Polytope of Type {8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4}*128b
if this polytope has a name.
Group : SmallGroup(128,928)
Rank : 3
Schlafli Type : {8,4}
Number of vertices, edges, etc : 16, 32, 8
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {8,4,2} of size 256
   {8,4,4} of size 512
   {8,4,6} of size 768
   {8,4,10} of size 1280
   {8,4,14} of size 1792
Vertex Figure Of :
   {2,8,4} of size 256
   {4,8,4} of size 512
   {4,8,4} of size 512
   {6,8,4} of size 768
   {3,8,4} of size 768
   {3,8,4} of size 768
   {10,8,4} of size 1280
   {14,8,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4}*64
   4-fold quotients : {4,4}*32
   8-fold quotients : {2,4}*16, {4,2}*16
   16-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4}*256a, {8,8}*256b, {8,8}*256c, {8,4}*256b, {8,4}*256d, {8,8}*256f, {8,8}*256h
   3-fold covers : {24,4}*384b, {8,12}*384b
   4-fold covers : {16,4}*512a, {8,16}*512a, {8,16}*512b, {8,8}*512c, {8,4}*512a, {8,8}*512d, {8,8}*512f, {8,8}*512g, {16,4}*512b, {8,4}*512b, {8,4}*512c, {8,8}*512h, {8,8}*512i, {8,8}*512l, {8,8}*512m, {8,8}*512n, {8,8}*512o, {16,4}*512c, {16,4}*512d, {8,8}*512p, {8,8}*512r, {8,16}*512g, {8,16}*512h, {16,4}*512e, {16,4}*512f
   5-fold covers : {40,4}*640b, {8,20}*640b
   6-fold covers : {8,12}*768a, {8,24}*768b, {24,8}*768b, {24,4}*768a, {24,8}*768c, {8,24}*768d, {24,4}*768b, {8,12}*768b, {24,8}*768e, {24,4}*768d, {8,12}*768d, {8,24}*768f, {24,8}*768g, {8,24}*768h
   7-fold covers : {56,4}*896b, {8,28}*896b
   9-fold covers : {72,4}*1152b, {8,36}*1152b, {24,12}*1152d, {24,12}*1152e, {24,12}*1152f, {8,4}*1152b, {8,12}*1152b, {24,4}*1152b
   10-fold covers : {8,20}*1280a, {8,40}*1280b, {40,8}*1280b, {40,4}*1280a, {40,8}*1280c, {8,40}*1280d, {40,4}*1280b, {8,20}*1280b, {40,8}*1280e, {40,4}*1280d, {8,20}*1280d, {8,40}*1280f, {40,8}*1280g, {8,40}*1280h
   11-fold covers : {88,4}*1408b, {8,44}*1408b
   13-fold covers : {104,4}*1664b, {8,52}*1664b
   14-fold covers : {8,28}*1792a, {8,56}*1792b, {56,8}*1792b, {56,4}*1792a, {56,8}*1792c, {8,56}*1792d, {56,4}*1792b, {8,28}*1792b, {56,8}*1792e, {56,4}*1792d, {8,28}*1792d, {8,56}*1792f, {56,8}*1792g, {8,56}*1792h
   15-fold covers : {120,4}*1920b, {8,60}*1920b, {40,12}*1920b, {24,20}*1920b
Permutation Representation (GAP) :

s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,15)( 6,16)( 7,13)( 8,14);;
s1 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15);;
s2 := ( 5, 7)( 6, 8)(13,15)(14,16);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(16)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,15)( 6,16)( 7,13)( 8,14);
s1 := Sym(16)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15);
s2 := Sym(16)!( 5, 7)( 6, 8)(13,15)(14,16);
poly := sub<Sym(16)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope