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# Polytope of Type {2,10,4,2}

Atlas Canonical Name : {2,10,4,2}*320
if this polytope has a name.
Group : SmallGroup(320,1612)
Rank : 5
Schlafli Type : {2,10,4,2}
Number of vertices, edges, etc : 2, 10, 20, 4, 2
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,10,4,2,2} of size 640
{2,10,4,2,3} of size 960
{2,10,4,2,4} of size 1280
{2,10,4,2,5} of size 1600
{2,10,4,2,6} of size 1920
Vertex Figure Of :
{2,2,10,4,2} of size 640
{3,2,10,4,2} of size 960
{4,2,10,4,2} of size 1280
{5,2,10,4,2} of size 1600
{6,2,10,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,10,2,2}*160
4-fold quotients : {2,5,2,2}*80
5-fold quotients : {2,2,4,2}*64
10-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,20,4,2}*640, {2,10,4,4}*640, {4,10,4,2}*640, {2,10,8,2}*640
3-fold covers : {2,10,12,2}*960, {2,10,4,6}*960, {6,10,4,2}*960, {2,30,4,2}*960a
4-fold covers : {2,20,4,4}*1280, {4,20,4,2}*1280, {4,10,4,4}*1280, {2,10,4,8}*1280a, {2,10,8,4}*1280a, {2,20,8,2}*1280a, {2,40,4,2}*1280a, {2,10,4,8}*1280b, {2,10,8,4}*1280b, {2,20,8,2}*1280b, {2,40,4,2}*1280b, {2,10,4,4}*1280, {2,20,4,2}*1280, {4,10,8,2}*1280, {8,10,4,2}*1280, {2,10,16,2}*1280
5-fold covers : {2,50,4,2}*1600, {2,10,20,2}*1600a, {2,10,4,10}*1600, {10,10,4,2}*1600a, {10,10,4,2}*1600b, {2,10,20,2}*1600c
6-fold covers : {2,30,4,4}*1920, {2,60,4,2}*1920a, {6,10,4,4}*1920, {2,10,4,12}*1920, {2,10,12,4}*1920a, {2,20,4,6}*1920, {6,20,4,2}*1920, {2,20,12,2}*1920, {4,30,4,2}*1920a, {4,10,4,6}*1920, {4,10,12,2}*1920, {12,10,4,2}*1920, {2,30,8,2}*1920, {2,10,8,6}*1920, {6,10,8,2}*1920, {2,10,24,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 8, 9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22);;
s2 := ( 3, 5)( 4,13)( 6,10)( 7, 8)( 9,19)(12,17)(14,15)(16,20)(18,21);;
s3 := ( 3, 4)( 5, 8)( 6, 9)( 7,12)(10,15)(11,16)(13,17)(14,18)(19,21)(20,22);;
s4 := (23,24);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(24)!(1,2);
s1 := Sym(24)!( 5, 6)( 8, 9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22);
s2 := Sym(24)!( 3, 5)( 4,13)( 6,10)( 7, 8)( 9,19)(12,17)(14,15)(16,20)(18,21);
s3 := Sym(24)!( 3, 4)( 5, 8)( 6, 9)( 7,12)(10,15)(11,16)(13,17)(14,18)(19,21)
(20,22);
s4 := Sym(24)!(23,24);
poly := sub<Sym(24)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*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 >;

to this polytope