Polytope of Type {4,2,11}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,11}*176
if this polytope has a name.
Group : SmallGroup(176,31)
Rank : 4
Schlafli Type : {4,2,11}
Number of vertices, edges, etc : 4, 4, 11, 11
Order of s₀s₁s₂s₃ : 44
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,11,2} of size 352
Vertex Figure Of :
   {2,4,2,11} of size 352
   {3,4,2,11} of size 528
   {4,4,2,11} of size 704
   {6,4,2,11} of size 1056
   {3,4,2,11} of size 1056
   {6,4,2,11} of size 1056
   {6,4,2,11} of size 1056
   {8,4,2,11} of size 1408
   {8,4,2,11} of size 1408
   {4,4,2,11} of size 1408
   {9,4,2,11} of size 1584
   {4,4,2,11} of size 1584
   {6,4,2,11} of size 1584
   {10,4,2,11} of size 1760
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,11}*88
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,11}*352, {4,2,22}*352
   3-fold covers : {12,2,11}*528, {4,2,33}*528
   4-fold covers : {16,2,11}*704, {4,2,44}*704, {4,4,22}*704, {8,2,22}*704
   5-fold covers : {20,2,11}*880, {4,2,55}*880
   6-fold covers : {24,2,11}*1056, {8,2,33}*1056, {12,2,22}*1056, {4,6,22}*1056a, {4,2,66}*1056
   7-fold covers : {28,2,11}*1232, {4,2,77}*1232
   8-fold covers : {32,2,11}*1408, {4,4,44}*1408, {4,8,22}*1408a, {8,4,22}*1408a, {4,8,22}*1408b, {8,4,22}*1408b, {4,4,22}*1408, {8,2,44}*1408, {4,2,88}*1408, {16,2,22}*1408
   9-fold covers : {36,2,11}*1584, {4,2,99}*1584, {12,2,33}*1584, {4,6,33}*1584
   10-fold covers : {40,2,11}*1760, {8,2,55}*1760, {20,2,22}*1760, {4,10,22}*1760, {4,2,110}*1760
   11-fold covers : {4,2,121}*1936, {44,2,11}*1936, {4,22,11}*1936
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope