Questions?
See the FAQ
or other info.

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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,2,3}*120
if this polytope has a name.
Group : SmallGroup(120,42)
Rank : 5
Schlafli Type : {2,5,2,3}
Number of vertices, edges, etc : 2, 5, 5, 3, 3
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,2,3,2} of size 240
   {2,5,2,3,3} of size 480
   {2,5,2,3,4} of size 480
   {2,5,2,3,6} of size 720
   {2,5,2,3,4} of size 960
   {2,5,2,3,6} of size 960
   {2,5,2,3,5} of size 1200
   {2,5,2,3,8} of size 1920
   {2,5,2,3,12} of size 1920
Vertex Figure Of :
   {2,2,5,2,3} of size 240
   {3,2,5,2,3} of size 360
   {4,2,5,2,3} of size 480
   {5,2,5,2,3} of size 600
   {6,2,5,2,3} of size 720
   {7,2,5,2,3} of size 840
   {8,2,5,2,3} of size 960
   {9,2,5,2,3} of size 1080
   {10,2,5,2,3} of size 1200
   {11,2,5,2,3} of size 1320
   {12,2,5,2,3} of size 1440
   {13,2,5,2,3} of size 1560
   {14,2,5,2,3} of size 1680
   {15,2,5,2,3} of size 1800
   {16,2,5,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,5,2,6}*240, {2,10,2,3}*240
   3-fold covers : {2,5,2,9}*360, {2,15,2,3}*360
   4-fold covers : {2,5,2,12}*480, {2,20,2,3}*480, {4,10,2,3}*480, {2,10,2,6}*480
   5-fold covers : {2,25,2,3}*600, {10,5,2,3}*600, {2,5,2,15}*600
   6-fold covers : {2,5,2,18}*720, {2,10,2,9}*720, {2,10,6,3}*720, {6,10,2,3}*720, {2,15,2,6}*720, {2,30,2,3}*720
   7-fold covers : {2,5,2,21}*840, {2,35,2,3}*840
   8-fold covers : {4,20,2,3}*960, {2,5,2,24}*960, {2,40,2,3}*960, {8,10,2,3}*960, {2,10,2,12}*960, {2,20,2,6}*960, {2,10,4,6}*960, {4,10,2,6}*960, {2,10,4,3}*960
   9-fold covers : {2,5,2,27}*1080, {2,45,2,3}*1080, {2,15,2,9}*1080, {2,15,6,3}*1080, {6,15,2,3}*1080
   10-fold covers : {2,25,2,6}*1200, {2,50,2,3}*1200, {2,5,10,6}*1200, {10,5,2,6}*1200, {10,10,2,3}*1200a, {10,10,2,3}*1200b, {2,5,2,30}*1200, {2,10,2,15}*1200
   11-fold covers : {2,5,2,33}*1320, {2,55,2,3}*1320
   12-fold covers : {2,5,2,36}*1440, {2,20,2,9}*1440, {4,10,2,9}*1440, {2,10,2,18}*1440, {12,10,2,3}*1440, {6,20,2,3}*1440a, {2,20,6,3}*1440, {4,10,6,3}*1440, {2,15,2,12}*1440, {2,60,2,3}*1440, {4,30,2,3}*1440a, {6,15,2,3}*1440, {4,15,2,3}*1440, {2,10,6,6}*1440a, {2,10,6,6}*1440b, {6,10,2,6}*1440, {2,30,2,6}*1440
   13-fold covers : {2,5,2,39}*1560, {2,65,2,3}*1560
   14-fold covers : {14,10,2,3}*1680, {2,5,2,42}*1680, {2,10,2,21}*1680, {2,35,2,6}*1680, {2,70,2,3}*1680
   15-fold covers : {2,25,2,9}*1800, {2,75,2,3}*1800, {10,5,2,9}*1800, {2,5,2,45}*1800, {10,15,2,3}*1800, {2,15,2,15}*1800
   16-fold covers : {8,20,2,3}*1920a, {4,40,2,3}*1920a, {8,20,2,3}*1920b, {4,40,2,3}*1920b, {4,20,2,3}*1920, {16,10,2,3}*1920, {2,5,2,48}*1920, {2,80,2,3}*1920, {2,10,4,12}*1920, {2,20,4,6}*1920, {4,20,2,6}*1920, {4,10,4,6}*1920, {4,10,2,12}*1920, {2,20,2,12}*1920, {2,10,8,6}*1920, {8,10,2,6}*1920, {2,10,2,24}*1920, {2,40,2,6}*1920, {2,20,4,3}*1920, {4,10,4,3}*1920, {2,10,8,3}*1920, {4,5,2,3}*1920, {2,10,4,6}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4)(5,6);;
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*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, s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!(1,2);
s1 := Sym(10)!(4,5)(6,7);
s2 := Sym(10)!(3,4)(5,6);
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*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, 
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

to this polytope