Polytope of Type {20,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,2,2}*160
if this polytope has a name.
Group : SmallGroup(160,215)
Rank : 4
Schlafli Type : {20,2,2}
Number of vertices, edges, etc : 20, 20, 2, 2
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{20,2,2,2} of size 320
{20,2,2,3} of size 480
{20,2,2,4} of size 640
{20,2,2,5} of size 800
{20,2,2,6} of size 960
{20,2,2,7} of size 1120
{20,2,2,8} of size 1280
{20,2,2,9} of size 1440
{20,2,2,10} of size 1600
{20,2,2,11} of size 1760
{20,2,2,12} of size 1920
Vertex Figure Of :
{2,20,2,2} of size 320
{4,20,2,2} of size 640
{6,20,2,2} of size 960
{6,20,2,2} of size 960
{8,20,2,2} of size 1280
{8,20,2,2} of size 1280
{4,20,2,2} of size 1280
{6,20,2,2} of size 1440
{10,20,2,2} of size 1600
{10,20,2,2} of size 1600
{10,20,2,2} of size 1600
{12,20,2,2} of size 1920
{6,20,2,2} of size 1920
{6,20,2,2} of size 1920
{6,20,2,2} of size 1920
{10,20,2,2} of size 1920
{10,20,2,2} of size 1920
{3,20,2,2} of size 1920
{5,20,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,2,2}*80
4-fold quotients : {5,2,2}*40
5-fold quotients : {4,2,2}*32
10-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,4,2}*320, {20,2,4}*320, {40,2,2}*320
3-fold covers : {20,2,6}*480, {20,6,2}*480a, {60,2,2}*480
4-fold covers : {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, {80,2,2}*640
5-fold covers : {100,2,2}*800, {20,2,10}*800, {20,10,2}*800a, {20,10,2}*800b
6-fold covers : {20,2,12}*960, {20,4,6}*960, {20,6,4}*960a, {40,2,6}*960, {40,6,2}*960, {20,12,2}*960, {60,4,2}*960a, {60,2,4}*960, {120,2,2}*960
7-fold covers : {20,2,14}*1120, {20,14,2}*1120, {140,2,2}*1120
8-fold covers : {20,8,2}*1280a, {40,4,2}*1280a, {40,8,2}*1280a, {40,8,2}*1280b, {40,8,2}*1280c, {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, {20,16,2}*1280a, {80,4,2}*1280a, {20,16,2}*1280b, {80,4,2}*1280b, {20,4,2}*1280a, {40,4,2}*1280b, {20,8,2}*1280b, {20,2,16}*1280, {80,2,4}*1280, {160,2,2}*1280
9-fold covers : {20,2,18}*1440, {20,18,2}*1440a, {180,2,2}*1440, {20,6,6}*1440a, {20,6,6}*1440b, {20,6,6}*1440c, {60,6,2}*1440a, {60,2,6}*1440, {60,6,2}*1440b, {60,6,2}*1440c, {20,6,2}*1440
10-fold covers : {100,4,2}*1600, {100,2,4}*1600, {200,2,2}*1600, {20,2,20}*1600, {20,10,4}*1600a, {20,4,10}*1600, {40,2,10}*1600, {40,10,2}*1600a, {40,10,2}*1600b, {20,20,2}*1600a, {20,20,2}*1600c, {20,10,4}*1600b
11-fold covers : {20,2,22}*1760, {20,22,2}*1760, {220,2,2}*1760
12-fold covers : {60,4,4}*1920, {20,12,4}*1920a, {20,4,12}*1920, {60,8,2}*1920a, {120,4,2}*1920a, {20,8,6}*1920a, {40,4,6}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {60,8,2}*1920b, {120,4,2}*1920b, {20,8,6}*1920b, {40,4,6}*1920b, {40,12,2}*1920b, {20,24,2}*1920b, {60,4,2}*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, {240,2,2}*1920, {80,2,6}*1920, {80,6,2}*1920, {20,4,6}*1920b, {20,6,4}*1920a, {20,6,6}*1920, {20,6,2}*1920a, {60,6,2}*1920a, {60,4,2}*1920b
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);;
s2 := (21,22);;
s3 := (23,24);;
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*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(24)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);
s1 := Sym(24)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)
(18,20);
s2 := Sym(24)!(21,22);
s3 := Sym(24)!(23,24);
poly := sub<Sym(24)|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*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