Polytope of Type {5,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,4}*160
Also Known As : {5,4}₅. if this polytope has another name.
Group : SmallGroup(160,234)
Rank : 3
Schlafli Type : {5,4}
Number of vertices, edges, etc : 20, 40, 16
Order of s₀s₁s₂ : 5
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {5,4,2} of size 320
Vertex Figure Of :
   {2,5,4} of size 320
   {3,5,4} of size 960
   {10,5,4} of size 1600
   {4,5,4} of size 1920
   {4,5,4} of size 1920
   {6,5,4} of size 1920
   {3,5,4} of size 1920
   {6,5,4} of size 1920
   {6,5,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,8}*320a, {5,8}*320b, {5,4}*320, {10,4}*320a, {10,4}*320b
   3-fold covers : {15,4}*480
   4-fold covers : {20,4}*640b, {20,4}*640c, {5,8}*640a, {10,8}*640a, {10,8}*640b, {10,8}*640c, {10,8}*640d, {5,4}*640, {5,8}*640b, {10,4}*640a, {20,4}*640d, {20,4}*640e, {10,4}*640b
   5-fold covers : {25,4}*800
   6-fold covers : {15,8}*960b, {15,8}*960c, {10,12}*960e, {15,4}*960, {30,4}*960c, {30,4}*960d
   7-fold covers : {35,4}*1120
   8-fold covers : {5,8}*1280, {10,8}*1280a, {10,8}*1280b, {20,8}*1280e, {20,8}*1280f, {20,8}*1280g, {20,8}*1280h, {20,8}*1280i, {20,8}*1280j, {20,8}*1280k, {20,8}*1280l, {40,4}*1280e, {40,4}*1280f, {40,4}*1280g, {40,4}*1280h, {10,4}*1280a, {20,4}*1280b, {20,4}*1280c, {10,8}*1280c, {10,4}*1280b, {10,8}*1280d, {20,4}*1280d, {20,4}*1280e, {10,4}*1280c, {10,8}*1280e, {10,8}*1280f
   9-fold covers : {45,4}*1440
   10-fold covers : {25,8}*1600a, {25,8}*1600b, {25,4}*1600, {50,4}*1600a, {50,4}*1600b, {5,20}*1600, {10,20}*1600
   11-fold covers : {55,4}*1760
   12-fold covers : {20,12}*1920d, {20,12}*1920e, {10,24}*1920a, {10,24}*1920b, {60,4}*1920f, {60,4}*1920g, {15,8}*1920b, {30,8}*1920h, {30,8}*1920i, {30,8}*1920j, {30,8}*1920k, {15,4}*1920a, {15,8}*1920c, {30,4}*1920c, {60,4}*1920h, {60,4}*1920i, {15,4}*1920b, {10,12}*1920a, {30,4}*1920d
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14);;
s1 := ( 2, 9)( 3,12)( 5,15)( 6, 7)( 8,14)(13,16);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
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, s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(16)!( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14);
s1 := Sym(16)!( 2, 9)( 3,12)( 5,15)( 6, 7)( 8,14)(13,16);
s2 := Sym(16)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
poly := sub<Sym(16)|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, s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 >;

References : None.
to this polytope