Questions?
See the FAQ
or other info.

# Polytope of Type {20,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8,2}*640a
if this polytope has a name.
Group : SmallGroup(640,12556)
Rank : 4
Schlafli Type : {20,8,2}
Number of vertices, edges, etc : 20, 80, 8, 2
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{20,8,2,2} of size 1280
{20,8,2,3} of size 1920
Vertex Figure Of :
{2,20,8,2} of size 1280
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20,4,2}*320, {10,8,2}*320
4-fold quotients : {20,2,2}*160, {10,4,2}*160
5-fold quotients : {4,8,2}*128a
8-fold quotients : {10,2,2}*80
10-fold quotients : {4,4,2}*64, {2,8,2}*64
16-fold quotients : {5,2,2}*40
20-fold quotients : {2,4,2}*32, {4,2,2}*32
40-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,8,2}*1280a, {40,8,2}*1280a, {40,8,2}*1280c, {20,8,4}*1280d, {20,16,2}*1280a, {20,16,2}*1280b
3-fold covers : {60,8,2}*1920a, {20,8,6}*1920a, {20,24,2}*1920a
Permutation Representation (GAP) :
```s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)
(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(41,61)(42,65)(43,64)(44,63)(45,62)
(46,66)(47,70)(48,69)(49,68)(50,67)(51,71)(52,75)(53,74)(54,73)(55,72)(56,76)
(57,80)(58,79)(59,78)(60,77);;
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)(21,62)
(22,61)(23,65)(24,64)(25,63)(26,67)(27,66)(28,70)(29,69)(30,68)(31,77)(32,76)
(33,80)(34,79)(35,78)(36,72)(37,71)(38,75)(39,74)(40,73);;
s2 := (11,16)(12,17)(13,18)(14,19)(15,20)(31,36)(32,37)(33,38)(34,39)(35,40)
(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(61,71)
(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80);;
s3 := (81,82);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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(82)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)
(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(41,61)(42,65)(43,64)(44,63)
(45,62)(46,66)(47,70)(48,69)(49,68)(50,67)(51,71)(52,75)(53,74)(54,73)(55,72)
(56,76)(57,80)(58,79)(59,78)(60,77);
s1 := Sym(82)!( 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)
(21,62)(22,61)(23,65)(24,64)(25,63)(26,67)(27,66)(28,70)(29,69)(30,68)(31,77)
(32,76)(33,80)(34,79)(35,78)(36,72)(37,71)(38,75)(39,74)(40,73);
s2 := Sym(82)!(11,16)(12,17)(13,18)(14,19)(15,20)(31,36)(32,37)(33,38)(34,39)
(35,40)(41,51)(42,52)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)
(61,71)(62,72)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80);
s3 := Sym(82)!(81,82);
poly := sub<Sym(82)|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, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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 >;

```

to this polytope