Polytope of Type {5,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,4}*120
if this polytope has a name.
Group : SmallGroup(120,34)
Rank : 3
Schlafli Type : {5,4}
Number of vertices, edges, etc : 15, 30, 12
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {5,4,2} of size 240
   {5,4,4} of size 480
   {5,4,6} of size 720
   {5,4,8} of size 960
   {5,4,10} of size 1200
   {5,4,12} of size 1440
   {5,4,14} of size 1680
   {5,4,16} of size 1920
Vertex Figure Of :
   {2,5,4} of size 240
   {4,5,4} of size 1440
   {3,5,4} of size 1920
   {4,5,4} of size 1920
   {4,5,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,4}*240, {10,4}*240a, {10,4}*240b
   4-fold covers : {5,8}*480, {10,4}*480a, {10,4}*480b, {10,4}*480c
   6-fold covers : {10,12}*720, {15,4}*720
   8-fold covers : {10,8}*960a, {10,8}*960b, {20,4}*960a, {20,4}*960b, {10,8}*960c, {10,8}*960d, {20,4}*960c, {20,4}*960d, {10,4}*960
   10-fold covers : {5,4}*1200, {5,20}*1200, {10,20}*1200
   12-fold covers : {10,12}*1440b, {10,12}*1440d, {15,8}*1440, {10,12}*1440g, {30,4}*1440
   14-fold covers : {10,28}*1680, {35,4}*1680
   16-fold covers : {10,16}*1920a, {10,16}*1920b, {20,4}*1920a, {10,8}*1920a, {40,4}*1920a, {40,4}*1920b, {10,8}*1920b, {20,4}*1920b, {10,4}*1920, {20,8}*1920a, {20,8}*1920b, {20,8}*1920c, {20,8}*1920d, {40,4}*1920c, {40,4}*1920d, {5,4}*1920, {5,8}*1920a, {5,8}*1920b
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (2,3);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(5)!(2,3)(4,5);
s1 := Sym(5)!(1,2)(3,4);
s2 := Sym(5)!(2,3);
poly := sub<Sym(5)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope