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Polytope of Type {3,2,2,7,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,7,2}*336
if this polytope has a name.
Group : SmallGroup(336,219)
Rank : 6
Schlafli Type : {3,2,2,7,2}
Number of vertices, edges, etc : 3, 3, 2, 7, 7, 2
Order of s0s1s2s3s4s5 : 42
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,2,7,2,2} of size 672
{3,2,2,7,2,3} of size 1008
{3,2,2,7,2,4} of size 1344
{3,2,2,7,2,5} of size 1680
Vertex Figure Of :
{2,3,2,2,7,2} of size 672
{3,3,2,2,7,2} of size 1344
{4,3,2,2,7,2} of size 1344
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,2,14,2}*672, {6,2,2,7,2}*672
3-fold covers : {9,2,2,7,2}*1008, {3,6,2,7,2}*1008, {3,2,2,21,2}*1008
4-fold covers : {12,2,2,7,2}*1344, {3,2,2,28,2}*1344, {3,2,2,14,4}*1344, {3,2,4,14,2}*1344, {6,4,2,7,2}*1344a, {3,4,2,7,2}*1344, {6,2,2,14,2}*1344
5-fold covers : {15,2,2,7,2}*1680, {3,2,2,35,2}*1680
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)( 9,10)(11,12);;
s4 := ( 6, 7)( 8, 9)(10,11);;
s5 := (13,14);;
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,
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(14)!(2,3);
s1 := Sym(14)!(1,2);
s2 := Sym(14)!(4,5);
s3 := Sym(14)!( 7, 8)( 9,10)(11,12);
s4 := Sym(14)!( 6, 7)( 8, 9)(10,11);
s5 := Sym(14)!(13,14);
poly := sub<Sym(14)|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, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope