20,10} of size 1280
{20,4} of size 1280
{20,10} of size 1280
{20,34} of size 1360
{20,36} of size 1440
{20,18} of size 1440
{20,3} of size 1440
{20,15} of size 1440
{20,4} of size 1440
{20,12} of size 1440
{20,3} of size 1440
{20,15} of size 1440
{20,38} of size 1520
{20,40} of size 1600
{20,20} of size 1600
{20,20} of size 1600
{20,20} of size 1600
{20,40} of size 1600
{20,40} of size 1600
{20,40} of size 1600
{20,40} of size 1600
{20,40} of size 1600
{20,4} of size 1600
{20,8} of size 1600
{20,8} of size 1600
{20,5} of size 1600
{20,10} of size 1600
{20,42} of size 1680
{20,8} of size 1680
{20,42} of size 1680
{20,44} of size 1760
{20,46} of size 1840
{20,24} of size 1920
{20,48} of size 1920
{20,48} of size 1920
{20,24} of size 1920
{20,12} of size 1920
{20,6} of size 1920
{20,24} of size 1920
{20,24} of size 1920
{20,6} of size 1920
{20,12} of size 1920
{20,12} of size 1920
{20,24} of size 1920
{20,24} of size 1920
{20,12} of size 1920
{20,12} of size 1920
{20,15} of size 1920
{20,15} of size 1920
{20,4} of size 1920
{20,12} of size 1920
{20,12} of size 1920
{20,20} of size 1920
{20,12} of size 1920
{20,4} of size 1920
{20,8} of size 1920
{20,8} of size 1920
{20,12} of size 1920
{20,12} of size 1920
{20,6} of size 1920
{20,8} of size 1920
{20,8} of size 1920
{20,6} of size 1920
{20,10} of size 1920
{20,12} of size 1920
{20,12} of size 1920
{20,12} of size 1920
{20,20} of size 1920
{20,20} of size 1920
{20,20} of size 1920
{20,14} of size 1960
{20,50} of size 2000
{20,10} of size 2000
{20,10} of size 2000
{20,50} of size 2000
{20,10} of size 2000
{20,4} of size 2000
{20,10} of size 2000
{20,10} of size 2000
{20,10} of size 2000
{20,10} of size 2000
{20,10} of size 2000
{20,4} of size 2000
{20,10} of size 2000
{20,10} of size 2000
Vertex Figure Of :
{2,20} of size 80
{4,20} of size 160
{6,20} of size 240
{6,20} of size 240
{4,20} of size 320
{8,20} of size 320
{8,20} of size 320
{6,20} of size 360
{10,20} of size 400
{10,20} of size 400
{10,20} of size 400
{12,20} of size 480
{6,20} of size 480
{6,20} of size 480
{10,20} of size 480
{10,20} of size 480
{3,20} of size 480
{5,20} of size 480
{6,20} of size 480
{14,20} of size 560
{8,20} of size 640
{4,20} of size 640
{8,20} of size 640
{16,20} of size 640
{16,20} of size 640
{4,20} of size 640
{4,20} of size 640
{4,20} of size 640
{4,20} of size 640
{5,20} of size 640
{5,20} of size 640
{18,20} of size 720
{18,20} of size 720
{4,20} of size 720
{6,20} of size 720
{20,20} of size 800
{20,20} of size 800
{20,20} of size 800
{4,20} of size 800
{22,20} of size 880
{12,20} of size 960
{24,20} of size 960
{24,20} of size 960
{4,20} of size 960
{4,20} of size 960
{4,20} of size 960
{4,20} of size 960
{6,20} of size 960
{6,20} of size 960
{6,20} of size 960
{10,20} of size 960
{6,20} of size 960
{10,20} of size 960
{12,20} of size 960
{6,20} of size 960
{12,20} of size 960
{4,20} of size 1000
{10,20} of size 1000
{10,20} of size 1000
{10,20} of size 1000
{10,20} of size 1000
{10,20} of size 1000
{26,20} of size 1040
{6,20} of size 1080
{28,20} of size 1120
{6,20} of size 1200
{6,20} of size 1200
{30,20} of size 1200
{30,20} of size 1200
{30,20} of size 1200
{5,20} of size 1200
{6,20} of size 1200
{10,20} of size 1200
{15,20} of size 1200
{30,20} of size 1200
{3,20} of size 1200
{6,20} of size 1200
{8,20} of size 1280
{16,20} of size 1280
{16,20} of size 1280
{32,20} of size 1280
{32,20} of size 1280
{4,20} of size 1280
{8,20} of size 1280
{8,20} of size 1280
{8,20} of size 1280
{5,20} of size 1280
{8,20} of size 1280
{8,20} of size 1280
{8,20} of size 1280
{8,20} of size 1280
{10,20} of size 1280
{10,20} of size 1280
{8,20} of size 1280
{8,20} of size 1280
{8,20} of size 1280
{8,20} of size 1280
{4,20} of size 1280
{10,20} of size 1280
{4,20} of size 1280
{4,20} of size 1280
{10,20} of size 1280
{10,20} of size 1280
{4,20} of size 1280
{10,20} of size 1280
{34,20} of size 1360
{36,20} of size 1440
{18,20} of size 1440
{3,20} of size 1440
{15,20} of size 1440
{4,20} of size 1440
{12,20} of size 1440
{3,20} of size 1440
{15,20} of size 1440
{38,20} of size 1520
{40,20} of size 1600
{20,20} of size 1600
{20,20} of size 1600
{20,20} of size 1600
{40,20} of size 1600
{40,20} of size 1600
{40,20} of size 1600
{40,20} of size 1600
{40,20} of size 1600
{4,20} of size 1600
{8,20} of size 1600
{8,20} of size 1600
{5,20} of size 1600
{10,20} of size 1600
{42,20} of size 1680
{8,20} of size 1680
{42,20} of size 1680
{44,20} of size 1760
{46,20} of size 1840
{24,20} of size 1920
{48,20} of size 1920
{48,20} of size 1920
{24,20} of size 1920
{12,20} of size 1920
{6,20} of size 1920
{24,20} of size 1920
{24,20} of size 1920
{6,20} of size 1920
{12,20} of size 1920
{12,20} of size 1920
{24,20} of size 1920
{24,20} of size 1920
{12,20} of size 1920
{12,20} of size 1920
{15,20} of size 1920
{15,20} of size 1920
{4,20} of size 1920
{12,20} of size 1920
{12,20} of size 1920
{20,20} of size 1920
{12,20} of size 1920
{4,20} of size 1920
{8,20} of size 1920
{8,20} of size 1920
{12,20} of size 1920
{12,20} of size 1920
{6,20} of size 1920
{8,20} of size 1920
{8,20} of size 1920
{6,20} of size 1920
{10,20} of size 1920
{12,20} of size 1920
{12,20} of size 1920
{12,20} of size 1920
{20,20} of size 1920
{20,20} of size 1920
{20,20} of size 1920
{14,20} of size 1960
{50,20} of size 2000
{10,20} of size 2000
{10,20} of size 2000
{50,20} of size 2000
{10,20} of size 2000
{4,20} of size 2000
{10,20} of size 2000
{10,20} of size 2000
{10,20} of size 2000
{10,20} of size 2000
{10,20} of size 2000
{4,20} of size 2000
{10,20} of size 2000
{10,20} of size 2000
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10}*20
4-fold quotients : {5}*10
5-fold quotients : {4}*8
10-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {40}*80
3-fold covers : {60}*120
4-fold covers : {80}*160
5-fold covers : {100}*200
6-fold covers : {120}*240
7-fold covers : {140}*280
8-fold covers : {160}*320
9-fold covers : {180}*360
10-fold covers : {200}*400
11-fold covers : {220}*440
12-fold covers : {240}*480
13-fold covers : {260}*520
14-fold covers : {280}*560
15-fold covers : {300}*600
16-fold covers : {320}*640
17-fold covers : {340}*680
18-fold covers : {360}*720
19-fold covers : {380}*760
20-fold covers : {400}*800
21-fold covers : {420}*840
22-fold covers : {440}*880
23-fold covers : {460}*920
24-fold covers : {480}*960
25-fold covers : {500}*1000
26-fold covers : {520}*1040
27-fold covers : {540}*1080
28-fold covers : {560}*1120
29-fold covers : {580}*1160
30-fold covers : {600}*1200
31-fold covers : {620}*1240
32-fold covers : {640}*1280
33-fold covers : {660}*1320
34-fold covers : {680}*1360
35-fold covers : {700}*1400
36-fold covers : {720}*1440
37-fold covers : {740}*1480
38-fold covers : {760}*1520
39-fold covers : {780}*1560
40-fold covers : {800}*1600
41-fold covers : {820}*1640
42-fold covers : {840}*1680
43-fold covers : {860}*1720
44-fold covers : {880}*1760
45-fold covers : {900}*1800
46-fold covers : {920}*1840
47-fold covers : {940}*1880
48-fold covers : {960}*1920
49-fold covers : {980}*1960
50-fold covers : {1000}*2000
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)(18,20);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(20)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);
s1 := Sym(20)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)
(18,20);
poly := sub<Sym(20)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope