Polytope of Type {3,2,8,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,8,10}*960
if this polytope has a name.
Group : SmallGroup(960,8239)
Rank : 5
Schlafli Type : {3,2,8,10}
Number of vertices, edges, etc : 3, 3, 8, 40, 10
Order of s0s1s2s3s4 : 120
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,8,10,2} of size 1920
Vertex Figure Of :
{2,3,2,8,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,4,10}*480
4-fold quotients : {3,2,2,10}*240
5-fold quotients : {3,2,8,2}*192
8-fold quotients : {3,2,2,5}*120
10-fold quotients : {3,2,4,2}*96
20-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,8,20}*1920a, {3,2,16,10}*1920, {6,2,8,10}*1920
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := (14,19)(15,20)(16,21)(17,22)(18,23)(24,39)(25,40)(26,41)(27,42)(28,43)
(29,34)(30,35)(31,36)(32,37)(33,38);;
s3 := ( 4,24)( 5,28)( 6,27)( 7,26)( 8,25)( 9,29)(10,33)(11,32)(12,31)(13,30)
(14,39)(15,43)(16,42)(17,41)(18,40)(19,34)(20,38)(21,37)(22,36)(23,35);;
s4 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,25)(26,28)
(29,30)(31,33)(34,35)(36,38)(39,40)(41,43);;
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, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*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(43)!(2,3);
s1 := Sym(43)!(1,2);
s2 := Sym(43)!(14,19)(15,20)(16,21)(17,22)(18,23)(24,39)(25,40)(26,41)(27,42)
(28,43)(29,34)(30,35)(31,36)(32,37)(33,38);
s3 := Sym(43)!( 4,24)( 5,28)( 6,27)( 7,26)( 8,25)( 9,29)(10,33)(11,32)(12,31)
(13,30)(14,39)(15,43)(16,42)(17,41)(18,40)(19,34)(20,38)(21,37)(22,36)(23,35);
s4 := Sym(43)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,25)
(26,28)(29,30)(31,33)(34,35)(36,38)(39,40)(41,43);
poly := sub<Sym(43)|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,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope