Polytope of Type {80}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {80}*160
Also Known As : 80-gon, {80}. if this polytope has another name.
Group : SmallGroup(160,6)
Rank : 2
Schlafli Type : {80}
Number of vertices, edges, etc : 80, 80
Order of s0s1 : 80
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{80,2} of size 320
{80,4} of size 640
{80,4} of size 640
{80,6} of size 960
{80,4} of size 1280
{80,4} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{80,10} of size 1600
{80,10} of size 1600
{80,10} of size 1600
{80,12} of size 1920
{80,12} of size 1920
{80,6} of size 1920
{80,6} of size 1920
{80,10} of size 1920
{80,10} of size 1920
Vertex Figure Of :
{2,80} of size 320
{4,80} of size 640
{4,80} of size 640
{6,80} of size 960
{4,80} of size 1280
{4,80} of size 1280
{8,80} of size 1280
{8,80} of size 1280
{8,80} of size 1280
{8,80} of size 1280
{8,80} of size 1280
{8,80} of size 1280
{10,80} of size 1600
{10,80} of size 1600
{10,80} of size 1600
{12,80} of size 1920
{12,80} of size 1920
{6,80} of size 1920
{6,80} of size 1920
{10,80} of size 1920
{10,80} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {40}*80
4-fold quotients : {20}*40
5-fold quotients : {16}*32
8-fold quotients : {10}*20
10-fold quotients : {8}*16
16-fold quotients : {5}*10
20-fold quotients : {4}*8
40-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {160}*320
3-fold covers : {240}*480
4-fold covers : {320}*640
5-fold covers : {400}*800
6-fold covers : {480}*960
7-fold covers : {560}*1120
8-fold covers : {640}*1280
9-fold covers : {720}*1440
10-fold covers : {800}*1600
11-fold covers : {880}*1760
12-fold covers : {960}*1920
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(11,16)(12,20)(13,19)(14,18)(15,17)(21,31)
(22,35)(23,34)(24,33)(25,32)(26,36)(27,40)(28,39)(29,38)(30,37)(41,61)(42,65)
(43,64)(44,63)(45,62)(46,66)(47,70)(48,69)(49,68)(50,67)(51,76)(52,80)(53,79)
(54,78)(55,77)(56,71)(57,75)(58,74)(59,73)(60,72);;
s1 := ( 1,42)( 2,41)( 3,45)( 4,44)( 5,43)( 6,47)( 7,46)( 8,50)( 9,49)(10,48)
(11,57)(12,56)(13,60)(14,59)(15,58)(16,52)(17,51)(18,55)(19,54)(20,53)(21,72)
(22,71)(23,75)(24,74)(25,73)(26,77)(27,76)(28,80)(29,79)(30,78)(31,62)(32,61)
(33,65)(34,64)(35,63)(36,67)(37,66)(38,70)(39,69)(40,68);;
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*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(80)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(11,16)(12,20)(13,19)(14,18)(15,17)
(21,31)(22,35)(23,34)(24,33)(25,32)(26,36)(27,40)(28,39)(29,38)(30,37)(41,61)
(42,65)(43,64)(44,63)(45,62)(46,66)(47,70)(48,69)(49,68)(50,67)(51,76)(52,80)
(53,79)(54,78)(55,77)(56,71)(57,75)(58,74)(59,73)(60,72);
s1 := Sym(80)!( 1,42)( 2,41)( 3,45)( 4,44)( 5,43)( 6,47)( 7,46)( 8,50)( 9,49)
(10,48)(11,57)(12,56)(13,60)(14,59)(15,58)(16,52)(17,51)(18,55)(19,54)(20,53)
(21,72)(22,71)(23,75)(24,74)(25,73)(26,77)(27,76)(28,80)(29,79)(30,78)(31,62)
(32,61)(33,65)(34,64)(35,63)(36,67)(37,66)(38,70)(39,69)(40,68);
poly := sub<Sym(80)|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*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