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

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

s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := ( 7, 8)( 9,10);;
s4 := (6,7)(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*s1*s0*s1, 
s0*s2*s0*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, s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope