Polytope of Type {8,2,7}

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

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

Permutation Representation (Magma) :

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

to this polytope