include("/home/bitnami/htdocs/websites/abstract-polytopes/www/subs.php"); ?>
Polytope of Type {4,2,2,4,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,4,14}*1792
if this polytope has a name.
Group : SmallGroup(1792,1076474)
Rank : 6
Schlafli Type : {4,2,2,4,14}
Number of vertices, edges, etc : 4, 4, 2, 4, 28, 14
Order of s0s1s2s3s4s5 : 28
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,4,14}*896, {4,2,2,2,14}*896
4-fold quotients : {4,2,2,2,7}*448, {2,2,2,2,14}*448
7-fold quotients : {4,2,2,4,2}*256
8-fold quotients : {2,2,2,2,7}*224
14-fold quotients : {2,2,2,4,2}*128, {4,2,2,2,2}*128
28-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (5,6);;
s3 := ( 8,11)(12,17)(13,18)(19,25)(20,26)(27,31)(28,32);;
s4 := ( 7, 8)( 9,13)(10,12)(11,16)(14,20)(15,19)(17,24)(18,23)(21,28)(22,27)
(25,30)(26,29)(31,34)(32,33);;
s5 := ( 7, 9)( 8,12)(10,14)(11,17)(13,19)(15,21)(16,23)(18,25)(20,27)(24,29)
(26,31)(30,33);;
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*s2*s0*s2, s1*s2*s1*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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(34)!(2,3);
s1 := Sym(34)!(1,2)(3,4);
s2 := Sym(34)!(5,6);
s3 := Sym(34)!( 8,11)(12,17)(13,18)(19,25)(20,26)(27,31)(28,32);
s4 := Sym(34)!( 7, 8)( 9,13)(10,12)(11,16)(14,20)(15,19)(17,24)(18,23)(21,28)
(22,27)(25,30)(26,29)(31,34)(32,33);
s5 := Sym(34)!( 7, 9)( 8,12)(10,14)(11,17)(13,19)(15,21)(16,23)(18,25)(20,27)
(24,29)(26,31)(30,33);
poly := sub<Sym(34)|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*s2*s0*s2, s1*s2*s1*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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;
to this polytope