Polytope of Type {2,20,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,2}*160
if this polytope has a name.
Group : SmallGroup(160,215)
Rank : 4
Schlafli Type : {2,20,2}
Number of vertices, edges, etc : 2, 20, 20, 2
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,20,2,2} of size 320
{2,20,2,3} of size 480
{2,20,2,4} of size 640
{2,20,2,5} of size 800
{2,20,2,6} of size 960
{2,20,2,7} of size 1120
{2,20,2,8} of size 1280
{2,20,2,9} of size 1440
{2,20,2,10} of size 1600
{2,20,2,11} of size 1760
{2,20,2,12} of size 1920
Vertex Figure Of :
{2,2,20,2} of size 320
{3,2,20,2} of size 480
{4,2,20,2} of size 640
{5,2,20,2} of size 800
{6,2,20,2} of size 960
{7,2,20,2} of size 1120
{8,2,20,2} of size 1280
{9,2,20,2} of size 1440
{10,2,20,2} of size 1600
{11,2,20,2} of size 1760
{12,2,20,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,10,2}*80
4-fold quotients : {2,5,2}*40
5-fold quotients : {2,4,2}*32
10-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,20,4}*320, {4,20,2}*320, {2,40,2}*320
3-fold covers : {2,20,6}*480a, {6,20,2}*480a, {2,60,2}*480
4-fold covers : {4,20,4}*640, {2,40,4}*640a, {4,40,2}*640a, {2,20,4}*640, {4,20,2}*640, {2,40,4}*640b, {4,40,2}*640b, {2,20,8}*640a, {8,20,2}*640a, {2,20,8}*640b, {8,20,2}*640b, {2,80,2}*640
5-fold covers : {2,100,2}*800, {2,20,10}*800a, {2,20,10}*800b, {10,20,2}*800a, {10,20,2}*800b
6-fold covers : {4,20,6}*960, {6,20,4}*960, {2,40,6}*960, {6,40,2}*960, {2,20,12}*960, {12,20,2}*960, {2,60,4}*960a, {4,60,2}*960a, {2,120,2}*960
7-fold covers : {2,20,14}*1120, {14,20,2}*1120, {2,140,2}*1120
8-fold covers : {2,20,8}*1280a, {8,20,2}*1280a, {2,40,4}*1280a, {4,40,2}*1280a, {2,40,8}*1280a, {8,40,2}*1280a, {2,40,8}*1280b, {2,40,8}*1280c, {8,40,2}*1280b, {8,40,2}*1280c, {2,40,8}*1280d, {8,40,2}*1280d, {4,20,8}*1280a, {8,20,4}*1280a, {4,20,8}*1280b, {8,20,4}*1280b, {4,40,4}*1280a, {4,20,4}*1280a, {4,20,4}*1280b, {4,40,4}*1280b, {4,40,4}*1280c, {4,40,4}*1280d, {2,20,16}*1280a, {16,20,2}*1280a, {2,80,4}*1280a, {4,80,2}*1280a, {2,20,16}*1280b, {16,20,2}*1280b, {2,80,4}*1280b, {4,80,2}*1280b, {2,20,4}*1280a, {2,40,4}*1280b, {4,20,2}*1280a, {4,40,2}*1280b, {2,20,8}*1280b, {8,20,2}*1280b, {2,160,2}*1280
9-fold covers : {2,20,18}*1440a, {18,20,2}*1440a, {2,180,2}*1440, {6,20,6}*1440, {2,60,6}*1440a, {6,60,2}*1440a, {2,60,6}*1440b, {2,60,6}*1440c, {6,60,2}*1440b, {6,60,2}*1440c, {2,20,6}*1440, {6,20,2}*1440
10-fold covers : {2,100,4}*1600, {4,100,2}*1600, {2,200,2}*1600, {4,20,10}*1600a, {4,20,10}*1600b, {10,20,4}*1600a, {10,20,4}*1600b, {2,40,10}*1600a, {2,40,10}*1600b, {10,40,2}*1600a, {10,40,2}*1600b, {2,20,20}*1600a, {2,20,20}*1600c, {20,20,2}*1600a, {20,20,2}*1600b
11-fold covers : {2,20,22}*1760, {22,20,2}*1760, {2,220,2}*1760
12-fold covers : {4,60,4}*1920a, {4,20,12}*1920, {12,20,4}*1920, {2,60,8}*1920a, {8,60,2}*1920a, {2,120,4}*1920a, {4,120,2}*1920a, {6,20,8}*1920a, {8,20,6}*1920a, {4,40,6}*1920a, {6,40,4}*1920a, {2,40,12}*1920a, {12,40,2}*1920a, {2,20,24}*1920a, {24,20,2}*1920a, {2,60,8}*1920b, {8,60,2}*1920b, {2,120,4}*1920b, {4,120,2}*1920b, {6,20,8}*1920b, {8,20,6}*1920b, {4,40,6}*1920b, {6,40,4}*1920b, {2,40,12}*1920b, {12,40,2}*1920b, {2,20,24}*1920b, {24,20,2}*1920b, {2,60,4}*1920a, {4,60,2}*1920a, {4,20,6}*1920a, {6,20,4}*1920a, {2,20,12}*1920a, {12,20,2}*1920a, {2,240,2}*1920, {2,80,6}*1920, {6,80,2}*1920, {2,20,6}*1920a, {2,60,6}*1920a, {6,20,2}*1920a, {6,60,2}*1920a, {2,60,4}*1920b, {4,60,2}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,21)(14,18)(16,19)(20,22);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(24)!(1,2);
s1 := Sym(24)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22);
s2 := Sym(24)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,21)(14,18)(16,19)
(20,22);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope