Polytope of Type {4,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,2}*128a
if this polytope has a name.
Group : SmallGroup(128,1728)
Rank : 4
Schlafli Type : {4,8,2}
Number of vertices, edges, etc : 4, 16, 8, 2
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,8,2,2} of size 256
   {4,8,2,3} of size 384
   {4,8,2,5} of size 640
   {4,8,2,6} of size 768
   {4,8,2,7} of size 896
   {4,8,2,9} of size 1152
   {4,8,2,10} of size 1280
   {4,8,2,11} of size 1408
   {4,8,2,13} of size 1664
   {4,8,2,14} of size 1792
   {4,8,2,15} of size 1920
Vertex Figure Of :
   {2,4,8,2} of size 256
   {4,4,8,2} of size 512
   {6,4,8,2} of size 768
   {3,4,8,2} of size 768
   {6,4,8,2} of size 1152
   {10,4,8,2} of size 1280
   {14,4,8,2} of size 1792
   {5,4,8,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,2}*64, {2,8,2}*64
   4-fold quotients : {2,4,2}*32, {4,2,2}*32
   8-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,8,2}*256a, {8,8,2}*256a, {8,8,2}*256b, {4,8,4}*256d, {4,16,2}*256a, {4,16,2}*256b
   3-fold covers : {4,24,2}*384a, {12,8,2}*384a, {4,8,6}*384a
   4-fold covers : {8,8,2}*512a, {4,8,8}*512e, {4,8,8}*512f, {8,8,4}*512e, {8,8,4}*512f, {4,8,4}*512a, {4,8,4}*512b, {4,8,2}*512a, {8,8,2}*512c, {4,16,2}*512a, {4,16,2}*512b, {16,8,2}*512a, {16,8,2}*512b, {8,16,2}*512c, {8,16,2}*512d, {16,8,2}*512d, {8,16,2}*512e, {8,16,2}*512f, {16,8,2}*512f, {4,16,4}*512a, {4,16,4}*512b, {4,16,4}*512c, {4,16,4}*512d, {4,32,2}*512a, {4,32,2}*512b
   5-fold covers : {4,40,2}*640a, {20,8,2}*640a, {4,8,10}*640a
   6-fold covers : {4,8,6}*768a, {12,8,2}*768a, {4,24,2}*768a, {8,8,6}*768a, {8,8,6}*768b, {24,8,2}*768a, {8,24,2}*768b, {8,24,2}*768c, {24,8,2}*768c, {4,8,12}*768d, {12,8,4}*768d, {4,24,4}*768d, {4,16,6}*768a, {12,16,2}*768a, {4,48,2}*768a, {4,16,6}*768b, {12,16,2}*768b, {4,48,2}*768b
   7-fold covers : {4,56,2}*896a, {28,8,2}*896a, {4,8,14}*896a
   9-fold covers : {4,8,18}*1152a, {36,8,2}*1152a, {4,72,2}*1152a, {12,8,6}*1152a, {4,24,6}*1152a, {4,24,6}*1152b, {4,24,6}*1152c, {12,24,2}*1152a, {12,24,2}*1152b, {12,24,2}*1152c, {4,8,2}*1152a, {4,24,2}*1152a, {12,8,2}*1152a, {4,8,6}*1152a
   10-fold covers : {4,8,10}*1280a, {20,8,2}*1280a, {4,40,2}*1280a, {8,8,10}*1280a, {8,8,10}*1280b, {40,8,2}*1280a, {8,40,2}*1280b, {8,40,2}*1280c, {40,8,2}*1280c, {4,8,20}*1280d, {20,8,4}*1280d, {4,40,4}*1280d, {4,16,10}*1280a, {20,16,2}*1280a, {4,80,2}*1280a, {4,16,10}*1280b, {20,16,2}*1280b, {4,80,2}*1280b
   11-fold covers : {4,8,22}*1408a, {44,8,2}*1408a, {4,88,2}*1408a
   13-fold covers : {4,8,26}*1664a, {52,8,2}*1664a, {4,104,2}*1664a
   14-fold covers : {4,8,14}*1792a, {28,8,2}*1792a, {4,56,2}*1792a, {8,8,14}*1792a, {8,8,14}*1792b, {56,8,2}*1792a, {8,56,2}*1792b, {8,56,2}*1792c, {56,8,2}*1792c, {4,8,28}*1792d, {28,8,4}*1792d, {4,56,4}*1792d, {4,16,14}*1792a, {28,16,2}*1792a, {4,112,2}*1792a, {4,16,14}*1792b, {28,16,2}*1792b, {4,112,2}*1792b
   15-fold covers : {4,8,30}*1920a, {60,8,2}*1920a, {4,120,2}*1920a, {12,8,10}*1920a, {20,8,6}*1920a, {4,24,10}*1920a, {4,40,6}*1920a, {12,40,2}*1920a, {20,24,2}*1920a
Permutation Representation (GAP) :

s0 := ( 2, 4)( 3, 6)(10,13)(12,15);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);;
s2 := ( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);;
s3 := (17,18);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!( 2, 4)( 3, 6)(10,13)(12,15);
s1 := Sym(18)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);
s2 := Sym(18)!( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);
s3 := Sym(18)!(17,18);
poly := sub<Sym(18)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope