Polytope of Type {2,28,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,2}*224
if this polytope has a name.
Group : SmallGroup(224,176)
Rank : 4
Schlafli Type : {2,28,2}
Number of vertices, edges, etc : 2, 28, 28, 2
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,28,2,2} of size 448
   {2,28,2,3} of size 672
   {2,28,2,4} of size 896
   {2,28,2,5} of size 1120
   {2,28,2,6} of size 1344
   {2,28,2,7} of size 1568
   {2,28,2,8} of size 1792
Vertex Figure Of :
   {2,2,28,2} of size 448
   {3,2,28,2} of size 672
   {4,2,28,2} of size 896
   {5,2,28,2} of size 1120
   {6,2,28,2} of size 1344
   {7,2,28,2} of size 1568
   {8,2,28,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,14,2}*112
   4-fold quotients : {2,7,2}*56
   7-fold quotients : {2,4,2}*32
   14-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,28,4}*448, {4,28,2}*448, {2,56,2}*448
   3-fold covers : {2,28,6}*672a, {6,28,2}*672a, {2,84,2}*672
   4-fold covers : {4,28,4}*896, {2,56,4}*896a, {4,56,2}*896a, {2,28,4}*896, {4,28,2}*896, {2,56,4}*896b, {4,56,2}*896b, {2,28,8}*896a, {8,28,2}*896a, {2,28,8}*896b, {8,28,2}*896b, {2,112,2}*896
   5-fold covers : {2,28,10}*1120, {10,28,2}*1120, {2,140,2}*1120
   6-fold covers : {4,28,6}*1344, {6,28,4}*1344, {2,56,6}*1344, {6,56,2}*1344, {2,28,12}*1344, {12,28,2}*1344, {2,84,4}*1344a, {4,84,2}*1344a, {2,168,2}*1344
   7-fold covers : {2,196,2}*1568, {2,28,14}*1568a, {2,28,14}*1568b, {14,28,2}*1568a, {14,28,2}*1568b
   8-fold covers : {2,28,8}*1792a, {8,28,2}*1792a, {2,56,4}*1792a, {4,56,2}*1792a, {2,56,8}*1792a, {8,56,2}*1792a, {2,56,8}*1792b, {2,56,8}*1792c, {8,56,2}*1792b, {8,56,2}*1792c, {2,56,8}*1792d, {8,56,2}*1792d, {4,28,8}*1792a, {8,28,4}*1792a, {4,28,8}*1792b, {8,28,4}*1792b, {4,56,4}*1792a, {4,28,4}*1792a, {4,28,4}*1792b, {4,56,4}*1792b, {4,56,4}*1792c, {4,56,4}*1792d, {2,28,16}*1792a, {16,28,2}*1792a, {2,112,4}*1792a, {4,112,2}*1792a, {2,28,16}*1792b, {16,28,2}*1792b, {2,112,4}*1792b, {4,112,2}*1792b, {2,28,4}*1792, {2,56,4}*1792b, {4,28,2}*1792, {4,56,2}*1792b, {2,28,8}*1792b, {8,28,2}*1792b, {2,224,2}*1792
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)
(25,28)(26,27)(29,30);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)(18,21)
(20,29)(22,26)(24,27)(28,30);;
s3 := (31,32);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!(1,2);
s1 := Sym(32)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)
(23,24)(25,28)(26,27)(29,30);
s2 := Sym(32)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)
(18,21)(20,29)(22,26)(24,27)(28,30);
s3 := Sym(32)!(31,32);
poly := sub<Sym(32)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope