Questions?
See the FAQ
or other info.

Polytope of Type {4,2,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,7}*224
if this polytope has a name.
Group : SmallGroup(224,178)
Rank : 5
Schlafli Type : {4,2,2,7}
Number of vertices, edges, etc : 4, 4, 2, 7, 7
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,2,7,2} of size 448
Vertex Figure Of :
   {2,4,2,2,7} of size 448
   {3,4,2,2,7} of size 672
   {4,4,2,2,7} of size 896
   {6,4,2,2,7} of size 1344
   {3,4,2,2,7} of size 1344
   {6,4,2,2,7} of size 1344
   {6,4,2,2,7} of size 1344
   {8,4,2,2,7} of size 1792
   {8,4,2,2,7} of size 1792
   {4,4,2,2,7} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,7}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,2,7}*448, {8,2,2,7}*448, {4,2,2,14}*448
   3-fold covers : {12,2,2,7}*672, {4,6,2,7}*672a, {4,2,2,21}*672
   4-fold covers : {4,8,2,7}*896a, {8,4,2,7}*896a, {4,8,2,7}*896b, {8,4,2,7}*896b, {4,4,2,7}*896, {16,2,2,7}*896, {4,2,2,28}*896, {4,4,2,14}*896, {4,2,4,14}*896, {8,2,2,14}*896
   5-fold covers : {20,2,2,7}*1120, {4,10,2,7}*1120, {4,2,2,35}*1120
   6-fold covers : {4,12,2,7}*1344a, {12,4,2,7}*1344a, {24,2,2,7}*1344, {8,6,2,7}*1344, {4,4,2,21}*1344, {8,2,2,21}*1344, {12,2,2,14}*1344, {4,2,6,14}*1344, {4,6,2,14}*1344a, {4,2,2,42}*1344
   7-fold covers : {4,2,2,49}*1568, {28,2,2,7}*1568, {4,2,14,7}*1568, {4,14,2,7}*1568
   8-fold covers : {4,8,2,7}*1792a, {8,4,2,7}*1792a, {8,8,2,7}*1792a, {8,8,2,7}*1792b, {8,8,2,7}*1792c, {8,8,2,7}*1792d, {4,16,2,7}*1792a, {16,4,2,7}*1792a, {4,16,2,7}*1792b, {16,4,2,7}*1792b, {4,4,2,7}*1792, {4,8,2,7}*1792b, {8,4,2,7}*1792b, {32,2,2,7}*1792, {4,4,4,14}*1792, {4,4,2,28}*1792, {4,2,4,28}*1792, {4,8,2,14}*1792a, {8,4,2,14}*1792a, {4,8,2,14}*1792b, {8,4,2,14}*1792b, {4,4,2,14}*1792, {4,2,8,14}*1792, {8,2,4,14}*1792, {8,2,2,28}*1792, {4,2,2,56}*1792, {16,2,2,14}*1792
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11)(12,13);;
s4 := ( 7, 8)( 9,10)(11,12);;
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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*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(13)!(2,3);
s1 := Sym(13)!(1,2)(3,4);
s2 := Sym(13)!(5,6);
s3 := Sym(13)!( 8, 9)(10,11)(12,13);
s4 := Sym(13)!( 7, 8)( 9,10)(11,12);
poly := sub<Sym(13)|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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

to this polytope