Polytope of Type {5,2,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,2,3}*120
if this polytope has a name.
Group : SmallGroup(120,42)
Rank : 5
Schlafli Type : {5,2,2,3}
Number of vertices, edges, etc : 5, 5, 2, 3, 3
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,2,3,2} of size 240
   {5,2,2,3,3} of size 480
   {5,2,2,3,4} of size 480
   {5,2,2,3,6} of size 720
   {5,2,2,3,4} of size 960
   {5,2,2,3,6} of size 960
   {5,2,2,3,5} of size 1200
   {5,2,2,3,8} of size 1920
   {5,2,2,3,12} of size 1920
Vertex Figure Of :
   {2,5,2,2,3} of size 240
   {3,5,2,2,3} of size 720
   {5,5,2,2,3} of size 720
   {10,5,2,2,3} of size 1200
   {4,5,2,2,3} of size 1440
   {6,5,2,2,3} of size 1440
   {3,5,2,2,3} of size 1440
   {5,5,2,2,3} of size 1440
   {6,5,2,2,3} of size 1440
   {6,5,2,2,3} of size 1440
   {10,5,2,2,3} of size 1440
   {10,5,2,2,3} of size 1440
   {4,5,2,2,3} of size 1920
   {5,5,2,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,2,6}*240, {10,2,2,3}*240
   3-fold covers : {5,2,2,9}*360, {5,2,6,3}*360, {15,2,2,3}*360
   4-fold covers : {5,2,2,12}*480, {20,2,2,3}*480, {5,2,4,6}*480a, {10,4,2,3}*480, {5,2,4,3}*480, {10,2,2,6}*480
   5-fold covers : {25,2,2,3}*600, {5,10,2,3}*600, {5,2,2,15}*600
   6-fold covers : {5,2,2,18}*720, {10,2,2,9}*720, {5,2,6,6}*720a, {5,2,6,6}*720b, {10,2,6,3}*720, {10,6,2,3}*720, {15,2,2,6}*720, {30,2,2,3}*720
   7-fold covers : {5,2,2,21}*840, {35,2,2,3}*840
   8-fold covers : {5,2,4,12}*960a, {20,4,2,3}*960, {5,2,2,24}*960, {40,2,2,3}*960, {5,2,8,6}*960, {10,8,2,3}*960, {5,2,8,3}*960, {10,2,2,12}*960, {20,2,2,6}*960, {10,2,4,6}*960a, {10,4,2,6}*960, {5,2,4,6}*960, {10,2,4,3}*960
   9-fold covers : {5,2,2,27}*1080, {5,2,6,9}*1080, {5,2,6,3}*1080, {45,2,2,3}*1080, {15,2,2,9}*1080, {15,2,6,3}*1080, {15,6,2,3}*1080
   10-fold covers : {25,2,2,6}*1200, {50,2,2,3}*1200, {5,2,10,6}*1200, {5,10,2,6}*1200, {10,10,2,3}*1200a, {10,10,2,3}*1200c, {5,2,2,30}*1200, {10,2,2,15}*1200
   11-fold covers : {5,2,2,33}*1320, {55,2,2,3}*1320
   12-fold covers : {5,2,2,36}*1440, {20,2,2,9}*1440, {5,2,4,18}*1440a, {10,4,2,9}*1440, {5,2,4,9}*1440, {10,2,2,18}*1440, {5,2,6,12}*1440a, {5,2,6,12}*1440b, {5,2,12,6}*1440a, {10,12,2,3}*1440, {20,2,6,3}*1440, {20,6,2,3}*1440a, {10,4,6,3}*1440, {5,2,12,6}*1440c, {15,2,2,12}*1440, {60,2,2,3}*1440, {15,2,4,6}*1440a, {30,4,2,3}*1440a, {5,2,6,3}*1440, {5,2,12,3}*1440, {15,6,2,3}*1440, {15,4,2,3}*1440, {15,2,4,3}*1440, {10,2,6,6}*1440a, {10,2,6,6}*1440b, {10,6,2,6}*1440, {30,2,2,6}*1440
   13-fold covers : {5,2,2,39}*1560, {65,2,2,3}*1560
   14-fold covers : {5,2,14,6}*1680, {10,14,2,3}*1680, {5,2,2,42}*1680, {10,2,2,21}*1680, {35,2,2,6}*1680, {70,2,2,3}*1680
   15-fold covers : {25,2,2,9}*1800, {25,2,6,3}*1800, {75,2,2,3}*1800, {5,10,2,9}*1800, {5,2,2,45}*1800, {5,2,6,15}*1800, {15,10,2,3}*1800, {5,10,6,3}*1800, {15,2,2,15}*1800
   16-fold covers : {5,2,8,12}*1920a, {20,8,2,3}*1920a, {5,2,4,24}*1920a, {40,4,2,3}*1920a, {5,2,8,12}*1920b, {20,8,2,3}*1920b, {5,2,4,24}*1920b, {40,4,2,3}*1920b, {5,2,4,12}*1920a, {20,4,2,3}*1920, {5,2,16,6}*1920, {10,16,2,3}*1920, {5,2,2,48}*1920, {80,2,2,3}*1920, {10,4,4,6}*1920, {10,2,4,12}*1920a, {20,4,2,6}*1920, {10,4,2,12}*1920, {20,2,4,6}*1920a, {20,2,2,12}*1920, {10,2,8,6}*1920, {10,8,2,6}*1920, {10,2,2,24}*1920, {40,2,2,6}*1920, {5,2,8,3}*1920, {5,2,4,12}*1920b, {20,2,4,3}*1920, {10,4,4,3}*1920b, {5,2,4,6}*1920b, {5,2,4,12}*1920c, {5,2,8,6}*1920b, {10,2,8,3}*1920, {5,2,8,6}*1920c, {5,4,2,3}*1920, {10,2,4,6}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := ( 9,10);;
s4 := (8,9);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(2,3)(4,5);
s1 := Sym(10)!(1,2)(3,4);
s2 := Sym(10)!(6,7);
s3 := Sym(10)!( 9,10);
s4 := Sym(10)!(8,9);
poly := sub<Sym(10)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, 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*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope