Polytope of Type {2,5,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,3}*120
if this polytope has a name.
Group : SmallGroup(120,35)
Rank : 4
Schlafli Type : {2,5,3}
Number of vertices, edges, etc : 2, 10, 15, 6
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,3,2} of size 240
Vertex Figure Of :
   {2,2,5,3} of size 240
   {3,2,5,3} of size 360
   {4,2,5,3} of size 480
   {5,2,5,3} of size 600
   {6,2,5,3} of size 720
   {7,2,5,3} of size 840
   {8,2,5,3} of size 960
   {9,2,5,3} of size 1080
   {10,2,5,3} of size 1200
   {11,2,5,3} of size 1320
   {12,2,5,3} of size 1440
   {13,2,5,3} of size 1560
   {14,2,5,3} of size 1680
   {15,2,5,3} of size 1800
   {16,2,5,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,5,3}*240, {2,5,6}*240b, {2,5,6}*240c, {2,10,3}*240a, {2,10,3}*240b
   4-fold covers : {4,10,3}*480, {2,5,6}*480b, {2,10,3}*480, {2,10,6}*480c, {2,10,6}*480d, {2,10,6}*480e, {2,10,6}*480f
   6-fold covers : {6,10,3}*720, {2,10,3}*720, {2,15,3}*720, {2,15,6}*720
   8-fold covers : {8,10,3}*960, {4,10,3}*960, {4,10,6}*960b, {4,10,6}*960c, {2,10,12}*960c, {2,10,12}*960d, {2,20,6}*960a, {2,20,6}*960b, {2,5,12}*960, {2,20,3}*960, {2,10,6}*960c
   10-fold covers : {2,5,6}*1200, {2,5,15}*1200, {2,10,15}*1200, {10,10,3}*1200
   12-fold covers : {12,10,3}*1440, {6,10,3}*1440, {6,10,6}*1440c, {6,10,6}*1440d, {2,10,3}*1440b, {2,10,6}*1440b, {2,10,6}*1440c, {2,15,6}*1440c, {2,15,6}*1440d, {2,30,3}*1440, {2,30,6}*1440a, {2,30,6}*1440b
   14-fold covers : {2,10,21}*1680, {2,35,6}*1680, {14,10,3}*1680
   16-fold covers : {16,10,3}*1920, {4,20,6}*1920d, {4,20,6}*1920e, {8,10,3}*1920, {8,10,6}*1920b, {8,10,6}*1920c, {2,10,24}*1920c, {2,10,24}*1920d, {2,40,6}*1920d, {2,40,6}*1920e, {4,10,6}*1920c, {2,10,12}*1920c, {2,20,6}*1920c, {4,20,3}*1920, {2,10,12}*1920e, {2,20,6}*1920e, {2,10,6}*1920b, {4,5,3}*1920b, {2,5,6}*1920, {4,5,3}*1920d
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope