Polytope of Type {3,2,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,10,2}*240
if this polytope has a name.
Group : SmallGroup(240,202)
Rank : 5
Schlafli Type : {3,2,10,2}
Number of vertices, edges, etc : 3, 3, 10, 10, 2
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,10,2,2} of size 480
   {3,2,10,2,3} of size 720
   {3,2,10,2,4} of size 960
   {3,2,10,2,5} of size 1200
   {3,2,10,2,6} of size 1440
   {3,2,10,2,7} of size 1680
   {3,2,10,2,8} of size 1920
Vertex Figure Of :
   {2,3,2,10,2} of size 480
   {3,3,2,10,2} of size 960
   {4,3,2,10,2} of size 960
   {6,3,2,10,2} of size 1440
   {4,3,2,10,2} of size 1920
   {6,3,2,10,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,5,2}*120
   5-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,20,2}*480, {3,2,10,4}*480, {6,2,10,2}*480
   3-fold covers : {9,2,10,2}*720, {3,2,10,6}*720, {3,6,10,2}*720, {3,2,30,2}*720
   4-fold covers : {3,2,20,4}*960, {3,2,40,2}*960, {3,2,10,8}*960, {12,2,10,2}*960, {6,2,20,2}*960, {6,2,10,4}*960, {6,4,10,2}*960, {3,4,10,2}*960
   5-fold covers : {3,2,50,2}*1200, {3,2,10,10}*1200a, {3,2,10,10}*1200c, {15,2,10,2}*1200
   6-fold covers : {9,2,20,2}*1440, {9,2,10,4}*1440, {18,2,10,2}*1440, {3,2,10,12}*1440, {3,2,20,6}*1440a, {3,6,20,2}*1440, {3,6,10,4}*1440, {3,2,60,2}*1440, {3,2,30,4}*1440a, {6,2,10,6}*1440, {6,6,10,2}*1440a, {6,6,10,2}*1440c, {6,2,30,2}*1440
   7-fold covers : {3,2,10,14}*1680, {21,2,10,2}*1680, {3,2,70,2}*1680
   8-fold covers : {3,2,20,8}*1920a, {3,2,40,4}*1920a, {3,2,20,8}*1920b, {3,2,40,4}*1920b, {3,2,20,4}*1920, {3,2,10,16}*1920, {3,2,80,2}*1920, {12,4,10,2}*1920, {6,2,20,4}*1920, {6,4,20,2}*1920, {6,4,10,4}*1920, {12,2,10,4}*1920, {12,2,20,2}*1920, {6,2,10,8}*1920, {6,8,10,2}*1920, {24,2,10,2}*1920, {6,2,40,2}*1920, {3,4,20,2}*1920, {3,4,10,4}*1920, {3,8,10,2}*1920, {6,4,10,2}*1920
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);;
s4 := (14,15);;
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, 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(15)!(2,3);
s1 := Sym(15)!(1,2);
s2 := Sym(15)!( 6, 7)( 8, 9)(10,11)(12,13);
s3 := Sym(15)!( 4, 8)( 5, 6)( 7,12)( 9,10)(11,13);
s4 := Sym(15)!(14,15);
poly := sub<Sym(15)|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, 
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 >;

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