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