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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,2,2,2}*128
if this polytope has a name.
Group : SmallGroup(128,2320)
Rank : 6
Schlafli Type : {2,4,2,2,2}
Number of vertices, edges, etc : 2, 4, 4, 2, 2, 2
Order of s0s1s2s3s4s5 : 4
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,2,2,2,2} of size 256
   {2,4,2,2,2,3} of size 384
   {2,4,2,2,2,4} of size 512
   {2,4,2,2,2,5} of size 640
   {2,4,2,2,2,6} of size 768
   {2,4,2,2,2,7} of size 896
   {2,4,2,2,2,9} of size 1152
   {2,4,2,2,2,10} of size 1280
   {2,4,2,2,2,11} of size 1408
   {2,4,2,2,2,13} of size 1664
   {2,4,2,2,2,14} of size 1792
   {2,4,2,2,2,15} of size 1920
Vertex Figure Of :
   {2,2,4,2,2,2} of size 256
   {3,2,4,2,2,2} of size 384
   {4,2,4,2,2,2} of size 512
   {5,2,4,2,2,2} of size 640
   {6,2,4,2,2,2} of size 768
   {7,2,4,2,2,2} of size 896
   {9,2,4,2,2,2} of size 1152
   {10,2,4,2,2,2} of size 1280
   {11,2,4,2,2,2} of size 1408
   {13,2,4,2,2,2} of size 1664
   {14,2,4,2,2,2} of size 1792
   {15,2,4,2,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,4,2,2}*256, {4,4,2,2,2}*256, {2,4,2,2,4}*256, {2,4,2,4,2}*256, {2,8,2,2,2}*256
   3-fold covers : {2,12,2,2,2}*384, {2,4,2,2,6}*384, {2,4,2,6,2}*384, {2,4,6,2,2}*384a, {6,4,2,2,2}*384a
   4-fold covers : {2,4,4,4,2}*512, {4,4,4,2,2}*512, {2,4,2,4,4}*512, {2,4,4,2,4}*512, {4,4,2,2,4}*512, {4,4,2,4,2}*512, {2,4,8,2,2}*512a, {2,8,4,2,2}*512a, {4,8,2,2,2}*512a, {8,4,2,2,2}*512a, {2,4,8,2,2}*512b, {2,8,4,2,2}*512b, {4,8,2,2,2}*512b, {8,4,2,2,2}*512b, {2,4,4,2,2}*512, {4,4,2,2,2}*512, {2,4,2,2,8}*512, {2,4,2,8,2}*512, {2,8,2,2,4}*512, {2,8,2,4,2}*512, {2,16,2,2,2}*512
   5-fold covers : {2,20,2,2,2}*640, {2,4,2,2,10}*640, {2,4,2,10,2}*640, {2,4,10,2,2}*640, {10,4,2,2,2}*640
   6-fold covers : {2,4,4,2,6}*768, {2,4,4,6,2}*768, {4,4,2,2,6}*768, {4,4,2,6,2}*768, {4,4,6,2,2}*768, {6,4,4,2,2}*768, {2,4,12,2,2}*768a, {2,12,4,2,2}*768a, {4,12,2,2,2}*768a, {12,4,2,2,2}*768a, {2,4,2,4,6}*768a, {2,4,2,6,4}*768a, {2,4,6,2,4}*768a, {6,4,2,2,4}*768a, {6,4,2,4,2}*768a, {2,4,6,4,2}*768a, {2,4,2,2,12}*768, {2,4,2,12,2}*768, {2,12,2,2,4}*768, {2,12,2,4,2}*768, {2,8,2,2,6}*768, {2,8,2,6,2}*768, {2,8,6,2,2}*768, {6,8,2,2,2}*768, {2,24,2,2,2}*768
   7-fold covers : {2,28,2,2,2}*896, {2,4,2,2,14}*896, {2,4,2,14,2}*896, {2,4,14,2,2}*896, {14,4,2,2,2}*896
   9-fold covers : {2,4,2,2,18}*1152, {2,4,2,18,2}*1152, {2,4,18,2,2}*1152a, {18,4,2,2,2}*1152a, {2,36,2,2,2}*1152, {2,4,2,6,6}*1152a, {2,4,2,6,6}*1152b, {2,4,2,6,6}*1152c, {2,4,6,2,6}*1152a, {2,4,6,6,2}*1152a, {2,4,6,6,2}*1152b, {6,4,2,2,6}*1152a, {6,4,2,6,2}*1152a, {6,4,6,2,2}*1152, {2,4,6,6,2}*1152c, {2,12,6,2,2}*1152a, {6,12,2,2,2}*1152a, {2,12,2,2,6}*1152, {2,12,2,6,2}*1152, {2,12,6,2,2}*1152b, {2,12,6,2,2}*1152c, {6,12,2,2,2}*1152b, {6,12,2,2,2}*1152c, {2,4,6,2,2}*1152, {6,4,2,2,2}*1152
   10-fold covers : {2,4,4,2,10}*1280, {2,4,4,10,2}*1280, {4,4,2,2,10}*1280, {4,4,2,10,2}*1280, {4,4,10,2,2}*1280, {10,4,4,2,2}*1280, {2,4,20,2,2}*1280, {2,20,4,2,2}*1280, {4,20,2,2,2}*1280, {20,4,2,2,2}*1280, {2,4,2,4,10}*1280, {2,4,2,10,4}*1280, {2,4,10,2,4}*1280, {10,4,2,2,4}*1280, {10,4,2,4,2}*1280, {2,4,10,4,2}*1280, {2,4,2,2,20}*1280, {2,4,2,20,2}*1280, {2,20,2,2,4}*1280, {2,20,2,4,2}*1280, {2,8,2,2,10}*1280, {2,8,2,10,2}*1280, {2,8,10,2,2}*1280, {10,8,2,2,2}*1280, {2,40,2,2,2}*1280
   11-fold covers : {2,4,2,2,22}*1408, {2,4,2,22,2}*1408, {2,4,22,2,2}*1408, {22,4,2,2,2}*1408, {2,44,2,2,2}*1408
   13-fold covers : {2,4,2,2,26}*1664, {2,4,2,26,2}*1664, {2,4,26,2,2}*1664, {26,4,2,2,2}*1664, {2,52,2,2,2}*1664
   14-fold covers : {2,4,4,2,14}*1792, {2,4,4,14,2}*1792, {4,4,2,2,14}*1792, {4,4,2,14,2}*1792, {4,4,14,2,2}*1792, {14,4,4,2,2}*1792, {2,4,28,2,2}*1792, {2,28,4,2,2}*1792, {4,28,2,2,2}*1792, {28,4,2,2,2}*1792, {2,4,2,4,14}*1792, {2,4,2,14,4}*1792, {2,4,14,2,4}*1792, {14,4,2,2,4}*1792, {14,4,2,4,2}*1792, {2,4,14,4,2}*1792, {2,4,2,2,28}*1792, {2,4,2,28,2}*1792, {2,28,2,2,4}*1792, {2,28,2,4,2}*1792, {2,8,2,2,14}*1792, {2,8,2,14,2}*1792, {2,8,14,2,2}*1792, {14,8,2,2,2}*1792, {2,56,2,2,2}*1792
   15-fold covers : {2,4,2,2,30}*1920, {2,4,2,30,2}*1920, {2,4,30,2,2}*1920a, {30,4,2,2,2}*1920a, {2,60,2,2,2}*1920, {2,4,2,6,10}*1920, {2,4,2,10,6}*1920, {2,4,6,2,10}*1920a, {2,4,6,10,2}*1920a, {2,4,10,2,6}*1920, {2,4,10,6,2}*1920, {6,4,2,2,10}*1920a, {6,4,2,10,2}*1920a, {6,4,10,2,2}*1920, {10,4,2,2,6}*1920, {10,4,2,6,2}*1920, {10,4,6,2,2}*1920, {2,12,2,2,10}*1920, {2,12,2,10,2}*1920, {2,12,10,2,2}*1920, {10,12,2,2,2}*1920, {2,20,2,2,6}*1920, {2,20,2,6,2}*1920, {2,20,6,2,2}*1920a, {6,20,2,2,2}*1920a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4)(5,6);;
s3 := (7,8);;
s4 := ( 9,10);;
s5 := (11,12);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*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, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(12)!(1,2);
s1 := Sym(12)!(4,5);
s2 := Sym(12)!(3,4)(5,6);
s3 := Sym(12)!(7,8);
s4 := Sym(12)!( 9,10);
s5 := Sym(12)!(11,12);
poly := sub<Sym(12)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*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, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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