Polytope of Type {4,2,4,9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,4,9}*576
if this polytope has a name.
Group : SmallGroup(576,4970)
Rank : 5
Schlafli Type : {4,2,4,9}
Number of vertices, edges, etc : 4, 4, 4, 18, 9
Order of s0s1s2s3s4 : 36
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,2,4,9,2} of size 1152
Vertex Figure Of :
{2,4,2,4,9} of size 1152
{3,4,2,4,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,4,9}*288
3-fold quotients : {4,2,4,3}*192
6-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,2,4,9}*1152, {4,2,4,9}*1152, {4,2,4,18}*1152b, {4,2,4,18}*1152c
3-fold covers : {4,2,4,27}*1728, {12,2,4,9}*1728
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6,11)( 7,13)( 8,15)( 9,17)(12,22)(14,24)(18,28)(25,34)(27,36)(29,37)
(31,38)(33,39);;
s3 := ( 5, 6)( 7,10)( 8, 9)(11,19)(12,18)(13,20)(14,16)(15,17)(21,27)(22,28)
(23,25)(24,26)(29,35)(30,36)(31,33)(32,34)(37,40)(38,39);;
s4 := ( 5,10)( 6, 8)( 7,18)( 9,14)(11,15)(12,27)(13,28)(16,23)(17,24)(19,20)
(21,35)(22,36)(25,31)(26,32)(29,33)(30,40)(34,38)(37,39);;
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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(40)!(2,3);
s1 := Sym(40)!(1,2)(3,4);
s2 := Sym(40)!( 6,11)( 7,13)( 8,15)( 9,17)(12,22)(14,24)(18,28)(25,34)(27,36)
(29,37)(31,38)(33,39);
s3 := Sym(40)!( 5, 6)( 7,10)( 8, 9)(11,19)(12,18)(13,20)(14,16)(15,17)(21,27)
(22,28)(23,25)(24,26)(29,35)(30,36)(31,33)(32,34)(37,40)(38,39);
s4 := Sym(40)!( 5,10)( 6, 8)( 7,18)( 9,14)(11,15)(12,27)(13,28)(16,23)(17,24)
(19,20)(21,35)(22,36)(25,31)(26,32)(29,33)(30,40)(34,38)(37,39);
poly := sub<Sym(40)|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*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope