Polytope of Type {7,2,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,8}*224
if this polytope has a name.
Group : SmallGroup(224,105)
Rank : 4
Schlafli Type : {7,2,8}
Number of vertices, edges, etc : 7, 7, 8, 8
Order of s₀s₁s₂s₃ : 56
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,8,2} of size 448
   {7,2,8,4} of size 896
   {7,2,8,4} of size 896
   {7,2,8,6} of size 1344
   {7,2,8,3} of size 1344
   {7,2,8,4} of size 1792
   {7,2,8,8} of size 1792
   {7,2,8,8} of size 1792
   {7,2,8,8} of size 1792
   {7,2,8,8} of size 1792
   {7,2,8,4} of size 1792
Vertex Figure Of :
   {2,7,2,8} of size 448
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,4}*112
   4-fold quotients : {7,2,2}*56
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,16}*448, {14,2,8}*448
   3-fold covers : {7,2,24}*672, {21,2,8}*672
   4-fold covers : {7,2,32}*896, {28,2,8}*896, {14,4,8}*896a, {14,2,16}*896
   5-fold covers : {7,2,40}*1120, {35,2,8}*1120
   6-fold covers : {7,2,48}*1344, {21,2,16}*1344, {14,2,24}*1344, {14,6,8}*1344, {42,2,8}*1344
   7-fold covers : {49,2,8}*1568, {7,2,56}*1568, {7,14,8}*1568
   8-fold covers : {7,2,64}*1792, {14,4,8}*1792a, {14,8,8}*1792a, {14,8,8}*1792b, {56,2,8}*1792, {28,4,8}*1792a, {14,4,16}*1792a, {14,4,16}*1792b, {28,2,16}*1792, {14,2,32}*1792
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,10)(11,12)(13,14);;
s3 := ( 8, 9)(10,11)(12,13)(14,15);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!(2,3)(4,5)(6,7);
s1 := Sym(15)!(1,2)(3,4)(5,6);
s2 := Sym(15)!( 9,10)(11,12)(13,14);
s3 := Sym(15)!( 8, 9)(10,11)(12,13)(14,15);
poly := sub<Sym(15)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope