Polytope of Type {3,2,8,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,8,3}*576
if this polytope has a name.
Group : SmallGroup(576,8340)
Rank : 5
Schlafli Type : {3,2,8,3}
Number of vertices, edges, etc : 3, 3, 16, 24, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,8,3,2} of size 1152
Vertex Figure Of :
{2,3,2,8,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,4,3}*288
4-fold quotients : {3,2,4,3}*144
8-fold quotients : {3,2,2,3}*72
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,8,6}*1152b, {6,2,8,3}*1152
3-fold covers : {9,2,8,3}*1728, {3,2,8,9}*1728, {3,2,24,3}*1728, {3,6,8,3}*1728
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,14)( 5,10)( 6, 9)( 7,30)( 8,32)(11,15)(12,19)(13,21)(16,18)(17,20)
(22,47)(23,51)(24,46)(25,49)(26,50)(27,48)(28,31)(29,33)(34,42)(35,44)(36,40)
(37,43)(38,45)(39,41);;
s3 := ( 5, 6)( 7, 8)( 9,22)(10,25)(12,17)(13,16)(14,34)(15,37)(18,40)(19,41)
(20,26)(21,23)(24,45)(27,44)(28,29)(30,46)(31,48)(32,35)(33,38)(36,50)(39,51)
(42,43);;
s4 := ( 4, 8)( 5,17)( 6,13)( 9,21)(10,20)(11,29)(12,16)(14,32)(15,33)(18,19)
(22,24)(23,45)(25,27)(26,44)(34,36)(35,50)(37,39)(38,51)(40,42)(41,43)(46,47)
(48,49);;
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, s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(51)!(2,3);
s1 := Sym(51)!(1,2);
s2 := Sym(51)!( 4,14)( 5,10)( 6, 9)( 7,30)( 8,32)(11,15)(12,19)(13,21)(16,18)
(17,20)(22,47)(23,51)(24,46)(25,49)(26,50)(27,48)(28,31)(29,33)(34,42)(35,44)
(36,40)(37,43)(38,45)(39,41);
s3 := Sym(51)!( 5, 6)( 7, 8)( 9,22)(10,25)(12,17)(13,16)(14,34)(15,37)(18,40)
(19,41)(20,26)(21,23)(24,45)(27,44)(28,29)(30,46)(31,48)(32,35)(33,38)(36,50)
(39,51)(42,43);
s4 := Sym(51)!( 4, 8)( 5,17)( 6,13)( 9,21)(10,20)(11,29)(12,16)(14,32)(15,33)
(18,19)(22,24)(23,45)(25,27)(26,44)(34,36)(35,50)(37,39)(38,51)(40,42)(41,43)
(46,47)(48,49);
poly := sub<Sym(51)|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,
s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope