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

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

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

to this polytope