Polytope of Type {2,4,2,2,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,2,2,5}*320
if this polytope has a name.
Group : SmallGroup(320,1612)
Rank : 6
Schlafli Type : {2,4,2,2,5}
Number of vertices, edges, etc : 2, 4, 4, 2, 5, 5
Order of s0s1s2s3s4s5 : 20
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,2,2,5,2} of size 640
{2,4,2,2,5,3} of size 1920
{2,4,2,2,5,5} of size 1920
Vertex Figure Of :
{2,2,4,2,2,5} of size 640
{3,2,4,2,2,5} of size 960
{4,2,4,2,2,5} of size 1280
{5,2,4,2,2,5} of size 1600
{6,2,4,2,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,2,5}*160
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,4,2,5}*640, {4,4,2,2,5}*640, {2,8,2,2,5}*640, {2,4,2,2,10}*640
3-fold covers : {2,12,2,2,5}*960, {2,4,6,2,5}*960a, {6,4,2,2,5}*960a, {2,4,2,2,15}*960
4-fold covers : {4,4,4,2,5}*1280, {2,4,8,2,5}*1280a, {2,8,4,2,5}*1280a, {4,8,2,2,5}*1280a, {8,4,2,2,5}*1280a, {2,4,8,2,5}*1280b, {2,8,4,2,5}*1280b, {4,8,2,2,5}*1280b, {8,4,2,2,5}*1280b, {2,4,4,2,5}*1280, {4,4,2,2,5}*1280, {2,16,2,2,5}*1280, {2,4,4,2,10}*1280, {4,4,2,2,10}*1280, {2,4,2,4,10}*1280, {2,4,2,2,20}*1280, {2,8,2,2,10}*1280
5-fold covers : {2,4,2,2,25}*1600, {2,20,2,2,5}*1600, {2,4,2,10,5}*1600, {2,4,10,2,5}*1600, {10,4,2,2,5}*1600
6-fold covers : {2,4,4,2,15}*1920, {4,4,2,2,15}*1920, {4,4,6,2,5}*1920, {6,4,4,2,5}*1920, {2,4,12,2,5}*1920a, {2,12,4,2,5}*1920a, {4,12,2,2,5}*1920a, {12,4,2,2,5}*1920a, {2,8,2,2,15}*1920, {2,8,6,2,5}*1920, {6,8,2,2,5}*1920, {2,24,2,2,5}*1920, {2,4,2,2,30}*1920, {2,4,2,6,10}*1920, {2,4,6,2,10}*1920a, {6,4,2,2,10}*1920a, {2,12,2,2,10}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4)(5,6);;
s3 := (7,8);;
s4 := (10,11)(12,13);;
s5 := ( 9,10)(11,12);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2*s1*s2,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(13)!(1,2);
s1 := Sym(13)!(4,5);
s2 := Sym(13)!(3,4)(5,6);
s3 := Sym(13)!(7,8);
s4 := Sym(13)!(10,11)(12,13);
s5 := Sym(13)!( 9,10)(11,12);
poly := sub<Sym(13)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s1*s2*s1*s2*s1*s2*s1*s2,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;
to this polytope