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Polytope of Type {8,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,2}*128b
if this polytope has a name.
Group : SmallGroup(128,1746)
Rank : 4
Schlafli Type : {8,4,2}
Number of vertices, edges, etc : 8, 16, 4, 2
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,4,2,2} of size 256
   {8,4,2,3} of size 384
   {8,4,2,5} of size 640
   {8,4,2,6} of size 768
   {8,4,2,7} of size 896
   {8,4,2,9} of size 1152
   {8,4,2,10} of size 1280
   {8,4,2,11} of size 1408
   {8,4,2,13} of size 1664
   {8,4,2,14} of size 1792
   {8,4,2,15} of size 1920
Vertex Figure Of :
   {2,8,4,2} of size 256
   {4,8,4,2} of size 512
   {4,8,4,2} of size 512
   {6,8,4,2} of size 768
   {10,8,4,2} of size 1280
   {14,8,4,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,2}*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 : {8,4,2}*256a, {8,8,2}*256a, {8,8,2}*256d, {8,4,4}*256b
   3-fold covers : {24,4,2}*384b, {8,12,2}*384b, {8,4,6}*384b
   4-fold covers : {8,8,2}*512a, {8,4,8}*512a, {8,8,4}*512b, {8,4,4}*512a, {8,8,4}*512d, {8,8,4}*512f, {8,8,4}*512h, {8,4,4}*512c, {8,4,8}*512d, {8,4,2}*512a, {8,8,2}*512d, {16,4,2}*512a, {16,4,2}*512b, {16,8,2}*512a, {16,8,2}*512b, {8,16,2}*512c, {8,16,2}*512e
   5-fold covers : {40,4,2}*640b, {8,20,2}*640b, {8,4,10}*640b
   6-fold covers : {8,4,6}*768a, {8,12,2}*768a, {24,4,2}*768a, {8,8,6}*768a, {24,8,2}*768a, {8,24,2}*768b, {8,8,6}*768d, {8,24,2}*768d, {24,8,2}*768d, {8,4,12}*768b, {8,12,4}*768b, {24,4,4}*768b
   7-fold covers : {56,4,2}*896b, {8,28,2}*896b, {8,4,14}*896b
   9-fold covers : {8,4,18}*1152b, {8,36,2}*1152b, {72,4,2}*1152b, {8,12,6}*1152d, {8,12,6}*1152e, {8,12,6}*1152f, {24,4,6}*1152b, {24,12,2}*1152d, {24,12,2}*1152e, {24,12,2}*1152f, {8,4,2}*1152b, {24,4,2}*1152b, {8,4,6}*1152b, {8,12,2}*1152b
   10-fold covers : {8,4,10}*1280a, {8,20,2}*1280a, {40,4,2}*1280a, {8,8,10}*1280a, {40,8,2}*1280a, {8,40,2}*1280b, {8,8,10}*1280d, {8,40,2}*1280d, {40,8,2}*1280d, {8,4,20}*1280b, {8,20,4}*1280b, {40,4,4}*1280b
   11-fold covers : {8,4,22}*1408b, {8,44,2}*1408b, {88,4,2}*1408b
   13-fold covers : {8,4,26}*1664b, {8,52,2}*1664b, {104,4,2}*1664b
   14-fold covers : {8,4,14}*1792a, {8,28,2}*1792a, {56,4,2}*1792a, {8,8,14}*1792a, {56,8,2}*1792a, {8,56,2}*1792b, {8,8,14}*1792d, {8,56,2}*1792d, {56,8,2}*1792d, {8,4,28}*1792b, {8,28,4}*1792b, {56,4,4}*1792b
   15-fold covers : {8,4,30}*1920b, {8,60,2}*1920b, {120,4,2}*1920b, {8,12,10}*1920b, {8,20,6}*1920b, {24,4,10}*1920b, {40,4,6}*1920b, {40,12,2}*1920b, {24,20,2}*1920b
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 6)( 5, 8)( 7,10)(11,14)(13,15);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,11)(10,13)(12,15)(14,16);;
s2 := ( 2, 4)( 3, 6)( 5, 8)( 9,12)(11,15)(13,14);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!( 2, 3)( 4, 6)( 5, 8)( 7,10)(11,14)(13,15);
s1 := Sym(18)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,11)(10,13)(12,15)(14,16);
s2 := Sym(18)!( 2, 4)( 3, 6)( 5, 8)( 9,12)(11,15)(13,14);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >; 
 

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