Polytope of Type {40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40}*80
Also Known As : 40-gon, {40}. if this polytope has another name.
Group : SmallGroup(80,7)
Rank : 2
Schlafli Type : {40}
Number of vertices, edges, etc : 40, 40
Order of s0s1 : 40
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{40,2} of size 160
{40,4} of size 320
{40,4} of size 320
{40,6} of size 480
{40,4} of size 640
{40,8} of size 640
{40,8} of size 640
{40,8} of size 640
{40,8} of size 640
{40,4} of size 640
{40,10} of size 800
{40,10} of size 800
{40,10} of size 800
{40,12} of size 960
{40,12} of size 960
{40,6} of size 960
{40,6} of size 960
{40,10} of size 960
{40,10} of size 960
{40,6} of size 960
{40,6} of size 960
{40,6} of size 960
{40,14} of size 1120
{40,8} of size 1280
{40,8} of size 1280
{40,4} of size 1280
{40,8} of size 1280
{40,8} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{40,16} of size 1280
{40,4} of size 1280
{40,8} of size 1280
{40,4} of size 1280
{40,4} of size 1280
{40,8} of size 1280
{40,8} of size 1280
{40,8} of size 1280
{40,4} of size 1280
{40,4} of size 1280
{40,4} of size 1280
{40,4} of size 1280
{40,18} of size 1440
{40,6} of size 1440
{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
{40,20} of size 1600
{40,4} of size 1600
{40,4} of size 1600
{40,22} of size 1760
{40,12} of size 1920
{40,24} of size 1920
{40,24} of size 1920
{40,24} of size 1920
{40,24} of size 1920
{40,12} of size 1920
{40,12} of size 1920
{40,12} of size 1920
{40,6} of size 1920
{40,12} of size 1920
{40,12} of size 1920
{40,6} of size 1920
{40,6} of size 1920
{40,6} of size 1920
{40,12} of size 1920
{40,12} of size 1920
{40,4} of size 1920
{40,6} of size 1920
{40,6} of size 1920
{40,10} of size 1920
{40,4} of size 1920
{40,4} of size 1920
{40,4} of size 1920
{40,6} of size 1920
{40,6} of size 1920
{40,10} of size 1920
Vertex Figure Of :
{2,40} of size 160
{4,40} of size 320
{4,40} of size 320
{6,40} of size 480
{4,40} of size 640
{8,40} of size 640
{8,40} of size 640
{8,40} of size 640
{8,40} of size 640
{4,40} of size 640
{10,40} of size 800
{10,40} of size 800
{10,40} of size 800
{12,40} of size 960
{12,40} of size 960
{6,40} of size 960
{6,40} of size 960
{10,40} of size 960
{10,40} of size 960
{6,40} of size 960
{6,40} of size 960
{6,40} of size 960
{14,40} of size 1120
{8,40} of size 1280
{8,40} of size 1280
{4,40} of size 1280
{8,40} of size 1280
{8,40} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{16,40} of size 1280
{4,40} of size 1280
{8,40} of size 1280
{4,40} of size 1280
{4,40} of size 1280
{8,40} of size 1280
{8,40} of size 1280
{8,40} of size 1280
{4,40} of size 1280
{4,40} of size 1280
{4,40} of size 1280
{4,40} of size 1280
{18,40} of size 1440
{6,40} of size 1440
{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
{20,40} of size 1600
{4,40} of size 1600
{4,40} of size 1600
{22,40} of size 1760
{12,40} of size 1920
{24,40} of size 1920
{24,40} of size 1920
{24,40} of size 1920
{24,40} of size 1920
{12,40} of size 1920
{12,40} of size 1920
{12,40} of size 1920
{6,40} of size 1920
{12,40} of size 1920
{12,40} of size 1920
{6,40} of size 1920
{6,40} of size 1920
{6,40} of size 1920
{12,40} of size 1920
{12,40} of size 1920
{4,40} of size 1920
{6,40} of size 1920
{6,40} of size 1920
{10,40} of size 1920
{4,40} of size 1920
{4,40} of size 1920
{4,40} of size 1920
{6,40} of size 1920
{6,40} of size 1920
{10,40} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20}*40
4-fold quotients : {10}*20
5-fold quotients : {8}*16
8-fold quotients : {5}*10
10-fold quotients : {4}*8
20-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {80}*160
3-fold covers : {120}*240
4-fold covers : {160}*320
5-fold covers : {200}*400
6-fold covers : {240}*480
7-fold covers : {280}*560
8-fold covers : {320}*640
9-fold covers : {360}*720
10-fold covers : {400}*800
11-fold covers : {440}*880
12-fold covers : {480}*960
13-fold covers : {520}*1040
14-fold covers : {560}*1120
15-fold covers : {600}*1200
16-fold covers : {640}*1280
17-fold covers : {680}*1360
18-fold covers : {720}*1440
19-fold covers : {760}*1520
20-fold covers : {800}*1600
21-fold covers : {840}*1680
22-fold covers : {880}*1760
23-fold covers : {920}*1840
24-fold covers : {960}*1920
25-fold covers : {1000}*2000
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)
(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);;
s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)(14,20)
(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);;
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*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(40)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)
(17,23)(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);
s1 := Sym(40)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)
(14,20)(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);
poly := sub<Sym(40)|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*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