Polytope of Type {3,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,10}*120
if this polytope has a name.
Group : SmallGroup(120,42)
Rank : 4
Schlafli Type : {3,2,10}
Number of vertices, edges, etc : 3, 3, 10, 10
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,10,2} of size 240
   {3,2,10,4} of size 480
   {3,2,10,5} of size 600
   {3,2,10,3} of size 720
   {3,2,10,3} of size 720
   {3,2,10,5} of size 720
   {3,2,10,5} of size 720
   {3,2,10,6} of size 720
   {3,2,10,8} of size 960
   {3,2,10,4} of size 1200
   {3,2,10,10} of size 1200
   {3,2,10,10} of size 1200
   {3,2,10,10} of size 1200
   {3,2,10,12} of size 1440
   {3,2,10,4} of size 1440
   {3,2,10,4} of size 1440
   {3,2,10,6} of size 1440
   {3,2,10,6} of size 1440
   {3,2,10,3} of size 1440
   {3,2,10,5} of size 1440
   {3,2,10,6} of size 1440
   {3,2,10,6} of size 1440
   {3,2,10,6} of size 1440
   {3,2,10,6} of size 1440
   {3,2,10,10} of size 1440
   {3,2,10,10} of size 1440
   {3,2,10,10} of size 1440
   {3,2,10,10} of size 1440
   {3,2,10,14} of size 1680
   {3,2,10,3} of size 1800
   {3,2,10,6} of size 1800
   {3,2,10,15} of size 1800
   {3,2,10,16} of size 1920
   {3,2,10,5} of size 1920
   {3,2,10,4} of size 1920
   {3,2,10,4} of size 1920
   {3,2,10,5} of size 1920
Vertex Figure Of :
   {2,3,2,10} of size 240
   {3,3,2,10} of size 480
   {4,3,2,10} of size 480
   {6,3,2,10} of size 720
   {4,3,2,10} of size 960
   {6,3,2,10} of size 960
   {5,3,2,10} of size 1200
   {8,3,2,10} of size 1920
   {12,3,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,5}*60
   5-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,20}*240, {6,2,10}*240
   3-fold covers : {9,2,10}*360, {3,6,10}*360, {3,2,30}*360
   4-fold covers : {3,2,40}*480, {12,2,10}*480, {6,2,20}*480, {6,4,10}*480, {3,4,10}*480
   5-fold covers : {3,2,50}*600, {15,2,10}*600
   6-fold covers : {9,2,20}*720, {18,2,10}*720, {3,6,20}*720, {3,2,60}*720, {6,6,10}*720a, {6,6,10}*720c, {6,2,30}*720
   7-fold covers : {21,2,10}*840, {3,2,70}*840
   8-fold covers : {3,2,80}*960, {12,2,20}*960, {12,4,10}*960, {6,4,20}*960, {24,2,10}*960, {6,2,40}*960, {6,8,10}*960, {3,4,20}*960, {3,8,10}*960, {6,4,10}*960
   9-fold covers : {27,2,10}*1080, {9,6,10}*1080, {3,6,10}*1080, {3,2,90}*1080, {9,2,30}*1080, {3,6,30}*1080a, {3,6,30}*1080b
   10-fold covers : {3,2,100}*1200, {6,2,50}*1200, {15,2,20}*1200, {6,10,10}*1200a, {6,10,10}*1200b, {30,2,10}*1200
   11-fold covers : {33,2,10}*1320, {3,2,110}*1320
   12-fold covers : {9,2,40}*1440, {36,2,10}*1440, {18,2,20}*1440, {18,4,10}*1440, {3,6,40}*1440, {3,2,120}*1440, {9,4,10}*1440, {6,12,10}*1440a, {12,6,10}*1440a, {12,6,10}*1440b, {6,6,20}*1440a, {6,6,20}*1440c, {6,12,10}*1440c, {12,2,30}*1440, {6,2,60}*1440, {6,4,30}*1440, {3,6,10}*1440, {3,12,10}*1440, {3,4,30}*1440
   13-fold covers : {39,2,10}*1560, {3,2,130}*1560
   14-fold covers : {21,2,20}*1680, {3,2,140}*1680, {6,14,10}*1680, {42,2,10}*1680, {6,2,70}*1680
   15-fold covers : {9,2,50}*1800, {3,6,50}*1800, {3,2,150}*1800, {45,2,10}*1800, {15,6,10}*1800, {15,2,30}*1800
   16-fold covers : {3,2,160}*1920, {12,4,20}*1920, {12,8,10}*1920a, {6,8,20}*1920a, {24,4,10}*1920a, {6,4,40}*1920a, {12,8,10}*1920b, {6,8,20}*1920b, {24,4,10}*1920b, {6,4,40}*1920b, {12,4,10}*1920a, {6,4,20}*1920a, {12,2,40}*1920, {24,2,20}*1920, {6,16,10}*1920, {48,2,10}*1920, {6,2,80}*1920, {3,8,20}*1920, {3,4,20}*1920, {3,8,10}*1920, {3,4,40}*1920, {12,4,10}*1920b, {6,4,20}*1920b, {6,4,10}*1920, {12,4,10}*1920c, {6,8,10}*1920a, {6,8,10}*1920b
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13);;
s3 := ( 4, 8)( 5, 6)( 7,12)( 9,10)(11,13);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(13)!(2,3);
s1 := Sym(13)!(1,2);
s2 := Sym(13)!( 6, 7)( 8, 9)(10,11)(12,13);
s3 := Sym(13)!( 4, 8)( 5, 6)( 7,12)( 9,10)(11,13);
poly := sub<Sym(13)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope